try for evaluation of parameters affecting arc plasma ...

Iranian Physical Journal, 1-2, 51-54 (2007)

Try For Evaluation of Parameters Affecting Arc Plasma Chute in a Typical Gas Interrupter S. M. Borghei1, 2, M. R. Abolhasani1.3 and A. Anvari4 1

Plasma Physics Research Center, Science and Research Campus, IslamicAzad University,Tehran, Iran. 2 Physics Department, Faculty of Science, Islamic Azad University, Karaj Branch, Karaj, Iran. 3 Physics Department, Faculty of Basic Science, Tarbiat Modares University, Tehran, Iran. 4 Physics Department, Sharif University of Technology, Tehran, Iran.

Abstract In this paper, we have studied a typical high voltage gas circuit breaker. The main goal of this study is to survey arc plasma and its behavior by use of generalized Mayr-type equation model that follows high voltage circuitbreakers interruption according to a semi-empirical one, named conductance model. Here, we have tried to evaluate some arc parameters affecting interrupting ability by performing a numerical analysis so that our model defines recorded experimental results of an actual test.

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Introduction Thermal plasmas and more particularly, electric arcs are used in a various industrial applications and devices like, arc lamps as light source or arc furnaces, arc welding and cutting plasma torches for metallurgical processes [1-6]. Here, we present a typical gas circuit-breaker (GCB) used for interruption of electric currents and switching phenomena. During GCB operation and opening of its two contacts, current flows through the interelectrode medium (generally Sulphurhexafluoride or its mixture) and electric arc forms through the plasma, between the contacts. Here different basic limits exist which determine the breaking capacity of a circuit breaker. As we know, the electric arc is a self-sustained discharge having low voltage drop and able to support great amount of current [7]. The study of arc in a circuit breaker enables us for better understanding of the main parameters which successful breaking is dependent on. The technical basis of a circuit breaker is initiating an arc plasma, flowing a large current and then cooling it effectively to avoid reignition and finally making a transition from a well-conducting medium into an insulating gas space in a very short time interval. Because the electrical conductivity in the interelectrode space will become so small, the current will tends to diminish, even if the applied voltage be considerable. In other words, for a successful interruption we need to know about power brought to the arc (heating effect) and that of removed (cooling effect). The power balance between these heating and cooling effects either result in a decay of the plasma and an interruption of the current, or in a reheating of the gas to the well-conducting arc column. Immediately after current zero, the transient recovery voltage drives a current through the remains of the decaying arc plasma [8]. Measuring the current

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form close to zero which is termed “Post-Arc current” has been known for a long time and different studies treat this phenomenon from theoretical or experimental point of views. This period is very important and interesting to study, because it precedes either successful interruption or reignition [9]. Understanding and development of related processes often needs modeling of arc plasma. In order to optimize switching process and better understanding of the appearing effects in the plasma it is necessary to deliberate the arc plasma characteristics according to the recorded results. In other words based on modeling the interaction of the arc with surrounding medium, electrodes, circuit and the network must be taken into account and for this reason we must use simulation methods. Some advantages of these methods are reduction of the costs for experimental investigation and shortening the development cycles. Also some disadvantages are, i.e only limited recorded results are available to validating theoretical results and short time interval near current zero. Arc Physics Study

Theoretical approach for arc physics study in circuit breakers has been focused on two main methods, Black –Box Models (BBM) and physical arc models(PAM). First method use a representation of the breaking arc as a non-linear resistance and consider its interaction with the external electrical circuit [10]. The arc is represented as a BBM since it is based on observed data. Black-Box arc models are mathematical descriptions of the electrical properties of the arc only and can not simulate the complex physical processes inside the circuit breaker [11].

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Borghei, et. al.

Iranian Physical Journal, 1-2 (2007)

The second approach, tries to describe the arc behavior by solving a whole system of equations, conservation of mass, energy and state law equations. In Table I. we have refered to examples for each of these methods [15-16] including our previous work [14], however for more details one can refer to the literature. A complete review of all theories and experimental results in this area can be found in [12-13].

current and is governed by the dynamical behavior of the electric arc. After this balance, we get the generalized Mayr-type equation as:

1 dg d (ln g ) 1 ⎡ ui ⎤ = = ⎢ − 1⎥ g dt dt τ ⎣P ⎦

(3)

Table I: Examples of different methods. Measured max Post Arc Current(A)

Category

Working gas

Modus operandi

Note

Reference

Reignition

Rotating Arc Rotating Arc Rotating Arc

N2 SF6 N2+SF6

------%25+%75

[14] [14] [14]

2

Puffer

SF6

measurement measurement measurement both measurement and

----

[14]

1.7 12

self generated flow self generated flow

SF6 N2

----

[16] [16]

5 ≤ 0.1

computation

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Basic Equations Circuit breaker interrupting ability is analyzed by representing its characteristics by a function of electrical properties. Usually for such a purpose the so-called “Black Box Modeling” is applied and a mathematical differential equation for description of the electrical properties is introduced. The model is based on the use of recorded current and voltage traces in the experiments. From these datas, we can find some electrical features such as arc resistance, arc conductance and also arc power. Mayr equation states that:

with u as arc voltage, i as arc current and P as dissipated power from the arc. From physical point of view, there is a competition between heating and cooling effects such as conduction, convection, radiation and turbulence that result in either reignition or successful interruption [15-18]: Each BBM brings up some arc parameters such as P and τ in our so-chosen model. Assuming these arc parameters kept constant gives rise to a deviation of theoretical model obtained from experimentally recorded results. Thus they must be determined experimentally for high voltage gas circuit breakers during full quenching activity. They characterize the performance of a breaker under test conditions. For this reason we considered them to be a power functions of electrical properties specially arc conductance as follows:

