Preface

Chapter 10 **Testing and Evaluating Results of Research in**

Olga Lucia Lopera Tellez, Alexander Borghgraef and Eric Mersch

**Mine Action 233** Yann Yvinec

**VI** Contents

Chapter 11 **The Special Case of Sea Mines 251**

Every day, civilians in dozens of countries around the world are injured and killed by land‐ mines and other lethal leftovers of conflict, years after hostilities of war have ended. In 2014 alone, an estimated 3.678 people were killed or maimed by mines and other explosive devi‐ ces that have been left behind by armed forces. Approximately 80% of casualties in 2014 were civilians, 39% of whom were children. Unfortunately, most of the accidents caused by landmines happen in countries with limited medical assistance. The amputees not only must be fitted with a prosthesis to recover mobility but also they need help to overcome mental distress and regain dignity. The economic consequences are also serious, especially due to reconstruction efforts after an armed conflict. Further, large polluted areas of territory pre‐ vent the production of food.

Laos is the most heavily bombed nation in the world on a per capita basis. Between the years 1964 and 1973, the United States flew more than half a million bombing missions, de‐ livering more than 2 million tons of explosive ordnance in Laos as part of the CIA *Rolling Thunder* operation, in an attempt to block the flow of North Vietnamese arms and troops through Laotian territory. The ordnance dropped includes more than 266 million submuni‐ tions released from cluster bombs. One-third of the bombs failed to explode on impact and have since claimed an average of 500 victims a year, mainly children and farmers forced to work on their contaminated fields to sustain their families. Despite tens of millions of dol‐ lars spent, only 1% of Laos territory has been cleared so far.

It soon became apparent that the only real solution to address the landmine crisis was a complete ban on antipersonnel mines and later on the cluster munitions. No technical changes or changes to the rules on their use could change the fact that antipersonnel mines or bomblets are inherently indiscriminate. Once planted, a mine will never be able to tell the difference between a military and civilian footstep, and a bomblet will continue to attract children and metal dealers.

In order to put an end to the suffering and casualties caused by antipersonnel mines, the *Con‐ vention on the Prohibition of the Use, Stockpiling, Production and Transfer of Anti-Personnel Mines and on their Destruction*, also called the Ottawa Convention or Mine Ban Treaty, was adopted in 1997. Further, in order to put an end for all time to the suffering and casualties caused by cluster munitions at the time of their use, when they fail to function as intended or when they are abandoned, the *Convention on the Use, Stockpiling, Production and Transfer of Cluster Muni‐ tions,* also known as the Oslo Convention, was adopted in 2008.

As a deminer using conventional tools clears an area of approximately 10 m2; every working day, humanitarian mine clearance operations must be understood and designed correctly, with the conviction that their main goal is to provide efficient aid to innocent people, who

### **Chapter 1**

## **Power Quality Data Compression**

### Gabriel Găşpăresc

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/53059

### **1. Introduction**

Nowadays we assist to the increasing of devices and equipments connected to power sys‐ tems (non-linear loads, industrial rectifiers and inverters, solid-state switching devices, com‐ puters, peripheral devices etc). Hence, the parameters of the power supply should be accurately estimated and monitorized. For this purpose have been proposed power quality monitoring systems that are abble to automatically detect and classify disturbances. They are using the most recent signal processing techniques for power quality analysis (Bollen et al., 2006), (Dungan et al., 2004), (Lin et al., 2009).

A power quality monitoring system provides huge volume of raw data from different loca‐ tions, acquired during long periods of time and the amount of data is increasing daily. The hardware of a power quality monitoring systems should have a high sampling rate because the power quality events cover a broad frequency range, starting from a few Hz (flicker) to a few MHz (transient phenomenon). A high sampling rate leads to large volume of aquired data (for example, one recorded event could requires megabytes of storage space) which should be transferred and stored. Therefore, it is necessary data compression to save storing space and to reduce the communication time. Any compression methode is a compromise between the resulted volume of data and the remained information. The aim is to obtain the smalest size with the highest information level (Barrera Nunez et al., 2008), (Lorio et al., 2004), (Wang et al., 2005).

In order to compress data there are many approaches used in digital communications and image compression. These may be divided in two broad categories: lossless and lossy techniques. The first category keep the signal information intact. The second cate‐ gory remove redundant information from signals to achieve a higher compression ratio (Ribeiro et al., 2004).

© 2013 Găşpăresc; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Găşpăresc; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In recent years, the results presented in scientific literature show that the most used compression methods in power quality are based on wavelet transform and Slantlet transform. This chapter will provide an overview of their applications for power quality signals.

### **2. Data compression using wavelet transform**

### **2.1. Wavelet transform**

The wavelet transform ensures a progressive resolution in time-frequency domain, suitable to track the nonstationary signals dynamics properly. It use a variable window size, wide for low frequencies and narrow for high frequencies, to achieve a good localization in time and frequency domains (Ribeiro et al., 2007), (Zhang et al., 2011).

The Continuous Wavelet Transform (CWT) of a signal *f* (*t*)∈ *L* <sup>2</sup> *R* is defined as

$$\text{CWT}(\tau,\gamma) = \bigcap\_{\sim 0}^{\sim} f(t) \overline{\Psi\_{\tau,\gamma}}(\frac{t-\tau}{\gamma}) dt \tag{1}$$

/2 , ( ) 2 (2 ) *k k*

In muliresolution analysis a continuous function *x(t)* is decomposed as follows

0

, () ( ) () *<sup>j</sup> j jk k At ck t* <sup>=</sup> å j

, () ( ) () *<sup>j</sup> j jk k Dt dk t* <sup>=</sup> å y

For a given signal *x(t)* and a three levels wavelet decomposition the relation (5) become

1 1 221 3321

.

The decomposition of signal *x(t)* in *A1* and *D1* is the first decomposition level. At each de‐

If the analysed signal contains a high frequency event (for instance, a transient phenomenon),

coefficients. This observation is useful for compressing power quality signals: only the details

A general data compression method based on wavelet decomposition and reconstruction is shown in Fig. 1. That is a lossy compression method which includes certain steps (Wu et al.,

the approximation coefficient is also kept for signal reconstruction (Santoso et al., 1997).

associated with the events are retained and all other coefficients are discarded. Moreover,

*ADD ADDD*

( ) 

*xt A D*

= + =++ =+++

composition level the signal is decomposed into an approximation and a detail.

reveals details of the signal and each approximation *Aj*

pass filtering and high-pass filtering.

