International Journal of Advancements in Research & Technology, Volume 2, Issue3, March-2013
ISSN 2278-7763
Electromagnetic Model of an Arc
Jignesh Desai1, Mrunal Parekh2, Ankur Desai3
Electrical Engineering (Electrical Power system), Nirma University Institute of Technology1, Ahmadabad, India;
Research and Development, Electrical Research and Development Association2, Baroda, India;
Shantilal Shah Engineering College, Gujarat Technological University3, Bhavnagar, India;
Emails:11MEEE04@nirmauni.ac.in1,mrunal_parekh@yahoo.co.in2,ankurdesai.vbt12345@gmail.com3.
ABSTRACT
In the beginning of this paper start with simple geometry taken sinusoidal voltage and current at both contacts respectively, by this the electric field and magnetic field distribution is clearly described. As all major models of an arc are based on its behavior due to electric field, in
this model the whole effect are discussed and measured with value of current density and electric field intensity. Finally at the last the paper
is concluded with arc resistivity in begining of few nanoseconds of arc development, it clearly shows that magnetic field is affecting the arc
resistance to extinguish an arc.
Keywords : Fluid flow, MHD.
1 INTRODUCTION
T
HE electrical arc is a complex phenomenon where lots of
physical process taken place at very short time. Actually it is
incondensed gas column physically between anode and cathode.
To understand the behavior of the arc its magnetic phenomenon
as well as fluid flow process is taken in to consideration.
To understand an arc, there are basically two models.
1) Black box arc model
2) Physical model
the momentum and the difference of momentum of flow entering
and leaving the volume. The right hand side of the equation
shows the pressure gradient and the surface forces acting on the
volume, also the Lorentz force and gravitational forces.
Conversion of the energy:
 
h
p  
  (v   ) h 
 (v  p) 
t
t
  
 
 
   h    qR    j  E
cp

… … … (3)
2 MHD EQUATION
To understand the physical phenomena, MHD equation has been
solved using analytical software tool. In this, we have used Ansys
14.0 software for solving those questions.
The equations are as below:
Conservation of mass:

 
 (   v )  0
t
… … … (1)
Equation (1) shows the total sum of the change in the density in
the control volume and the the difference between mass flow
entering and the leaving the volume.
Conversation of momentum:

  
v
   ( v   )v 
t

   

4   
 p   (  v )     (  v )  j  B    g
3
… … … (2)
In equation (2), the left hand side shows the time rate change of
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The above equation represents the sum of the enthalpy change
in the control volume and the enthalpy of the fluid entering and
leaving the given control volume minus the worked needed for
the pressure change and the worked performed by the pressure
gradient to be equal to the heat losses conduction, radiation and
the electric energy dissipated in the control volume.
Maxwell Equations:


B
 E  
t

 H  j

  E  q

 B  0
… … … (4)
… … … (5)
… … … (6)
… … … (7)
Where:

t: Time; : Gas density; v : Velocity of the gas;
p: Pressure;: Viscosity
 of the fluid; E : Electric field;
j : Current density; B : Magnetic flux density;
h: Gas enthalpy; cp: Specific heat under constant pressure;
: Thermal conductivity;;g: Gravity acceleration
International Journal of Advancements in Research & Technology, Volume 2, Issue3, March-2013
ISSN 2278-7763
Thus, electric arc physical models consider the conservation
laws for mass; momentum and energy for arc macroscopic
elements, but extra source terms
 are added. On one hand Lorentz-force density term ( j  B) added in the momentum
 
