International
Journal of Electrical Engineering
and OF
Technology
(IJEET), ISSN 0976 –
INTERNATIONAL
JOURNAL
ELECTRICAL
6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
ENGINEERING & TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 3, Issue 1, January- June (2012), pp. 69-78
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IJEET
©IAEME
BLACK BOX ARC MODELING OF HIGH VOLTAGE CIRCUIT
BREAKER USING MATLAB/SIMULINK
Mr. Nilesh S. Mahajan
Student, Department of Electrical Engineering,
Government College of Engineering
Aurangabad, (MS), India.
Email - nilesh17_mahajan@rediffmail.com
Mrs. A. A. Bhole
Assistant Professor, HOD, Department of Electrical Engineering,
Government College of Engineering
Aurangabad, (MS), India.
Email - bholeanita66@gmail.com
ABSTRACT
Over the years, as our knowledge of the interrupting process progressed, many
techniques have been developed to test the circuit breakers and simulated arc model
There are three models (Physical Model Black Box Model and Parameter Model) that
describe the behavior of f arc. This paper evaluates the black-box arc model for circuitbreakers with the purpose of finding criteria for the breaking ability. A black-box model
is a model that requires no knowledge from the user of the underlying physical processes.
In this paper, knowledge of the physical processes is required when evaluating and
developing the arc models. This paper is meant to give a detailed study of black box
model with the purpose to evaluate, combine, improve and apply to already existing
circuit-breakers. Cassie-Mayr arc models was evaluated. Cassie’s model gives good
results for large currents, while Mayr’s model is better for currents near zero. Therefore,
a combination of the Cassie and Mayr model will be used to obtain better result.
Keywords: Black-box arc model, cassie-mayr, circuit-breaker, Matlab/Simulink
I. INTRODUCTION
Circuit-breakers are very important electric power transmission equipment related
to quality of service, because they can isolate faults that otherwise could cause total
power system breakdowns. When circuit breaker contacts separate to initiate the
interruption process, an electrical arc of extremely high temperature is always produced
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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
and becomes the conducting medium in which current interruption will occur. With
modern high-voltage breakers, the arc is blown with gas in the same way as a match is
blown out with your breath, but with 100 million times the blowing power. [1]
In simple terms, circuit-breakers consist of a plug that is in connection with a
contact when the breaker is closed. The current then flows right through the breaker. To
interrupt the current, the plug and the contact is separated with rather high speed,
resulting in an electric arc in the contact gap between the plug and the contact. This is
illustrated in Figure:1 Since short-circuit currents in most high-voltage power systems
frequently reach 50 to 100 kilo amperes, the consequent arc temperature goes beyond
10,000 degrees (C), which is far above the melting point of any known material.[2]
Figure: 1 Simplification of the contact gap
Because of these extreme temperatures, investigation and knowledge of current
interruption through arc diagnostics is very difficult and limited. Hence, circuit breaker
design is still done for a major part on full-sized prototypes by a cut-and-try method and
has remained more of an art than a science. It is now possible to measure and predict by
modeling the interrupting limits of modern breakers. [1]
In this paper the characteristics of the electric arc are described with the aim of
characterizing the interruption process in high voltage circuit breakers. In addition, an
overview of the most important model such as Cassie-Mayr arc model and simulation
method using MATLAB/SIMULINK is exposed.
II. BLACK-BOX MODELS
“Black box” models define the interaction between the arc and the electrical
circuit during the current interruption process. In these models the most important issue is
the behavior of the arc and not how the interruption process develops. Many of these
models are based on the equations proposed by Cassie and Mayr, which represent the
variation in the conductance of the arc by a differential equation obtained from physical
considerations and implementation of simplifications. In this way, Mayr assumed that the
arc has fixed cross-sectional area losing energy only by radial thermal conduction. In
contrast, Cassie assumed that the arc has a fixed temperature being cooled by forced
convection. [3]
Thus, "black box" models are in general represented by one differential equation
relating the arc conductance with magnitudes such as voltage and arc current.