*(k)* are the scaling function coefficients, *dj*

detail at level *j* (Azam et al., 2004), (Zhang et al., 2011).

scale, *φ(t)* is the scaling function, *Aj*

where

*cj*

Each detail *Dj*

*Dj*

the magnitude of details *Dj*

**2.2. Data compression with wavelet transform**

The wavelet transform is the most used multiresolution analysis (MRA) technique of sig‐ nals. Multiresolutions signal decompositon is based on subbads decomposition using low-

0

0 () () () *j j j j xt A t D t* =

*k n* Y =Y- *t tn* (4)

Power Quality Data Compression http://dx.doi.org/10.5772/53059 3

= + å (5)

(6)

(7)

*(k)* are the wavelet function coefficients, *j0* is the

*(t)* is called the

shows corse information.

(8)

*(t)* is called approximation at level *j* and *Dj*

associated with the event are significant larger than the rest of the

where *τ* is the scale factor, *γ* is the translation factor and *Ψτ,γ* is the mother wavelet.

The Fourier analysis decomposes a signal into a sum of harmonics and wavelet analysis into set of functions called wavelets. A wavelet is a waveform of limited duration, usually irreg‐ ular and asymmetric. These functions are obtained by dilations and translations of a unique function called mother wavelet *Ψτ,γ* and the function set *(Ψτ,γ)* is called the wavelet family

$$\Psi\_{\mathbf{r},\chi}(t) = \frac{1}{\sqrt{\chi}} \Psi(\frac{t-\tau}{\chi}), \chi > 0, \tau \in \mathbb{R} \tag{2}$$

The Inverse Continuous Wavelet Transform (ICWT) is given as

$$f(t) = \frac{1}{C\_{\Psi}} \int\_{-\infty}^{\infty} \int\_{-\infty}^{\infty} \text{CWT}(\tau, \gamma) \Psi\_{\tau, \gamma}(t) \frac{d\tau d\gamma}{\tau^2} \tag{3}$$

where *CΨ* is the normalized constant.

In power quality analysis we work with acquired signals. These are discrete-time signals. Moreover, the CWT provides a redundant signal reprezentation in continuous-time, because the initial signal is possible to be reconstructed by a discrete version of CWT. The CWT is evaluated at dyadic intervals: the factor *τ* and *γ* are discretezed as *τ=2<sup>k</sup>* , *γ=2<sup>k</sup> n* where *n,kєZ*. The relation (2) becomes (Dash et al., 2007), (Qian, 2002)

$$
\Psi\_{k,n}(t) = 2^{k/2} \Psi(2^k t - n) \tag{4}
$$

The wavelet transform is the most used multiresolution analysis (MRA) technique of sig‐ nals. Multiresolutions signal decompositon is based on subbads decomposition using lowpass filtering and high-pass filtering.

In muliresolution analysis a continuous function *x(t)* is decomposed as follows

$$\text{tr}(t) = A\_{j\_0}(t) + \sum\_{j=0}^{j\_0} D\_j(t) \tag{5}$$

where

In recent years, the results presented in scientific literature show that the most used compression methods in power quality are based on wavelet transform and Slantlet transform. This chapter will provide an overview of their applications for power quality

The wavelet transform ensures a progressive resolution in time-frequency domain, suitable to track the nonstationary signals dynamics properly. It use a variable window size, wide for low frequencies and narrow for high frequencies, to achieve a good localization in time

The Continuous Wavelet Transform (CWT) of a signal *f* (*t*)∈ *L* <sup>2</sup> *R* is defined as

¥ -¥

where *τ* is the scale factor, *γ* is the translation factor and *Ψτ,γ* is the mother wavelet.

<sup>1</sup> ( ) ( ), 0, *<sup>t</sup>*

<sup>1</sup> ( ) ( , ) () *d d f t CWT t <sup>C</sup>*

t g

In power quality analysis we work with acquired signals. These are discrete-time signals. Moreover, the CWT provides a redundant signal reprezentation in continuous-time, because the initial signal is possible to be reconstructed by a discrete version of CWT. The CWT is

g

¥ ¥ Y -¥ -¥

evaluated at dyadic intervals: the factor *τ* and *γ* are discretezed as *τ=2<sup>k</sup>*

The relation (2) becomes (Dash et al., 2007), (Qian, 2002)

 *t R* t g t

g

The Fourier analysis decomposes a signal into a sum of harmonics and wavelet analysis into set of functions called wavelets. A wavelet is a waveform of limited duration, usually irreg‐ ular and asymmetric. These functions are obtained by dilations and translations of a unique function called mother wavelet *Ψτ,γ* and the function set *(Ψτ,γ)* is called the wavelet family

, ( , ) () ( ) *<sup>t</sup> CWT f t dt* t g

t

, 2

t g

t

t g



<sup>=</sup> ò ò <sup>Y</sup> (3)

, *γ=2<sup>k</sup>*

*n* where *n,kєZ*.

g

**2. Data compression using wavelet transform**

and frequency domains (Ribeiro et al., 2007), (Zhang et al., 2011).

t g

,

t g

The Inverse Continuous Wavelet Transform (ICWT) is given as

where *CΨ* is the normalized constant.

signals.

2 Power Quality Issues

**2.1. Wavelet transform**

$$\mathcal{A}\_{j}(t) = \sum\_{k} c\_{j}(k)\wp\_{j,k}(t) \tag{6}$$

$$D\_j(t) = \sum\_k d\_j(k)\nu\_{j,k}(t)\tag{7}$$

*cj (k)* are the scaling function coefficients, *dj (k)* are the wavelet function coefficients, *j0* is the scale, *φ(t)* is the scaling function, *Aj (t)* is called approximation at level *j* and *Dj (t)* is called the detail at level *j* (Azam et al., 2004), (Zhang et al., 2011).

For a given signal *x(t)* and a three levels wavelet decomposition the relation (5) become

$$\begin{aligned} \text{tr}(t) &= A\_1 + D\_1 \\ &= A\_2 + D\_2 + D\_1 \\ &= A\_3 + D\_3 + D\_2 + D\_1. \end{aligned} \tag{8}$$

The decomposition of signal *x(t)* in *A1* and *D1* is the first decomposition level. At each de‐ composition level the signal is decomposed into an approximation and a detail.

