Energy and Power Engineering, 2013, 5, 833-837
doi:10.4236/epe.2013.54B160 Published Online July 2013 (http://www.scirp.org/journal/epe)
Simulation of Fault Arc Using Conventional Arc Models
Ling Yuan, Lin Sun, Huaren Wu
School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, China
Received April, 2013
ABSTRACT
Conventional arc models are usually used to research the interaction between switching arc and circuit. It is important to
simulate the fault arc for arc flash calculations, choice of electrical equipments and power system protection. This paper
investigates several conventional arc models for calculating the fault arcing current. Simulation results show that con-
ventional arc models can be used to simulate the fault arc if the parameters of arc models are given properly. This paper
provides the parameters of 5 popular arc models and describes the simulation results of the fault arc.
Keywords: Arc; Arc Flash; Arc Model; Plasma; Power System
1. Introduction
Short circuit in power systems is serious fault. The short
circuit current must be calculated for the choice of elec-
trical equipments and the setting of power system protec-
tion. An arc presents usually at the fault location in pow-
er systems. The fault arc could destroy electrical equip-
ment and threaten human life. It is important to calculate
the arc fault current for reducing loss.
An arc model must be used for calculation of the arc
fault current. There are a lot of arc models for describing
the arc. Arc models can be classified in three groups:
physical models, black box models and models based on
graphics and diagrams. Black box models describe only
the relation between input and output signals. Black box
models define the interaction between the arc and the
electrical circuit during the fault. In black box models,
the arc is described by one differential equation or sev-
eral differential equations relating the arc conductance
which describes the energy balance of the arc column.
Cassie arc model was presented by Cassie in 1939 [1].
Cassie assumed that the arc has a fixed temperature being
cooled by forced convection. This implies that the
cross-section area of the arc is proportional to the current
and that the voltage over the arc is constant. Cassie arc
model is suitable for arcs with high currents.
Mayr arc model was introduced in 1943 [2, 3]. Mayr
assumed that power losses are caused by thermal con-
duction and the arc conductance is dependent on tem-
perature. The cross-section area of the arc is assumed
constant. Mayr arc model is fit for currents near zero.
Schwarz developed a modified Mayr arc model in
1971[4]. The time constant and the cooling power in the
model are dependent on the arc conductance [5].
Habedank arc model is a series connection of a Cassie
and Mayr arc model [6]. It is suitable for arcs with high
currents and for currents near zero.
A modified Mayr arc model was presented in 1992 [7].
The cooling power in the model is current-dependent.
Schavemaker arc model is also a modified Mayr arc
model with a constant time parameter [8]. The cooling
power in the model is a function of the electrical power
input.
The above-mentioned arc models are black box mod-
els, that is, conventional arc models. They are usually
used to research the interaction between switching arc
and circuit during the interruption process of circuit
breakers. The characteristics of the fault arc are different
from that of the switching arc. This paper describes the
simulation methods of the fault arc using conventional
arc models. First of all the arcing fault was tested in the
high-power test laboratory and the arc voltage and the arc
current are depicted. Then 5 arc models are investigated
and their parameters are determined for simulation of the
fault arc. Conventional arc models can be used to simu-
late the fault arc.
2. Simulation of Fault Arc
Short circuit was tested in the high-power test laboratory.
The simplified laboratory test circuit is shown in Figure
1. The supply voltage is 400V.
The arc was initiated by means of a fuse wire between
2 electrodes. The arc voltage and the arc current were
recorded with the sampling frequency of 40 kHz and are
depicted in Figure 2. Figure 2 shows that arc voltage
and arc current are in phase and the arc is resistive. The
arc voltage ought to be represented for simulation the

L. YUAN ET AL.
834
fault arc by a periodic rectangular wave changing its sign
at each zero crossing of the arc current.
The circuit equation of Figure 1 is as follows:
sdi
uRiL u
dt
  (1)
where i is the arc current, u is the voltage across the arc
and us is the supply voltage.
2sin( )
ss
uU t

 
2.1. Cassie Arc Model
Cassie arc model represents dynamic properties of an AC
arc by the following differential equation [1].
2
2
11 1
c
dg u
gdt U 







(2)
where g is the conductance of the arc, τ is the arc time
constant, Uc is one constant.
/uig (3)
,andig ucan be obtained by solving Equation (1), Equa-
tion (2) and Equation (3). Figure 3 shows the arc volt-
ages. The curve 1 in Figure 3 describes the arc voltages
with τ=0.000006 and Uc=80, the curve 2 with τ=0.0008
and Uc=80 and the curve 3 with τ=0.000012 and Uc=80.
The curve 1 in Figure 3 shows big restrike voltage.
The curve 2 is not a periodic rectangular wave. The curve
3 has the expected characteristic. The parameter τ deter-
mines the curve form and Uc effects the mean value of
the arc voltage in Figure 3. The greater Uc, the greater
the mean value of the arc voltage is. Therefore, select τ =
0.000012 for simulation the fault arc and Uc is deter-
mined by the arc voltages from test results.
Figure 1. Test circuit.
Figure 2. Test results
Figure 3. Arc voltages with different parameters.
Figure 4. Arc current.
Figure 5. Arc conductance.
Figure 4 depicts an arc current with τ = 0.000012 and
Uc = 80 and it has similar wave form as the test result in
Figure 2. Figure 5 shows an arc conductance. The arc
conductance is time-varying nonlinear.
Cassie arc model can also simulate three-phase short
circuit arcs. A three-phase circuit is shown in Figure 6.
Three-phase arcs are expressed by 3 Cassie arc models.
Figure 7 shows three-phase arc voltages. Figure 8
shows three-phase arc currents. Figure 9 shows three-
phase arc power. Figure 10 shows arc energy.