balance and on the other hand the ohmic heating term ( j  E )
in the energy balance. Those extra terms couple flow dynamics
with electromagnetic process, described by Maxwell’s equation [(4)-(7)].
For solving combine MHD Equations magnetic model of an
arc is described in detail which shows the behavior of an Arc.
3
ELECTROMAGNETIC MODEL
4
SIMULATION RESULTS
The simulation is carried out with Ansoft Maxwell 15.0 and
Ansys 14.5 software tools.
4.1 Time varying j, E and w
Above figure show the t=0 time there is no magnetic field applied .after that the t=0.4ns the magnetic field has been start
developing in the air in the enclosure the direction of the vector j is also shown in the figure 3.2.The intensity of the field is
strong near the contact as arc starts developing in this stage.
3.1 Model geometry
The geometry used here is enclosure without opening with
copper copper contact in the air as fluid inside the enclosure.
The contacts are fixed and the whole geometry is in positive
xyz region. As shown in the figure 1.3 the fixed length has
been taken for the measure of behavior of the arc.
Figure 3.1 Current density j at t=0 sec.
Figure 3.1 Geometry for Arc Model.
The wall of the enclosure taken here is insulating type. The distance between two contacts is very small. The model has taken z –
axis as reference for gravity.
3.2 The simulations inputs and test data
The geometry shown in figure has been applied voltage and
current source. One contact has been applied fixed current at
the fixed direction and voltage to other contact with fixed direction. The simulation time for the analysis 5ms and whole
result are analyses for 0 to 1ns.
Copyright © 2013 SciResPub.
Figure 3.2 Current density j at 0.4ns
International Journal of Advancements in Research & Technology, Volume 2, Issue3, March-2013
ISSN 2278-7763
Figure 3.3 Current Density j at 1ns.
Graph 4.1 conductivity of Arc vs. time
2) Transient behavior:
The electric field and magnetic field values from the t=0 to
t=1ns has been observed by model .The heat losses is rapidly
increases during the t = 0+.As current zero achieved the direction of the j and E reversed as sinusoidal voltage and current
has been applied and so at current zero heat looses is low and
that is the time to open the contact so as much as safe operation has been followed and finally arc will extinguished.
4
ANALYSES OF THE SIMULATION
To find the characteristically behavior of the intercontact gap.
Using E and j values,
j= σE
… … … (8)
σ = j/E
… … … (9)
R=1/σ
… … … (10)
Where,
j=Current density in the air, (A/m2);
E=Electric field intensity in air, (V/m)
R=resistance of an arc, (Ω)
σ = Conductivity of an Arc, (Ʊ)
Using above Equation (8) and (9),
The behavior of the arc is shown in graphs,
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Graph 4.2 Resistivity of Arc vs. Time
5 CONCLUSION
The arc resistivity clearly shows that in the beginning at t=0
arc resistance in 106Ω than rapidly decreased in the few ns. It
is zero at 1.76 ×10-10 sec. Arc is taken place with thermal break
down of the air. The current density rapidly starts increases as
shown in the model, as this model shows the dynamic behavior of an arc.
International Journal of Advancements in Research & Technology, Volume 2, Issue3, March-2013
ISSN 2278-7763
5 ACKNOWLEDGMENTS
We would like to thanks Dr.M.K.Shah for his Support
throughout the work. We would also like to thanks
Dr.V.Shrinet for giving me lots of space to work in the technical environments.
6 REFERENCES
[1]
[2]
[3]
Wu Xi-xiu1, Li Zhen-Biao2, Tian Yun2, Mao Wenjun3, Xie Xun, " Investigate on the Simulation of black box arc model," 2011 1st International Conference on Electric Power Equipment - Switching Technology - Xi'an - China, pp. 629-639,2011.
A. Iturregi1, E. Torres2, I. Zamora3 , “Analysis of the Electric Arc in
Low Voltage Circuit Breakers,” International Conference on Renewable Energies and Power Quality, Las Palmas de Gran Canaria
(Spain), 13th to 15th April, 2011
William Bussire Pascal An Dr.David Rochette, Stphane Clain and
Charles Besnard,” Porous _lter optimization to improve the safetyof
the medium-voltage electrical installations during an internal arc
fault,” IEEE transactions on power delivery, 25, no. 4, october2010.
7. BIOGRAPHIES
[1] Mr.Jignesh Desai was born in Surat,
India. He received his bachelor of engineering in electrical from Veer Narmad
South Gujarat University, surat.his currently interests in power system and
electronics. He is perusing his M.tech
Electrical from Nirma University.
[2]Mrunal G Parekh is a native of
Bharuch, India. He received B.E. degree
from the University of veer narmad
south Gujarat and M.Tech degree from
VJTI (Veermata Jijabai technological
Institute), Mumbai both in electrical
engineering.
[3]A. P. Desai has received the B.E degree
in Electrical Engineering from South Veer
Narmad South Gujarat University, Surat
Gujarat, in 2008. Currently he studies in
M.E. (electrical engineering) of Shantilal
shah Engineering College, Bhavnagar Gujarat, India.
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