Each detail *Dj* reveals details of the signal and each approximation *Aj* shows corse information. If the analysed signal contains a high frequency event (for instance, a transient phenomenon), the magnitude of details *Dj* associated with the event are significant larger than the rest of the coefficients. This observation is useful for compressing power quality signals: only the details *Dj* associated with the events are retained and all other coefficients are discarded. Moreover, the approximation coefficient is also kept for signal reconstruction (Santoso et al., 1997).

### **2.2. Data compression with wavelet transform**

A general data compression method based on wavelet decomposition and reconstruction is shown in Fig. 1. That is a lossy compression method which includes certain steps (Wu et al., 2003), (Hamid et al., 2002), (Littler et al., 1999) : first, the signal is decomposed into several wavelet transform coefficients (WTCs) using the DWT, thresholding of WTCs (useful to ex‐ tract information and remove redundancy) and finally the signal is reconstructed from the retained WTCs.

**Figure 1.** A general multi-scale wavelet compression method

One of the methods for the thresholding of WTCs is to set a threshold than only the coeffi‐ cients above threshold are retained. Those below threshold are set to zero and are discarded (almost 90% of WTCs, some information will be lost). As a result, the amount of stored data is reduced.

The threshold is calculated based on absolute maximum value of the WTCs as

$$\eta\_{\mathbb{S}} = (1 - \mu) \times \max \{ \left| D\_i(\mathbf{u}) \right| \}\tag{9}$$

The quality of reconstructed signal is evaluated using the normalized mean-square error

*X n*

where *X(n)* is the original signal and *Xc(n)* is the compressed signal. A low value of NMSE

In the sections 2.2.1-2.2.2 is tested the performances of the general multi-scale wavelet com‐ pression method for transient phenomena and voltage swell. The influence of the order of Daubechies scaling function and the number of decomposition levels on data compression are analysed. The signals are simulated in Matlab environment. The details and the results

Transient phenomena are sudden and short-duration change in the steady-state condition of the voltage, current or both. These are classified in two categories: impulsive and oscillatory transient (Fig. 2). The first category has exponential rise and falling fronts and it is character‐ ized by magnitude, rise time (the time required for a signal to rise from 10% to 90% of final value), decay time (the time until a signal is greater than ½ from its magnitude) and its spec‐ tral content. The second category is characterized by magnitude, decay time and predomi‐

*Xn X n <sup>C</sup> NMSE*

corresponds to a small error between the original and reconstructed signal.

nant frequence (Dungan et al., 2004), (Găşpăresc, 2011).

2 2 () () ( )


Power Quality Data Compression http://dx.doi.org/10.5772/53059 5

which is defined as

are presented below.

*2.2.1. Transient phenomena*

**Figure 2.** Transient phenomena

where *u* take values in the range *0≤u≤1* and *s* is the associated scale.

Thresholding of WTCs is given by

$$D\_{i\mathbb{S}}(n) = \begin{cases} \left| \mathcal{D}\_i(n), \ \left| \mathcal{D}\_i(n) \right| \ge \eta\_s \\ 0, \ \left| \mathcal{D}\_i(n) \right| < \eta\_s \end{cases} \tag{10}$$

and the retained WTCs are stored together along with their temporal positions.

To evaluate the performance of signal compression are used the compression ratio (CR) and the normalized mean-square error (NMSE).

The data compression ratio is defined by

$$CR = \frac{S\_o}{S\_c} \tag{11}$$

where *So* is the size of original file and *Sc* is the size of compressed file.

The quality of reconstructed signal is evaluated using the normalized mean-square error which is defined as

$$NMSE = \frac{\left\| X(n) - X\_{\subset}(n) \right\|^2}{\left\| X(n) \right\|^2} \tag{12}$$

where *X(n)* is the original signal and *Xc(n)* is the compressed signal. A low value of NMSE corresponds to a small error between the original and reconstructed signal.

In the sections 2.2.1-2.2.2 is tested the performances of the general multi-scale wavelet com‐ pression method for transient phenomena and voltage swell. The influence of the order of Daubechies scaling function and the number of decomposition levels on data compression are analysed. The signals are simulated in Matlab environment. The details and the results are presented below.

### *2.2.1. Transient phenomena*

2003), (Hamid et al., 2002), (Littler et al., 1999) : first, the signal is decomposed into several wavelet transform coefficients (WTCs) using the DWT, thresholding of WTCs (useful to ex‐ tract information and remove redundancy) and finally the signal is reconstructed from the

One of the methods for the thresholding of WTCs is to set a threshold than only the coeffi‐ cients above threshold are retained. Those below threshold are set to zero and are discarded (almost 90% of WTCs, some information will be lost). As a result, the amount of stored data

The threshold is calculated based on absolute maximum value of the WTCs as

h

where *u* take values in the range *0≤u≤1* and *s* is the associated scale.

*iS*

where *So* is the size of original file and *Sc* is the size of compressed file.

*D n <sup>n</sup>*

and the retained WTCs are stored together along with their temporal positions.

(1 ) max{ ( ) } *S i*

i i ( ), D ( ) ( ) 0, D ( )

To evaluate the performance of signal compression are used the compression ratio (CR) and

*o c <sup>S</sup> CR*

*Dn n*

<sup>ì</sup> <sup>³</sup> <sup>ï</sup> <sup>=</sup> <sup>í</sup> <sup>ï</sup> <sup>&</sup>lt; <sup>î</sup>

*i s*

*s*

h

h

=-´ *u Dn* (9)

*<sup>S</sup>* <sup>=</sup> (11)

(10)

retained WTCs.

4 Power Quality Issues

is reduced.

**Figure 1.** A general multi-scale wavelet compression method

Thresholding of WTCs is given by

the normalized mean-square error (NMSE).

The data compression ratio is defined by

Transient phenomena are sudden and short-duration change in the steady-state condition of the voltage, current or both. These are classified in two categories: impulsive and oscillatory transient (Fig. 2). The first category has exponential rise and falling fronts and it is character‐ ized by magnitude, rise time (the time required for a signal to rise from 10% to 90% of final value), decay time (the time until a signal is greater than ½ from its magnitude) and its spec‐ tral content. The second category is characterized by magnitude, decay time and predomi‐ nant frequence (Dungan et al., 2004), (Găşpăresc, 2011).

