Page 46 - IJEEE-2022-Vol18-ISSUE-1

42 | Saeed, Abdulhassan & Khudair

The DWT generates signal approximations and details decomposition stage of the Db2 related DWT analysis is as
by employing a collection of low and high pass filters. The
presence of such a collection of filters is dependent upon high, accurate, and computationally cost effective as
the existence of two distinct sorts of functions, namely the
scaling function and the wavelet function, both of which are required to distinguish between healthy and faulty series and
unique to particular types of mother wavelets [14], [15]. parallel arc fault system states. And it’s found that CD1 in

The iterative process of analyzing the signal within the the first level and the rest of the levels is the best detail
set of DWT filters is called the Multi Resolution Analysis
(MRA). At the first decomposition stage, the signal enters coefficient to extract the series and parallel arc fault
the low pass filter (LPF) specific to a certain mother wavelet
scaling function. The approximation coefficients (CA) will effectively.so, the first level was chosen for the presence of
be obtained after the convolution of signal samples with the
transfer function coefficients of such a filter and down CD1in it.
sampling by 2 [14].
TABLE 1
To acquire the signal's detailed coefficients (CD) at the
first stage of decomposition, it must be sent through a high- Results of the Best Mother Wavelet Test
pass FIR filter (HPF) adjusted to the wavelet function, with
its samples convolved with the filter transfer function Mother Wavelet Average Error Value
coefficients, and then down sampled by two. At the second
decomposition step, the first stage approximation Db2 1.4634e-08
coefficients will be handled identically to the input signal in Db3 1.3081e-07
order to get the second stage approximation and detail Db4 2.8235e-08
coefficients. Db5 4.5494e-08
Db6 2.8010e-08
Db7 3.4447e-08
Db8 6.0712e-08

V. IMPLEMENTATION OF WAVELET & FFT
TRANSFORMATION IN MODEL

A. Series And Parallel Arc Fault Wavelet Analysis
Simulation Model

To design the series and parallel arc fault circuit with
Wavelet analysis it’s very important to selecting the best

mother wavelet function, having eight cycles and 256

number of samples per cycle means having a sampling time

(Ts) of ?? which equals 7.8125 × 10-5 ?????? , the
??????×????

inverse is the sampling frequency (fs) which equals 12.8

kHz. A program routine is written within MATLAB m-file

editor environment in order to perform the suitable mother

wavelet test. In this test, the wavelets used are the Fig:7. Best mother wavelet test results for the detection
Daubechies of the orders of 2 - 8 [116]. Test results for the scheme dedicated for the simple test system.

system are given in the Table (1), a plot revealing the The mother wavelet function is Daubechies of order 2 is
the best mother wavelet here and the best level is 1.
relation between each mother wavelet function and the Therefore, this analysis adopts db2 wavelet, analyzes arc
voltage and current waveforms in one-dimensional multi
average error calculated is shown in Fig.7. It can be seen scale. It is decomposed the two dimensions; the series arc
fault occurs when the voltage supply is reaching to ascertain
from the results that the winner is the Db2 mother wavelet value. and the parallel arc fault occurs at 0. 05sec.where CA1
is the approximate coefficient and the CD1 is the details
due to having the least average error value. This mother coefficient 1, the model MATLAB/Simulink of series and
parallel arc fault is will be as shown in Fig. 8 and 9.
wavelet function can then be exploited in analyzing signals

to be presented to the decision-making system dedicated for

the detection of faults.
Now it’s also important to select the number of

decomposition level of wavelet analysis. Therefore, if the

aspects of signals to be extracted by the DWT can be

captured and discriminated at lower decomposition stages,

then such stages will be preferred over higher ones, as regard

to the selection of the best stage for the analysis, it is found

after performing a number of tests that the first