L. YUAN ET AL. 835
Figure 6. three-phase circuit.
Figure 7. Three-phase arc voltages.
Figure 8. Three-phase arc currents.
Figure 9. Three-phase arc power.
Figure 10. Three-phase arc energy.
2.2. Schwarz Arc Model
Schwarz arc model also includes one differential equa-
tion [4].
11 1
ab
dg ui
gdt gPg 






(4)
where P is the cooling constant, a and b are the constants.
Select τ = 0.0001, P = 2000, a = 0.1 and b = 1.2.
are obtained by solving Equation (1), Equa-
tion (3) and Equation (4). The arc voltage is shown in
Figure 11 and the arc current in Figure 12. The curve of
the arc voltage in Figure 11 has expected form. The pa-
rameters τ, a and b define the waveform of the arc volt-
age, and P ensures the mean value of the arc voltage. So
τ= 0.0001, a= 0.1 and b= 1.2 are used and the parameter
P is determined by the arc voltages from test results.
,andig u
2.3. Habedank Arc Model
Habedank arc model is a series connection of a Cassie
and Mayr arc model and consists of two differential equ-
ations and one algebraic equation [6].
2
11 1
c
cccc
dg ug
gdtUg 










(5)
22
0
11 1
m
mmm
dg ug
gdt Pg 






(6)
11 1
cm
g
gg
 (7)
where gc is the arc conductance in the Cassie equation, τc
is the Cassie time constant, gm is the arc conductance in
the Mayr equation, τm is the Mayr time constant and P0 is
the constant.
Solve Equation (1), Equation (3), Equation (5), Equa-
tion (6) and Equation (7) to get . The arc volt-
,andig u

L. YUAN ET AL.
836
age is shown in Figure 13 and the arc current in Figure
14 with τc =0.0001, τm =0.0001, P0 =100 and Uc =80. The
curve of the arc voltage in Figure 13 has expected form
and Habedank arc model can simulate the fault arc.
Therefore select τc = 0.0001, τm = 0.0001 and P0= 100,
and Uc is determined by the arc voltages from test results.
2.4. Modified Mayr Arc Model
Modified Mayr arc model contains one differential equa-
tion [7].
Figure 11. Arc voltage simulated by Schwarz arc model.
Figure 12. Arc current simulated by Schwarz arc model.
Figure 13. Arc voltage simulated by Habedank arc model.
0
11 1
i
dg ui
gdtP Ci










(8)
where Ci is the current constant.
The arc voltage is shown in Figure 15 and the arc
current in Figure 16 with τ= 0.000012, P0= 1000 and Ci=
80. The curve of the arc voltage in Figure 15 has ex-
pected waveform and Modified Mayr arc model can
simulate the fault arc. Therefore select τc= 0.000012, and
P0= 1000, and Ci is determined by the arc voltages from
test results.
Figure 14. Arc current simulated by Habedank arc model.
Figure 15. Arc voltage simulated by modified Mayr model.
Figure 16. Arc current simulated by modified Mayr model.

L. YUAN ET AL.
837
Figure 17. Arc voltage simulated by Schavemaker model.
Figure 18. Arc current simulated by Schavemaker model.
2.5. Schavemaker Arc Model
Schavemaker arc model is a modified Mayr arc model
with a constant time parameter τ and the cooling power
that is a function of the electrical power input. Schave-
maker arc model includes one differential equation [8].

01
11 1
max ,
arc
dg ui
gdt UiPPui












(9)
where P1 is the cooling constant and Uarc is the constant
that determines the mean value of the arc voltage.
The arc voltage is shown in Figure 17 and the arc
current in Figure 18 with τ= 0.0001, P0= 10000, P1= 0.8
and Uarc= 80. Consequently, τ= 0.0001, P0= 10000 and
P1= 0.8 are used and Uarc depends on the arc voltages
from test results for simulation of the fault arc.
3. Conclusions
The fault arc could destroy electrical equipment and
threaten human life. It is important to research the simu-
lation of the fault arc. Black box models are simple and
suitable to simulate the fault arc for arc flash calculations,
choice of electrical equipments and power system pro-
tection. The arc voltage ought to be represented by a pe-
riodic rectangular wave changing its sign at each zero
crossing of the arc current for simulation the fault arc.
Some black box models can create the arc voltage with
the expected waveform if the parameters of arc model are
given properly. This paper provides the parameters of 5
popular arc models and describes the simulation results
of the fault arc. Schwarz arc model is the best arc model
of 5 arc models for the simulation the fault arc.
This paper investigated conventional arc models for
the arcing fault with fixed electrodes. The next task will
be to research conventional arc models for the simulation
of the arcing fault occurred at overhead lines.
REFERENCES
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