**Figure 2.** Transient phenomena

Fig. 3 shows the first test signal, an impulsive transient with magnitude of 1000 V superim‐ posed on a sinusoidal signal with amplitude of 230 V and frequency of 50 Hz, corrupted with additive white noise. The sampling rate is 20 kHz. The signal is decomposed into three, four and five levels based on wavelet decomposition (Daubechies scaling function of order 3rd, 4th and 5th is used). Than the signal it is compressed using the threshold values 1, 5, 7 and 10. The results are presented in table 1.

**Signal Ψ(t) Levels η<sup>S</sup> NMSE [%] CR**

The initial value of threshold is 1. The size of the WTCs obtained after thresholding using the relations (9) and (10) is reduced as follows (first line from table 1): the coefficient *D1* at scale 1 has 2\*303=606 samples (303 samples nonzero and their temporal positions), the coef‐ ficient *D2* at scale 2 has 2\*167=334 samples, the coefficient *D3* has 2\*85=170 samples and the coefficient A3 has 250 samples. The compressed signal has 1360 samples and the initial test

From table 1 can be observed that the highest compression rate is 15.04. This value is ob‐ tained for Daubechies scaling function of order 3 (*Db3*), 5 levels of decomposition and the

If the threshold value is greater than or equal to 5 (Fig. 4), the signal distortions start to rise especially in the area of the overlapped impulsive transient. The enlargement of threshold

Db3 3 1 5.5154e-006 1.47 Db3 3 5 2.7151e-005 6.54 Db3 3 7 2.7827e-005 7.09 Db3 3 10 2.6502e-005 7.14 Db3 4 5 2.9240e-005 10.7 Db3 4 7 3.1081e-005 11.17 Db3 4 10 3.1515e-005 11.7 Db3 5 5 3.6143e-005 9.66 Db3 5 7 4.0148e-005 12.42 Db3 5 10 5.6165e-005 15.04 Db4 3 5 2.9386e-005 6.94 Db4 3 7 2.9246e-005 7.14 Db4 3 10 2.9481e-005 7.3 Db4 4 5 3.2845e-005 10.47 Db4 4 7 3.0742e-005 10.93 Db4 4 10 3.1029e-005 11.05 Db5 4 5 3.0875e-005 9.85 Db5 4 7 2.8626e-005 10.36 Db5 4 10 3.1029e-005 10.69

Power Quality Data Compression http://dx.doi.org/10.5772/53059 7

Impulsive transient

**Table 1.** Compression results for impulsive transient

signal has 2000. The compression ratio is 2000/1360=1.47.

threshold value of 10. The order of *NMSE* error is 10-6.

leads to more and more information discarded and NMSE grow up.

**Figure 3.** Impulsive transient compression with threshold value 1


**Table 1.** Compression results for impulsive transient

Fig. 3 shows the first test signal, an impulsive transient with magnitude of 1000 V superim‐ posed on a sinusoidal signal with amplitude of 230 V and frequency of 50 Hz, corrupted with additive white noise. The sampling rate is 20 kHz. The signal is decomposed into three, four and five levels based on wavelet decomposition (Daubechies scaling function of order 3rd, 4th and 5th is used). Than the signal it is compressed using the threshold values 1, 5, 7

and 10. The results are presented in table 1.

6 Power Quality Issues

**Figure 3.** Impulsive transient compression with threshold value 1

The initial value of threshold is 1. The size of the WTCs obtained after thresholding using the relations (9) and (10) is reduced as follows (first line from table 1): the coefficient *D1* at scale 1 has 2\*303=606 samples (303 samples nonzero and their temporal positions), the coef‐ ficient *D2* at scale 2 has 2\*167=334 samples, the coefficient *D3* has 2\*85=170 samples and the coefficient A3 has 250 samples. The compressed signal has 1360 samples and the initial test signal has 2000. The compression ratio is 2000/1360=1.47.

From table 1 can be observed that the highest compression rate is 15.04. This value is ob‐ tained for Daubechies scaling function of order 3 (*Db3*), 5 levels of decomposition and the threshold value of 10. The order of *NMSE* error is 10-6.

If the threshold value is greater than or equal to 5 (Fig. 4), the signal distortions start to rise especially in the area of the overlapped impulsive transient. The enlargement of threshold leads to more and more information discarded and NMSE grow up.

**Figure 5.** Oscillatory transient compression with threshold value 1

Oscillatory transient

**Table 2.** Compression results for oscillatory transient

**Signal Ψ(t) Levels η<sup>S</sup> NMSE [%] CR**

Db3 3 1 4.7257e-006 1.35 Db3 3 5 2.9394e-005 4.85 Db3 3 7 2.6282e-005 5.02 Db3 3 10 3.7811e-005 5.21 Db3 4 5 2.9285e-005 6.31 Db3 4 7 3.3209e-005 6.6 Db3 4 10 4.5275e-005 7.07 Db3 5 5 3.3699e-005 6.08 Db3 5 7 4.4197e-005 6.69 Db3 5 10 6.7879e-005 8.3 Db4 3 5 2.8067e-005 5.05 Db4 3 7 3.0176e-005 5.18 Db4 3 10 4.0081e-005 5.43 Db4 4 5 2.9924e-005 6.47 Db4 4 7 3,2733e-005 6.87 Db4 4 10 4.2280e-005 7.38 Db5 4 5 2,9223e-005 6.89 Db5 4 7 3.6702e-005 7.22 Db5 4 10 4.7778e-005 7.84

Power Quality Data Compression http://dx.doi.org/10.5772/53059 9

**Figure 4.** Impulsive transient compression with threshold value 5

Fig. 5 shows the second test signal, an oscillatory transient superimposed on a sinusoidal signal. The signal parameters and the decomposition parameters have the same values as the first test signal. The results are presented in table 2.

From table 2 the highest compression rate is 7.84. The value is lower than for the first test signal. This compression rate is obtained using the same settings: Daubechies scaling func‐ tion of order 3 (*Db3*), 5 levels of decomposition and the threshold value of 10. The order of *NMSE* error is 10-5.