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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
(1)
Where:
G : Arc conductance
u : Arc voltage
i : Arc current
P, T: Parameters of the model
The fundamental purpose of "black box" models is to obtain a mathematical model that
represents the circuit breaker test and can be applied in predicting the behavior of the
circuit breaker under different conditions. These models can only be applied if the
particular process that takes place is governed by the conductance. In other cases, such
as in the dielectric region of breakdown processes, these models are not directly
applicable. [2]
III. ROLE OF ARC IN CURRENT INTERRUPTION
When two current carrying contacts open, an arc bridges the contact gap and
prevents an abrupt interruption of current. This arc is useful in a way as it provides a low
resistance path for the current after contact separation, thereby preventing current
chopping and associated abnormal switching over voltages in system. In case of
alternating current (ac), arc is momentarily extinguished at every current zero. To make
the interruption complete and successful, re-ignition of the arc between the contacts has
to be prevented after a current zero. [4]
It is thus evident that arc plays an important role in current interruption and
therefore must not be regarded as undesirable phenomenon. It must also be realized that,
in absence of arc the current flow would be interrupted instantaneously, and due to the
rate of collapse of associated magnetic field, very high voltage would be induced which
would severely stress the insulation of the system. On the other hand, the arc provides
gradual, but quick transition from current carrying to current breaking states of the
contacts. It thus permits the disconnection to take place at zero current without inducing
the potentials of dangerous values.[3]
IV. ARC INTERRUPTION THEORIES [5]
The physical complexity in behavior of electric arc during the interrupting process
has always provided the incentive for researchers to develop suitable models to describe
this process. Over the years many researchers have advanced a variety of theories. Some
of the very important theories are:
• Slepian’s Theory
• Prince’s Theory
• Cassie’s Theory
• Mayr’s Theory
• Browne’s Theory
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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
A. CASSIE MAYR’S ARC THEORY
In 1939 Cassie proposed a model of arc in which the arc was assumed to have
cylindrical column with uniform temperature and current density, so that its area varies to
accommodate the change in current. The power dissipation was assumed to be
proportional to the column cross section. This model was intended to represent an air
blast arc and was represented by following differential equation:
Rd/dt (1/R) =1/ θ {(v /vo)2 - 1}
(2)
Where R is the arc resistance, v, is arc voltage at any instant, v0, is arc voltage in steady
state, and θ the arc time constant i.e. the ration of energy stored per unit volume to the
energy loss rate per unit volume. Cassie assumed that only convection causes the power
losses, which means that the temperature in the arc is constant. This implies that the
cross-section area of the arc is proportional to the current and that the voltage over the arc
is constant. [9]
A few years later, in 1943, Mayr proposed a somewhat improved model, in which
arc was assumed to be of fixed diameter but of varying temperature and conductivity, the
power loss occurred from the surface of the arc only. This model was described by
differential equation:
Rd/dt (1/R) =1/ θ {(vi /wo) 2- 1}
(3)
Where i is the arc current at any instant and wo is the energy loss from periphery
of the arc at steady state. Mayr assumed power losses are caused by thermal conduction
at small currents. This means that the conductance is strongly temperature dependent but
fairly independent of the cross-section area of the arc. The area is therefore assumed
constant. It has been found that Cassie’s model best describes the period before current
zero where as Mayr’s model represent better the post arc regime. [9]
V. TEST CIRCUIT
The arc models can be implemented in a circuit in a straight forward way. [5]
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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
Current
Voltage
V
+
+
I
-
Breaker
Continuous
Powergui
Figure: 2 Arc Model Test Circuit
VI. CASSIE-MAYR’S ARC MODEL [10]
A. CASSIE ARC MODEL
(4)
Where g is the conductance of the arc, u is the voltage across the arc, i is the current
through the arc, τ is the arc time constant, Uc is the constant arc voltage.
Cassie’s arc model can be implemented with test circuit shown above. The figure 3
shows the Cassie’s arc model [5]
1
U
+
V
-
Voltage Measurement1
Controlled Current Source1
Cassie arc model
S
+
-
2
-I1
DEE
Step
Hit
Crossing
Figure: 3 Implementation of the Cassie’s Arc Model
B. MAYR’S ARC MODEL
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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
(5)
Where g is the arc conductance, u is the arc voltage, i is the arc current, τ the arc time
constant, P is the cooling power. The figure 4 shows the Mayr’s arc model
Controlled Current Source
1
U
+
V
-
Voltage Measurement
Mayr arc
model
DEE
S
+
-
2
-I
Hit
Crossing
Step
Figure: 4 Implementation of the Mayr Arc Model
The initial conductance of the arc g (0) can be altered. Furthermore, the time at which the
contact separation of the circuit breaker takes place can be specified. Until that time the
arc model behaves as a conductance with the value g (0). [5]
C. COMBINED CASSIE-MAYR’S ARC MODEL
Two identical circuits are displayed: one with a Cassie and one with a Mayr arc
model. The circuit is a simple representation of a circuit breaker interrupting a short-line
fault. At the source side of the circuit breaker a circuit is present for reproducing a (2
parameter IEC) transient recovery voltage, while the RLC circuit at the line side
represents a short transmission line that is short circuited.
