**4. Investigation of WT application on islanding state and fault location**

In this section, the detailed analysis of two important application of wavelet analysis, carried on detection of the islanding state and fault location by the authors, will be illustrated.

#### **4.1 Islanding detection**

#### **4.1.1 Methodology**

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

wavelets become more localized and oscillate less due to the dilation nature of the WT analysis. Hence, fast and short transient disturbances will be detected at lower scales whereas slow and long transient disturbances will be detected at higher scales. Thus, both

Apart from the application of wavelets to introduce new identification, classification and analysis methods such as those presented previously, at the moment is also studied the application of wavelets to develop new components models; for example (Abur et al., 2001) extends the results of previous works (Magnago & Abur, 2000) and describes a transmission line model which is based on WT taking into account frequency dependence of modal transformation matrices into the transients simulation. This allows the use of accurate modal transformation matrices that vary with frequency and yet still remain in the time domain

Although wavelet analysis usually combined with a large number of neural networks provides efficient classification of PQ events, the time-domain featured disturbances, such as sags, swells, etc. may not easily be classified. In addition, some important disturbance frequency component may not be precisely extracted by WT. Therefore, (Reddy & Mohanta, 2004) presents a new transform by incorporating phase correction to WT and is known as S– transform. The S-transform separates the localizing-in-time aspect of the real valued Gaussian window with modulation (selection of frequency) so that the window translates, but does not get modulated. (Reddy & Mohanta, 2010) extends the use of S-transform for detection, localization and classification of impulsive transients. The results obtained from S-transform are compared with those obtained from WT to validate the superiority of Stransform for PQ and transients analysis of complex disturbances. To do a case study the technique proposed in (Liao, 2010) is again studied, but for capacitor switching leading to the oscillatory transient. The results obtained are shown in Fig. 7. The dominant features of capacitor switching event was obtained as Δ*Ed*3 to Δ*Ed*5 mapped to the 3th to 5th energy

Fig. 7. (a) Simulated data of oscillatory transient with noise. (b) Energy spectrum of the simulated signals without noise suppression. (c) Energy spectrum of the simulated signals

fast and slow transients can be detected with a single type of analyzing wavelets.

during the simulations.

spectrums of the WTCs.

with noise suppression.

The proposed algorithm is based on the study of disturbances existed in the waveform of terminal current of DGs. It should be noted that once the islanding event is occurred, a transient component continues only for a very short time after the switching operation and then it is removed. But in non-islanding events this transient component continues for longer time, so it should be distinguished. In the proposed method, after studies done by the authors, it was found out that third decomposition level with 20 samples as the length of data window and 17 samples as the moving size of data window is accurate leading to detect the islanding state within maximum 54 samples i.e. 5.4 *ms*. In the first step, the ratio of maximum current magnitude in *r*th window to the previous window is calculated as follows:

$$Ratio-I\_{\underline{t}}(r) = \frac{\min \, \text{and} \, \max I\_{\underline{t}}(r)}{\max I\_{\underline{t}}(r-1)} \tag{11}$$

where, the threshold values are:

$$0.98 \le \text{Ratio} - I\_{\text{f}}(\text{r}) \le 1.02 \tag{12}$$

These threshold values are selected according to simulate the different events. If the calculated ratio satisfies (12) then there is no problem and this means that islanding has not been occurred. For values out of range of (12), the following criteria could be used to check whether the islanding event is taken place or not:

$$\text{Ratio} - D\_{\text{3}}(r) = \frac{\max D\_{\text{3}}(r)}{\max D\_{\text{3}}(r - 2)} \tag{13}$$

Considering different studies done, threshold value chosen for (13) is 0.02. This condition can be expressed by:

$$\text{Ratio} \ -D\_{\mathfrak{z}}(r) \le 0.0 \,\, \text{2} \tag{14}$$

This threshold value is also adopted according to simulate the different events. If value of (14) is less than 0.02, then the islanding event is occurred and trip command should be issued for islanded DGs. The algorithm diagram is shown in (Shariatinasab & Akbari, 2010).

It is worth to point out that moving size of the data window in the proposed algorithm is an important parameter. As decreasing the moving size reduces total time of detection, so the moving size should be decreased as possible.

Application of Wavelet Analysis in Power Systems 237

Fig. 10. The waveform of terminal current of DG2, due to breaker opening on line 7-8, d1-d3

**Number of Samples** 

20 samples length data window is considered. In this window, ratio of the changed current is 1.003 for DG1 which satisfies (12). So as it is expected the algorithm would not issued a trip command for DG1. It is important to point out that in order to get a conservative result; it was assumed that the generated power of DG2 is equal to the customer load at the connected bus. Therefore, DG2 is islanded, the difference between the generated and consumed power in bus 8 will be zero, while the ratio of the changed current in related data window for DG2 is 0.0971 that is less than 0.98 and therefore (12) is not satisfied. Then data window is twice shifted to the right, either one up to 17 samples. In this new window, the obtained value of (13) is nearly zero, in which this value satisfies (14). So the proposed algorithm detects the islanding event in maximum time within 54 samples of 10 *kHz* sampling frequency, i.e. 5.4 *ms,* and issues a trip