Again, if the threshold value is greater than or equal to 5 (Fig. 6), the signal distortions start to rise especially in the area of the overlapped oscillatory transient and NMSE grow up too.

**Figure 5.** Oscillatory transient compression with threshold value 1


**Table 2.** Compression results for oscillatory transient

**Figure 4.** Impulsive transient compression with threshold value 5

the first test signal. The results are presented in table 2.

*NMSE* error is 10-5.

8 Power Quality Issues

Fig. 5 shows the second test signal, an oscillatory transient superimposed on a sinusoidal signal. The signal parameters and the decomposition parameters have the same values as

From table 2 the highest compression rate is 7.84. The value is lower than for the first test signal. This compression rate is obtained using the same settings: Daubechies scaling func‐ tion of order 3 (*Db3*), 5 levels of decomposition and the threshold value of 10. The order of

Again, if the threshold value is greater than or equal to 5 (Fig. 6), the signal distortions start to rise especially in the area of the overlapped oscillatory transient and NMSE grow up too.

**Figure 7.** Voltage swell compression with threshold value 1

Voltage sag

**Table 3.** Compression results for swell

**Signal Ψ(t) Levels η<sup>S</sup> NMSE [%] CR**

Db3 3 1 3.6484e-006 1.21 Db3 3 5 3.3454e-005 6.9 Db3 3 7 3.4048e-005 7.14 Db3 3 10 3.5194e-005 7.19 Db3 4 5 3.7718e-005 10,47 Db3 4 7 4.0528e-005 11.17 Db3 4 10 4.1284e-005 11.7 Db3 5 5 3.7621e-005 9.05 Db3 5 7 4.4344e-005 10.47 Db3 5 10 5.8101e-005 13.42 Db4 3 5 3.4595e-005 6.62 Db4 3 7 3.2270e-005 6.99 Db4 3 10 3.5533e-005 7.14 Db4 4 5 3.8236e-006 9.3 Db4 4 7 6.4098e-006 10.47 Db4 4 10 3.9005e-005 10.81 Db5 4 5 3.7183e-005 9.13 Db5 4 7 3.9994e-0056 9.95 Db5 4 10 4.1631e-005 10.36

Power Quality Data Compression http://dx.doi.org/10.5772/53059 11

**Figure 6.** Oscillatory transient compression with threshold value 5

### *2.2.2. Voltage swell*

Fig. 7 shows the third test signal, a swell with magnitude of 375 V superimposed on a sinus‐ oidal signal. The rest of signal parameters and the decomposition parameters have the same values as the previous test signals. The results are presented in table 3.

**Figure 7.** Voltage swell compression with threshold value 1


**Table 3.** Compression results for swell

**Figure 6.** Oscillatory transient compression with threshold value 5

Fig. 7 shows the third test signal, a swell with magnitude of 375 V superimposed on a sinus‐ oidal signal. The rest of signal parameters and the decomposition parameters have the same

values as the previous test signals. The results are presented in table 3.

*2.2.2. Voltage swell*

10 Power Quality Issues

and it has the largest number of samples from all the coefficients of signal decomposition. In order to obtain a higher sample rate this coefficient is decimated with a decimation factor *Fd* and at signal reconstruction will be interpolated. The cost is the increase of *NMSE* error.

Given an interval *[a,b]* and a divizion ∆:a=x0<x1<...<xn=b, a function *S : [a,b]→R* is called cubic

**•** *S* is a polynomial of degree at most 3 on any interval *(xk,xk+1)*, *k=1,…,N* (relation 13);

2 3

The proposed technique is tested using an impulsive transient with magnitude of 700 V su‐ perimposed on a sinusoidal signal (Fig. 9-10). The sampling rate is 5 MHz in this case. The signal is decomposed using a Daubechies scaling function of order 4 and 5 and respectively 4 levels of decomposition. Than the signal it is compressed using a threshold (Table 4).

<sup>1</sup> ( ) , [ ,] *ii i i i i S x a bx cx dx x x x* - = + + + "Î (13)

Power Quality Data Compression http://dx.doi.org/10.5772/53059 13

spline interpolation function if this function meets the next conditions:

*), iє(o,1,..., n)*, where *f(x)* is the interpolated function.

**Figure 9.** Impulsive transient compression with decimation factor *Fd=2*

**•** *SєC<sup>2</sup>*

**•** *S(xi*

*([a,b])*;

*)=f(xi*

**Figure 8.** Volatge swell compression with threshold value 5

From table 3 the highest compression rate is 13.42. The value is higher than for the second test signal. This compression rate is obtained using the same settings as for previous test sig‐ nals: Daubechies scaling function of order 3 (*Db3*), 5 levels of decomposition and the thresh‐ old value of 10. The order of *NMSE* error is 10-5.

Again, if the threshold value is greater than or equal to 5 (Fig. 8), the signal distortions start to rise especially in the area of the overlapped disturbance and NMSE grow up too.

A few conclusions are described below:


### **2.3. New wavelet-based data compression technique using decimation and spline interpolation**

This chapter describes a new technique proposed for signal compression based on wavelet decomposition and spline interpolation method (Găşpăresc, 2010). It follows to obtain a higher compression ratio than the general data compression method used for the test signals analysed before, where for a given signal it is applied a signal decomposition and than thresholding of WTCs *Di* , *i=1,...,N*. Using this method the coefficient *AN* is not thresholded and it has the largest number of samples from all the coefficients of signal decomposition. In order to obtain a higher sample rate this coefficient is decimated with a decimation factor *Fd* and at signal reconstruction will be interpolated. The cost is the increase of *NMSE* error.

Given an interval *[a,b]* and a divizion ∆:a=x0<x1<...<xn=b, a function *S : [a,b]→R* is called cubic spline interpolation function if this function meets the next conditions:


**Figure 8.** Volatge swell compression with threshold value 5

old value of 10. The order of *NMSE* error is 10-5.