Figure: 5 Combined Cassie-Mayr Arc Model
VII. RESULT
A. CASE - I
When the circuit breaker contact separation starts at t = 0 s, the following arc
voltage and arc current are computed (overall and detail around the current zero
crossing). [10], [5]
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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
CASSIE’S ARC MODEL
Figure 6: Voltage Current Comparisons for the Cassie Model. (At T=0 S)
MAYR’S ARC MODEL
Figure 7: Voltage Current Comparisons for the Mayr’s Model. (At T=0 S)
CASSIE -MAYR’S ARC MODEL
Figure 8: Voltage Comparisons for the Cassie and Mayr Arc Models. . (At T=0 S)
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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
Figure 9: Current Comparisons for the Cassie and Mayr Arc Model.
B. CASE – II
When the contact separation starts at t = 9 ms, the following arc voltage and arc current
are computed. [5], [10]
CASSIE’S ARC MODEL
Figure 10: Voltage Current Comparisons for the Cassie Model. (At T=9 ms)
MAYR’S ARC MODEL
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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
Figure 11: Voltage Current Comparisons for the Mayr’s Model. (At T=9 ms)
CASSIE-MAYR’S ARC MODEL
Figure:12 Voltage Comparisons for the Cassie and Mayr Arc Models. (At T=9 ms)
Figure 13: Current Comparisons for the Cassie and Mayr Arc Models. (At T=9 ms)
VIII. CONCLUSION
Matlab/Simulink is a very powerful tool for developing arc models. Through this work a
Cassie-Mayr arc model has been studied and implemented as a “black-box” model in
MATLAB/SIMULINK. The simulation produced current and voltage oscillograms are
very useful for studying complex current interruption process in the circuit breakers
without considering the underlying complex physical phenomenon.
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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 –
6545(Print), ISSN 0976 – 6553(Online) Volume 3, Issue 1, January-June (2012), © IAEME
REFERENCES
[1] Guy St-Jean, Institute de recherche d Hydro-Quebec “Modeling Electrical Arcs
for Power Circuit Breakers” IEEE Power Engineering Review, November 1991
[2] Niklas Gustavsson, “Evaluation and Simulation of Black-box Arc Models for
High Voltage Circuit-breakers,” IEEE Transactions on Power Delivery,vol.7,
no.4, Oct. 1992, pp. 2037-2045
[3] Smaranda Nitu, Constantin Nitu, and Paula Anghelita “Electric Arc Model, for
High Power Interrupters,” EUROCON 2005, Serbia & Montenegro, Belgrade,
November 22-24, 2005
[4] L. van derSluis, “Transients in Power Systems,” John Wiley & Sons, 2001.
[5] P.H. Schavemakerand L. van derSluis, “The Arc Model Blockset,” Proceedings
of the Second IASTED International Conference, June 25-28, Greece.
[6] L. van derSluis, W. R. Rutgers, and C.G.A. Doreman, “A Physical Arc Model for
the Simulation of Current Zero Behavior of High-Voltage Circuit Breakers,”
IEEE transactions on Power Delivery, vol. 7, no. 2, April 1992, pp. 1016 -1022.
(Modified Mayr Model)
[7] L. van dersluis, and W.R. Rutgers, “Comparison of Test Circuits for HighVoltage Circuit Breakers by Numerical Calculations with Arc Models,” IEEE
Transactions on Power Delivery,vol.7, no.4, Oct. 1992, pp. 2037-2045.
[8] V. Phanirajand, A.G.Phadke, “Modeling of Circuit Breakers in the
Electromagnetic Transients Program,” IEEE Transactions on Power Systems,
vol.3, no.2, May 1988, pp. 799-805. (Mayr Model Implementation)
[9] W. Gimenez, 0. Hevia, "Method to Determine the Parameters of the Electric Arc
from Test Data," in Apendice III: Articulos Publicados en Congresos
Internacionales, 2000, Universidad Tecnologica Nacional, Fac. Reg. Santa Fe,
Argentina, pp.41-45.
[10] O. M. Cassie, "Arc rupture and circuit severity," Cigre, vol. Report Nº102, 1939.
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