The more research is done for various combinations and conditions of islanding for both

In order to perform a comprehensive study to check the accuracy of the proposed method, motor starting and capacitor switching are also investigated; as they may cause a similar situation to islanding state and hence should be distinguished correctly. To perform the motor starting study, a 15 *kVA* induction motor starting is studied, and results are shown in Figs. 11-12. For DG1 the value of (11) obtained under this condition is 1.353 that is more than 1.02 and the value of (13) is 0.054 that is more than 0.02. Also, for DG2 the obtained value of (11) is 2.392 and the value of (13) is 0.079, in which both values are more than criteria adopted in the proposed algorithm. Hence, the proposed method distinguishes this situation correctly, i.e. an islanding state is not detected for DGs under motor starting

DG1 and DG2 available in (Shariatinasab & Akbari, 2010).

are detail components of main signal

command for DG2.

condition.

#### **4.1.2 Case study**

The study system consists of two synchronous DGs (DG1 and DG2) operating on PQ mode, and is a part of Iranian distribution network located in Tehran (Fig. 8). The data of the network are available in (Shariatinasab & Akbari, 2010).

Fig. 8. Test system for islanding detection study

#### **4.1.3 Simulation results**

To be ensured of accuracy of the proposed algorithm, all the cases affecting the terminal current of DGs are analyzed. Figs. 9 and 10, show RMS current form and related three decomposition levels using 'Haar' mother wavelet for non-islanded DG1 and islanded DG2, respectively.

Fig. 9. The waveform of terminal current of DG1, due to breaker opening on line 7-8, d1-d3 are detail components of main signal

The study system consists of two synchronous DGs (DG1 and DG2) operating on PQ mode, and is a part of Iranian distribution network located in Tehran (Fig. 8). The data of the

To be ensured of accuracy of the proposed algorithm, all the cases affecting the terminal current of DGs are analyzed. Figs. 9 and 10, show RMS current form and related three decomposition levels using 'Haar' mother wavelet for non-islanded DG1 and islanded DG2, respectively.

Fig. 9. The waveform of terminal current of DG1, due to breaker opening on line 7-8, d1-d3

**Number of Samples** 

network are available in (Shariatinasab & Akbari, 2010).

Fig. 8. Test system for islanding detection study

**4.1.3 Simulation results** 

are detail components of main signal

**4.1.2 Case study** 

Fig. 10. The waveform of terminal current of DG2, due to breaker opening on line 7-8, d1-d3 are detail components of main signal

20 samples length data window is considered. In this window, ratio of the changed current is 1.003 for DG1 which satisfies (12). So as it is expected the algorithm would not issued a trip command for DG1. It is important to point out that in order to get a conservative result; it was assumed that the generated power of DG2 is equal to the customer load at the connected bus. Therefore, DG2 is islanded, the difference between the generated and consumed power in bus 8 will be zero, while the ratio of the changed current in related data window for DG2 is 0.0971 that is less than 0.98 and therefore (12) is not satisfied. Then data window is twice shifted to the right, either one up to 17 samples. In this new window, the obtained value of (13) is nearly zero, in which this value satisfies (14). So the proposed algorithm detects the islanding event in maximum time within 54 samples of 10 *kHz* sampling frequency, i.e. 5.4 *ms,* and issues a trip command for DG2.

The more research is done for various combinations and conditions of islanding for both DG1 and DG2 available in (Shariatinasab & Akbari, 2010).

In order to perform a comprehensive study to check the accuracy of the proposed method, motor starting and capacitor switching are also investigated; as they may cause a similar situation to islanding state and hence should be distinguished correctly. To perform the motor starting study, a 15 *kVA* induction motor starting is studied, and results are shown in Figs. 11-12. For DG1 the value of (11) obtained under this condition is 1.353 that is more than 1.02 and the value of (13) is 0.054 that is more than 0.02. Also, for DG2 the obtained value of (11) is 2.392 and the value of (13) is 0.079, in which both values are more than criteria adopted in the proposed algorithm. Hence, the proposed method distinguishes this situation correctly, i.e. an islanding state is not detected for DGs under motor starting condition.

Application of Wavelet Analysis in Power Systems 239

software is then transformed to MATLAB software in order to apply the wavelet analysis. Only 46 samples/10 *kHz* sampling rate (equal to 4.6 *ms*) of data are considered after fault time. According to the analyses done, db4 mother wavelet was selected as a suitable

After DWT analysis, it is necessary to extract the characteristics of this transform to provide inputs of NN. To this, 2nd norm (norm2) of signal details was considered as NN inputs.