A few conclusions are described below:

distorsions grow up;

thresholding of WTCs *Di*

**interpolation**

12 Power Quality Issues

is obtained the highest compression rate;

From table 3 the highest compression rate is 13.42. The value is higher than for the second test signal. This compression rate is obtained using the same settings as for previous test sig‐ nals: Daubechies scaling function of order 3 (*Db3*), 5 levels of decomposition and the thresh‐

Again, if the threshold value is greater than or equal to 5 (Fig. 8), the signal distortions start

**•** using 5 levels of decomposition, Daubechies scaling function of order 3 (*Db3*) and 5 (*Db5*)

**•** for a higher threshold value the compression rate will be higher, but NMSE and signal

**•** for different types of disturbances using the same settings the compression rate is different.

This chapter describes a new technique proposed for signal compression based on wavelet decomposition and spline interpolation method (Găşpăresc, 2010). It follows to obtain a higher compression ratio than the general data compression method used for the test signals analysed before, where for a given signal it is applied a signal decomposition and than

, *i=1,...,N*. Using this method the coefficient *AN* is not thresholded

**2.3. New wavelet-based data compression technique using decimation and spline**

to rise especially in the area of the overlapped disturbance and NMSE grow up too.

**•** *S(xi )=f(xi ), iє(o,1,..., n)*, where *f(x)* is the interpolated function.

$$\mathbf{S(x)} = a\_i + b\_i \mathbf{x} + c\_i \mathbf{x}^2 + d\_i \mathbf{x}^3, \forall \mathbf{x} \in \{\mathbf{x}\_{i-1}, \mathbf{x}\_i\} \tag{13}$$

The proposed technique is tested using an impulsive transient with magnitude of 700 V su‐ perimposed on a sinusoidal signal (Fig. 9-10). The sampling rate is 5 MHz in this case. The signal is decomposed using a Daubechies scaling function of order 4 and 5 and respectively 4 levels of decomposition. Than the signal it is compressed using a threshold (Table 4).

**Figure 9.** Impulsive transient compression with decimation factor *Fd=2*

**3. Data compression using slantlet transform**

time localization (Selesnick, 1999), (Panda et al., 2002), (Duda, 2008).

calization is improved but SLT filterbank is less frequency selective.

The Slantlet transform (SLT) is a relatively new multiresolution technique base on DWT. In fact, it is an orthogonal DWT with two zero moments and compared to DWT provides better

Power Quality Data Compression http://dx.doi.org/10.5772/53059 15

In (Panda et al., 2002) is proposed a new approach for power quality data compression based on SLT. The technique is compared with the discrete cosine transform (DCT) and the discrete wavelet transform (DWT) using various types of power quality disturbances (im‐ pulse, sag, swell, harmonics, momentary interruption, oscillatory transient, voltage flicker).

In order to compare DWT and SLT is considered a two-scale iterated filterbank (Fig. 11) and a two-scale slantlet filterbank (Fig. 12). First three blocks from Fig. 12 are not products. The filters have shorter length and the difference grows with the number of stages. The time lo‐

**3.1. Slantlet transform**

**Figure 11.** Two-scale iterated filterbank

**Figure 12.** Two-scale slantlet filterbank

**Figure 10.** Impulsive transient compression with decimation factor *Fd=4*


**Table 4.** Compression results for impulsive transient using the proposed technique

From table 4 can be observed that the highest compression ratio is 63.99. This value is ob‐ tained for Daubechies scaling function of order 4 (*Db4*), 4 levels of decomposition, threshold value of 3 and the decimation factor value of 4. The order of *NMSE* error is 10-4. The resulted compresion ratio is 4 times higher than the values from the prevoius tables, but the NMSE error is higher also.

This proposed technique is efficient especially for signals acquired at high sample rates, when are acquired a sufficient number of samples of the disturbance overlapped on the power supply signal. If this number is small, after the decimation of coefficient *AN* are losed disturbance details which cannot be reconstructed by interpolation and the reconstructed signal will contain distortions on the disturbance area.

### **3. Data compression using slantlet transform**

### **3.1. Slantlet transform**

The Slantlet transform (SLT) is a relatively new multiresolution technique base on DWT. In fact, it is an orthogonal DWT with two zero moments and compared to DWT provides better time localization (Selesnick, 1999), (Panda et al., 2002), (Duda, 2008).

In (Panda et al., 2002) is proposed a new approach for power quality data compression based on SLT. The technique is compared with the discrete cosine transform (DCT) and the discrete wavelet transform (DWT) using various types of power quality disturbances (im‐ pulse, sag, swell, harmonics, momentary interruption, oscillatory transient, voltage flicker).

In order to compare DWT and SLT is considered a two-scale iterated filterbank (Fig. 11) and a two-scale slantlet filterbank (Fig. 12). First three blocks from Fig. 12 are not products. The filters have shorter length and the difference grows with the number of stages. The time lo‐ calization is improved but SLT filterbank is less frequency selective.

**Figure 11.** Two-scale iterated filterbank

**Figure 10.** Impulsive transient compression with decimation factor *Fd=4*

Impulsive transient

signal will contain distortions on the disturbance area.

error is higher also.

14 Power Quality Issues

**Table 4.** Compression results for impulsive transient using the proposed technique

**Signal Ψ(t) η<sup>S</sup> Fd NMSE [%] CRa**

From table 4 can be observed that the highest compression ratio is 63.99. This value is ob‐ tained for Daubechies scaling function of order 4 (*Db4*), 4 levels of decomposition, threshold value of 3 and the decimation factor value of 4. The order of *NMSE* error is 10-4. The resulted compresion ratio is 4 times higher than the values from the prevoius tables, but the NMSE

This proposed technique is efficient especially for signals acquired at high sample rates, when are acquired a sufficient number of samples of the disturbance overlapped on the power supply signal. If this number is small, after the decimation of coefficient *AN* are losed disturbance details which cannot be reconstructed by interpolation and the reconstructed

Db4 3 2 2.2901e-004 32

Db5 3 2 2.2901e-004 32

Db4 3 4 9.8005e-004 63.99

Db5 3 4 2.2830e-004 63.98

**Figure 12.** Two-scale slantlet filterbank

The SLT is based on the principle of designing different filters for different scales unlike iter‐ ated filterbank approaches for DWT. In (Selesnick, 1999) are described the basis for filter‐ bank design, polynomial expresions to determine the filter coefficients and an algorithm to calculate the transform.

