Page 43 - IJEEE-2022-Vol18-ISSUE-1

Saeed, Abdulhassan & Khudair | 39

reflecting the features of real-world series and parallel e: electric intensity in arc column.
faults. Moreover, to investigate the various arc detection
technologies that are currently available and to evaluate P loss: power loss per unit arc length.
their limitations. With the use of MATLAB simulation,
examine and execute the new approach, Wavelet The model may be stated in the form of conductance
Transformation, and compare the results with the traditional
method (FFT-Fast Fourier Transform). since the arc resistance value is relatively small [10].

II. SERIES AND PARALLEL ARC FAULT MODEL ?? = 1 = ?? = ??(??(??)) (2)
?? ?? (3)
Arc faults may be classified into two types: series and ???? = ?? (1) = ????(??) × ???? = (?? × ??) × ????(??)
parallel. The much more prevalent form of model is depicted ???? ???? ?? ???? ???? ????
in Fig. 1 (a), and it occurs when a single power conductor
breaks. As a result of the connection in series, the maximum For Mayr's arc model, the differential equation given by:
arc current is restricted by the load current, which is
substantially less than the CB rated current, and the arc ??(??) = ?? × ????/??0 (4)
current may or may not create enough heat to ignite a fire, ???? = (?? × ??) × ?? × ????/??0 (5)
dependent on the load. [5].
???? ??0
When the insulator is damaged by mechanical, thermal
stress, or aging, a parallel arc fault occurs between the ???? = (?? × ?? - ?????????? ) × 1 × ??(??) (6)
neutral/ground and phase conductor [6]. The high- ???? ??0 (7)
impedance arc melts and carbonizes the insulator first in (8)
this condition, following by the creation of the low- ???? = (?? × ?? - ?????????? ) × ??
impedance current path. Intense temperatures cause the trail ???? ??0 (9)
to develop, and if left unchecked, it might ignite a fire. (10)
1 × ???? = ?????????? × (( ??×?? ) - 1)
?? ???? ??0 ??????????

Let ?? = ??0

??????????

1 × ???? = 1 × (( ??×?? ) - 1)
?? ???? ?? ??????????

1 × ???? = 1 × (( ??×??×?? ) - 1)
?? ???? ?? ??×??????????

1 × ???? = 1 × ((??×??) - 1) (11)
?? ???? ?? ??0

Where:

Fig. 1: (a) Series arc-fault. (b) Parallel arc fault. u: arc voltage, ?? = ?? × ??
??0: Power loss in arc column,??0 = ?? × ?????????? = ????2 × ??
????: arc voltage constant

g:arc conductance

A. Arc mathematical model 1 × ???? = 1 × ((??????2××?? ??) - 1) (12)
?? ???? ??

The arc fault is described as a self-sustaining electrical ?? = ?? × ??

discharge in conductive ionized gas [7], with circuit 1 × ???? = 1 × ((??????22) - 1) (13)
?? ???? ??
operation conditions limiting the maximum current. Arc

may simply shorten the life of electrical devices or it can get

dangerous (for example, in metal conductors) and cause ?? ln ?? 1 ((??????22)
???? ??
spectacular occurrences like fires and explosions. The arc = × - 1) (14)

fault is nonlinear, discontinuous, and lacks sinusoidal

features. B. Model parameters

There are several models that may be used to 1) Determination of T

characterize its behavior. Cassie (for analyzing the arc T: is the time constant of the arc fault, and can be

under high current and high plasma ambient temperature) expressed as below:

and Mayr's arc model are one of the most recognized. ?? = ??×???? (15)

[8]. The latter maintains a constant arc diameter and power ????

loss and represents arc conductance around zero current. Where:

This model is excellent for arc fault modeling in residential Ip : is the peak current in the arc volt-ampere characteristic
curvet. ???? = 25??
and office wiring since it works well for very low currents Alpha is the empirical value [9], take a=2.9 × 10-5

(tens of Amperes). Mayr arc model is based on energy

balance theory, accordingly L p: is the arc length which is approximate-constant [9].
???? = 2????
Mayr’s arc fault model expression [9]:

???? = ?? × ?? - ?????????? (1) 2) Determination of u c
????
It is a constant voltage of arc and is expressed below [9]:
Where:
???? = 25 × ????
????: storage energy variations per arc length
(16)
????

?? ×i: input power per unit arc length.

i: arc current.