To describe the work, norm2 of 3rd level details versus fault distance from a generator (G3) is illustrated in Fig. 14. As shown in Fig. 14, the more fault distance, the lower value of norm2 is reached. In this study, norm2 of details of five levels were used. The NN used in this study was consisted of 3 hidden layers either with 20 neurons. The optimal number of neurons was determined based on the trial and error approach. The transfer functions applied in input, hidden and output layers were considered **tansig**, **tansig** and **purelin**,

For study system, fault was applied in 120 points which 85 points was considered as

Also, the details of 5 levels were obtained as the optimal solution to train the NN.

respectively, and training algorithm was also considered as **trainlm**.

Fig. 13. Schematic diagram of test system for fault location study

training patterns of NN and 35 points was considered for testing.

Fig. 14. Norm2 of 3rd level details (d3) for G3

**4.2.2 Simulation results** 

solution.

Fig. 11. The waveform of terminal current of DG1, due to motor starting at bus 3, d1-d3 are detail components of main signal

Fig. 12. The waveform of terminal current of DG2, due to motor starting at bus 3, d1-d3 are detail components of main signal

Results of the capacitor bank switching are also available in (Shariatinasab & Akbari, 2010).

#### **4.2 Fault location**

#### **4.2.1 Methodology and study system**

In this section, the fault location by DWT and a trained NN will be discussed. The case study is IEEE 9-bus test system as shown in Fig. 13. This system is a 400 *kV* transmission system included 3 generators and 6 lines. Each line is divided to 20 points and then a fault is separately applied in each point. Totally 120 faults is applied in 120 points. As the most of faults occurred in transmission systems have low fault impedance, so fault impedance was considered equal to zero in this study. Then the terminal current signal of G1, G2 and G3 during the fault is obtained with sampling rate 10 *kHz*. The fault signals collected in ETAP

Fig. 11. The waveform of terminal current of DG1, due to motor starting at bus 3, d1-d3 are

**Number of Samples** 

Fig. 12. The waveform of terminal current of DG2, due to motor starting at bus 3, d1-d3 are

**Number of Samples** 

Results of the capacitor bank switching are also available in (Shariatinasab & Akbari, 2010).

In this section, the fault location by DWT and a trained NN will be discussed. The case study is IEEE 9-bus test system as shown in Fig. 13. This system is a 400 *kV* transmission system included 3 generators and 6 lines. Each line is divided to 20 points and then a fault is separately applied in each point. Totally 120 faults is applied in 120 points. As the most of faults occurred in transmission systems have low fault impedance, so fault impedance was considered equal to zero in this study. Then the terminal current signal of G1, G2 and G3 during the fault is obtained with sampling rate 10 *kHz*. The fault signals collected in ETAP

detail components of main signal

detail components of main signal

**4.2.1 Methodology and study system** 

**4.2 Fault location** 

software is then transformed to MATLAB software in order to apply the wavelet analysis. Only 46 samples/10 *kHz* sampling rate (equal to 4.6 *ms*) of data are considered after fault time. According to the analyses done, db4 mother wavelet was selected as a suitable solution.

After DWT analysis, it is necessary to extract the characteristics of this transform to provide inputs of NN. To this, 2nd norm (norm2) of signal details was considered as NN inputs. Also, the details of 5 levels were obtained as the optimal solution to train the NN.

To describe the work, norm2 of 3rd level details versus fault distance from a generator (G3) is illustrated in Fig. 14. As shown in Fig. 14, the more fault distance, the lower value of norm2 is reached. In this study, norm2 of details of five levels were used. The NN used in this study was consisted of 3 hidden layers either with 20 neurons. The optimal number of neurons was determined based on the trial and error approach. The transfer functions applied in input, hidden and output layers were considered **tansig**, **tansig** and **purelin**, respectively, and training algorithm was also considered as **trainlm**.

Fig. 13. Schematic diagram of test system for fault location study

Fig. 14. Norm2 of 3rd level details (d3) for G3

#### **4.2.2 Simulation results**

For study system, fault was applied in 120 points which 85 points was considered as training patterns of NN and 35 points was considered for testing.

According to the definition in (IEEE Std. PC37.114, 2004), error percentage of fault location estimation is determined as follows:

$$error\,\,\%=\frac{error\,\,\,\,value}{line\,\,length} \tag{15}$$

Application of Wavelet Analysis in Power Systems 241

Further, Although there have been a great effort in references to prove that one wavelet is more suitable than another, there have not been a comprehensive analysis involving a number of wavelets to prove the point of view suggested. Also, the method of comparison

Therefore, in this chapter for each application in power systems, it was tried to introduce principles and algorithms in order to determine the optimal mother wavelet. According to the literature review, Daubechies family has been the most of applications in power systems analysis. Further, often db4 have been the satisfactory results than the other mother wavelets of Daubechies family. However, it is should be noted that the type of mother wavelet, the number of decomposition levels and etc, may be changed from one application

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Some results obtained from the proposed DWT-NN technique are shown in Table 2. As seen in results, the error values are reasonable values and satisfactory. According to 4.2.1, the time of the fault detection and location is 4.6 *ms* equal to 46 samples per 10 *kHz* sampling rate. Therefore, this technique can be well used to estimate the fault detection and location in a specific transmission system.


Table 2. The results of fault location under db4 mother wavelet and 5 decomposition levels