2

Impulse 88.01 91.13 94.01 -10.67 -13.54 -16.98 Sag 87.81 90.01 93.20 -10.08 -13.04 -17.54 Swell 89.46 91.01 94.44 -11.88 -13.77 -17.95 Harmonics 87.69 90.89 93.14 -11.04 -13.31 -17.68

Momentary Interruption 90.44 91.10 94.11 -12.27 -15.89 -18.79 Oscillatory Transient 91.63 90.88 95.04 -12.98 -14.45 -19.07 Voltage Flicker 90.75 91.34 95.18 -10.76 -14.74 -19.78

The research results on data compression using DWT presented in this work show the opti‐ mal order of Daubechies scaling function recommended in order to achieve the best com‐ pression ratio for three types of power quality disturbances and the necessary number of decomposition levels. An compression algorithm base on spline interpolation method that

The Slantlet transform is analysed as a new approach for power quality data compression. The compression performance using SLT was compared based on percentage of energy re‐ tained and mean square error in decibels. The computer simulation tests using various pow‐ er quality disturbances shows that SLT provides a more accurate reconstruction of the

ë û <sup>å</sup> (16)

Power Quality Data Compression http://dx.doi.org/10.5772/53059 17

**Energy Retained [%] MSE [dB] DCT DWT SLT DCT DWT SLT**

10

*MSE dB xi xi N* <sup>=</sup> é ù <sup>=</sup> ê ú -

**Signal**

**4. Conclusions**

**Author details**

Gabriel Găşpăresc

**Table 5.** Test results obtained using DCT, DWT and SLT (CR=10)

allows higher compression rates is also presented.

"Politehnica" University of Timişoara, Romania

original signal than DCT and DWT.

1 <sup>1</sup> [ ] 10 log ( ( ) ( ) ) <sup>ˆ</sup> *<sup>N</sup> i*

The filter coefficients are

1 2 0 1 3 1 2 1 2 3 4 10 2 3 10 2 3 10 2 () () ( ) ( ) 20 4 20 4 20 4 10 2 20 4 7 5 3 55 5 55 9 5 55 () () ( ) ( ) 80 80 80 80 80 80 17 5 3 55 17 5 3 55 9 5 55 80 80 80 80 80 80 *Ez Gz z z z Ez Fz z z z z* - - - - - - æ ö = =- - + + + - + ç ÷ è ø æ ö + - ç ÷ è ø æ ö = = - +- - + - + ç ÷ è ø æ öæ öæ ö +- + + + + + ç ÷ç ÷ç è øè øè ø 5 6 7 1 2 2 2 345 6 7 3 3 2 5 55 7 5 3 55 80 80 80 80 1 11 3 11 5 11 () () ( ) ( ) ( ) 16 16 16 16 16 16 7 11 7 11 5 11 ( )( )( ) 16 16 16 16 16 16 3 11 1 11 ( )( ) 16 16 16 16 <sup>1</sup> () ( ) *z z z Ez Hz z z zzz z z Ez zE <sup>z</sup>* - - - - - --- - - - ÷ ÷ æ öæ ö + - +- - ç ÷ç ÷ è øè ø = =+ ++ ++ ++ + - + - +- + - = (14)

Table 5 displays the test results obtained using DCT, DWT and SLT (Panda et al., 2002). The compression performance is analysed based on percentage of energy retained (relation 15) and mean square error (MSE) in decibels (relation 16). The compression rate is 10. The re‐ sults shows improved values for energy retained (near 4%) and MSEs.

$$
\left[ \frac{\text{Vector norm of the retained SLT coefficients}}{\text{after thresholding}} \right] \times 100\tag{15}
$$

$$
\left[ \text{Vector norm of the original SLT coefficients} \right]
$$

$$MSE[dB] = 10\left[\log\_{10}\left(\frac{1}{N}\sum\_{i=1}^{N} \left\|\mathbf{x}(i) - \hat{\mathbf{x}}(i)\right\|^2\right)\right] \tag{16}$$


**Table 5.** Test results obtained using DCT, DWT and SLT (CR=10)

### **4. Conclusions**

The SLT is based on the principle of designing different filters for different scales unlike iter‐ ated filterbank approaches for DWT. In (Selesnick, 1999) are described the basis for filter‐ bank design, polynomial expresions to determine the filter coefficients and an algorithm to

1 2

è ø


1 2

è ø

´

5

(14)

(15)


*z*

÷ ÷


1 2


calculate the transform. The filter coefficients are

16 Power Quality Issues

0 1

10 2 20 4

æ ö + - ç ÷ è ø

1 2

2 2

3 3 2

+- + -

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


*Ez zE <sup>z</sup>*

=

3 11 1 11 ( )( ) 16 16 16 16

3

5 55 7 5 3 55 80 80 80 80

æ öæ ö + - +- - ç ÷ç ÷ è øè ø


*z*

3 4

17 5 3 55 17 5 3 55 9 5 55 80 80 80 80 80 80


*z z*

345

Table 5 displays the test results obtained using DCT, DWT and SLT (Panda et al., 2002). The compression performance is analysed based on percentage of energy retained (relation 15) and mean square error (MSE) in decibels (relation 16). The compression rate is 10. The re‐

> norm of the retained SLT coefficients after thresholding <sup>100</sup> Vector norm of the original SLT coefficients

é ù *Vector* ê ú

ë û


1 11 3 11 5 11 () () ( ) ( ) ( ) 16 16 16 16 16 16

*zzz*

*Ez Hz z z*

= =+ ++ ++

6 7


*z z*

6 7

sults shows improved values for energy retained (near 4%) and MSEs.


*z z*

++ + - + -

7 11 7 11 5 11 ( )( )( ) 16 16 16 16 16 16

æ öæ öæ ö +- + + + + + ç ÷ç ÷ç è øè øè ø

7 5 3 55 5 55 9 5 55 () () ( ) ( ) 80 80 80 80 80 80

*Ez Fz z z*

æ ö = = - +- - + - + ç ÷

10 2 3 10 2 3 10 2 () () ( ) ( ) 20 4 20 4 20 4

*Ez Gz z z*

æ ö = =- - + + + - + ç ÷

The research results on data compression using DWT presented in this work show the opti‐ mal order of Daubechies scaling function recommended in order to achieve the best com‐ pression ratio for three types of power quality disturbances and the necessary number of decomposition levels. An compression algorithm base on spline interpolation method that allows higher compression rates is also presented.

The Slantlet transform is analysed as a new approach for power quality data compression. The compression performance using SLT was compared based on percentage of energy re‐ tained and mean square error in decibels. The computer simulation tests using various pow‐ er quality disturbances shows that SLT provides a more accurate reconstruction of the original signal than DCT and DWT.

### **Author details**

Gabriel Găşpăresc

"Politehnica" University of Timişoara, Romania

### **References**

[1] Azam, M. S. ., Tu, F. ., Pattipati, K. R. ., & Karanam, R. (2004). A Dependency Model Based Approach for Identifying and Evaluating Power Quality Problems, IEEE Transactions on Power Delivery 19(3), , 1154-1166.

[14] Panda, G. ., Dash, P. K., Pradhan, A. K., & Meher, S. K. (2002). Data Compression of Power Qualtity Events Using the Slantlet Transform, IEEE Transactions on Power

Power Quality Data Compression http://dx.doi.org/10.5772/53059 19

[15] Ribeiro, M. V. ., Park, S. H. ., Romano, J. M. T. ., & Duque, C. A. (2004). An Improved Method for Signal Processing and Compression in Power Quality Evaluation. *IEEE*

[16] Ribeiro, M. V. ., Park, S. H. ., Romano, J. M. T. ., & Mitra, S. K. (2007). A Novel MDLbased Compression Method for Power Quality Applications. IEEE Transactions on

[17] Santoso, S. ., Powers, E. J. ., & Grady, W. M. (1997). Power Quality Disturbance Data Compression using Wavelet Transform Methods. IEEE Transactions on Power Deliv‐

[18] Selesnick, I. W. (1999). The Slantlet Transform. *IEEE Transactions on Signal Processing*,

[19] Zhang, M. ., Li, K. ., & Hu, Y. (2011). A High Efficient Compression Method for Pow‐ er Quality Applications, IEEE Transaction on Power Delivery 60(6), , 1976-1985. [20] Wang, J. ., & Wang, C. (2005). Compression of Power Quality Disturbance Data Based on Energy and Adaptive Arithmetic Encoding, Proceedings of the TENCON.

[21] Wu, C. J. ., & Fu, T. H. (2003). Data compression applied to electric power quality tracking of arc furnance load, Journal of Marine Science and Technology 11, , 39-47.

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[14] Panda, G. ., Dash, P. K., Pradhan, A. K., & Meher, S. K. (2002). Data Compression of Power Qualtity Events Using the Slantlet Transform, IEEE Transactions on Power Delivery 17(2), , 662-667.

**References**

18 Power Quality Issues

Wiley & Sons.

[1] Azam, M. S. ., Tu, F. ., Pattipati, K. R. ., & Karanam, R. (2004). A Dependency Model Based Approach for Identifying and Evaluating Power Quality Problems, IEEE

[2] Barrera, Nunez. V. ., Melendez, Frigola. J. ., & Herraiz, Jaramillo. S. (2008). A Survey on Voltage Dip Events in Power Systems, Proceedings of the International Confer‐

[3] Bollen, M. ., & Gu, I. (2006). Signal Processing of Power Quality Disturbances. John

[4] Dash, P. K. ., Nayak, M. ., Senapati, M. R., & Lee, I. W. C. (2007). Mining for similari‐ ties in time series data using wavelet-based feature vectors and neural networks. *En‐*

[5] Duda, K. (2008). Lifting Based Compression Algorithm for Power Systems Signals,

[6] Dungan, R. C. ., Mc Granaghan, M. F. ., Santoso, S. ., & Beaty, H. W. (2004). Electrical

[7] Găşpăresc, G. (2010). Data compression of power quality disturbances using wavelet transform and spline interpolation method, Proceedings of the 9th International Con‐

[8] Găşpăresc, G. (2011). Methodes of Power Quality Analysis, in Power Quality- Moni‐ toring, Analysis and Enhancement, Ed. Ahmed Zobaa, Mario Manana Canteli and

[9] Hamid, E. Y. ., & Kawasasaki, Z. I. (2002). Wavelet-based data compression of power disturbances using the minimum description length criterion, IEEE. Transactions on

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[11] Littler, T. B. ., & Morrow, D. J. (1999). Wavelets for the analysis and compression of power system disturbances. IEEE Transactions on Power Delivery 14, , 358-364. [12] Lorio, F. ., & Magnago, F. (2004). Analysis of Data Compression Methods for Power Qualiy Events, Proceedings of the Power Engineering Society General Meeting.

[13] Qian, S. (2002). Time-Frequency and Wavelet Transforms, Prentice Hall PTR.

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and Measurement.

Power System Quality, McGraw-Hill.


**Chapter 2**

**Electric Power Quality Recognition and Classification in**

The power quality problem is now of a great concern to electric utilities of power industry and they are trying hard to supply their customers with a good quality of power especially in the open market. Due to the wide spread use of power electronics in every place in the power industry, the power supplied to the customers are now distorted in either the voltage signal or current signal or both of them. This distortion has a great effect on the sensitive equipments and may cause interruption to such equipments that result in very expensive consequence. It has been reported that 30% voltage sag for very short duration can reset programmable controllers for the entire assembly line. As such an accurate algorithm is needed for identifi‐

Power quality involves how close the voltage waveform is to being a perfect sinusoid with a constant frequency and amplitude. Historically, it has been the utilities' responsibility to provide a "clean" voltage waveform, and most customers' load did no affect the quality of their power. Today, a new factor, harmonics, has been added to the power quality scenario because utility customers, including residential ones, are using electronic devices that require

The presence of power system harmonics is not a new problem; it has been well known since the first generator was built. However, nowadays due to the widespread use of electronic equipment, arcing devices, such as arc furnaces and equipment with saturated ferromagnetic cores, such as transformers, power engineers pay more attention to power system harmonics. The presence of voltage and current waveform distortion is generally expressed in terms of harmonic frequencies that are integral multiples of the power system nominal frequency. It is

> © 2013 Soliman and Alammari; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Soliman and Alammari; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Distribution Networks**

Soliman Abdel-Hady Soliman and Rashid Abdel-Kader Alammari

cation and measurements of these events

non-sinusoidal currents, currents rich in harmonics.

http://dx.doi.org/10.5772/53081

**1. Introduction**

Additional information is available at the end of the chapter