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1 dg 1 =− τ g dt

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(1)

with g as arc conductance and τ as arc time constant. If we limit ourselves to thermal processes, the dynamic behavior of the plasma column can be taken into account by writing an energy balance equation according to [12]:

dQ = Pin − Pout dt

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physical model physical model

1 dg d (ln g ) 1 = = g dt dt τ 0 gα

⎡ ui ⎤ − 1 ⎢ ⎥ β ⎢⎣ P0 g ⎥⎦

α and β are the parameters that P and τ ، whereas P0 is arc cooling

(2)

(4)

influence on power. This

equation contains four free scalar parameters that should be evaluated and adopted according to the device and circuit conditions.

where Q is the accumulated energy, Pin is electrical arc input power equal to ui (heating effects or joule heating) and Pout is the dissipated power from

Measured and Computed Result Curves

the arc (cooling effects). By applying this heat balance term to the equation (1), we can introduce a correction term for better understanding of current interruption. This requires that the interelectrode gap of a breaker changes from conductive plasma into an insulating gas media. This transition occurs around zero value of the

For determining the above four free parameters of electric arc in the model, we first get the traces of the current and the voltage from a real test. Then we read the values of current, voltage and the time from our traces and create a matrix of three columns [19]. In the

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Try for Evaluation …

Iranian Physical Journal, 1-2 (2007) By using these experimental results, we find

next step, we find some arc properties such as arc conductance (g = i/u) and arc power which are shown in Figures (1) and (2):

d (ln g measure ) dt curve as shown in Fig (4) by the dotted line. The initial estimation of the parameters is a guess and there is no way of knowing exact initial parameter set apriori. Based on the predicted value for p 0 and τ 0 , we can try to define remaining parameters by a curve fitting technique. In other words to get the best fit of our curves we have changed the values of alpha and beta in an appropriate range [8, 12, 20, 21]. Employing numerical method of simulation, we find the best fit for the measured and computed d (ln g ) dt curve as shown by the solid line in Fig (4). This fitting of the curves corresponds to the values of Po =2.5 Mw, τ 0 = 7.9 microseconds, α =0.697 and β =0.713 for the four free parameters used in the prechosen model. The values of these parameters are in the range of other similar works [15]. In this way we can determine and evaluate the model parameters and their influence on the arc plasma chute. There are several energy exchange mechanisms, but gas blast arcs in the current zero phase and thermal period are dominantly controlled by turbulence. In this period, the turbulent energy exchange plays an important role [18].

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Fig 1: Measured arc conductance ( g measure ) using current and voltage traces of a successful interruption.

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Fig 2: Electric arc power.

The values of arc parameters، according to these traces، define our model. From arc conductance we find g

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and also dg/dt, as shown in Fig (3):

d (ln g measure ) dt (Dotted line) and d (ln g computed ) dt (Solid line) Versus time.

A Fig 3: Derived

dg measure dt

Fig 4: Plot of

As we see from Fig (1), arc conductance obeys the general exponential form introduced by the model. However but in point A on the curve g is undefined, because in this point arc voltage and also arc current reach to their zero value simultaneously. Before point A, both arc current and voltage fall down, whereas after that the current rises up. As a result dg/dt shows a peak in this point as is shown in Fig (3). In Fig (2), points A and C belong to zero value of the arc current. Between points A and B, because of driving Post Arc Current, gas heats and as a results arc power goes up to point B. In this point cooling effects exceed the heating effects and therefore current goes toward its second zero value (point C). In other words, in point B

according to recorded

results.

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Borghei, et. al.

Iranian Physical Journal, 1-2 (2007) [11]

S. M. Borghei and A. Bazrafshan: Proc. Of XVth Int. Conf. on Gas Discharge and their Applications (Toulouse-France) vol 1 (Paul Sabatier university) 2004 p. 153.

[12]

WG 13.01: Electra 149 (1993) 41-71.

In this paper an attempt has been made to study, characterize and understand some arc behaviors such as arc power, arc conductance and their time changes according to the recorded current and voltage traces for modeling the interaction between an arc and its circuit. A useful theoretical model and a simple way to study of arc-circuit interaction, is using an appropriate black-box model. From physical point of view, there are different phenomena that affect the arc behavior. By using this method we have tried to find the appropriate parameters for fitting and studing the results.

[13]

WG 13.01: Electra118 (1988) 65-79.

[14]

J. Mahdavi: Rev.Gén. Electricité (RGE) 5 (1986) 21-26.

[15]

B. Blez and C. Guilloux: IEEE Trans. on power Deliv. 3 (1988) 1692-97.

[16]

A. Gleizes, M. Mitiche and P. van Doan: IEEE Trans. on Plasma Science 19 (1991) 12-19.

[17]

S. M. Borghei and J. Mahdavi: Proc.of XXVI Int. Conf. onPhenomena in Ionized

Acknowledgments

[18]

Gases (Greifswald-Germany) vol 4 (Local Organizing Committee) 2003 p. 107.

The authors wish to express their sincere thanks first to Dr M. Gholipour for his great helps in computer programming and also Dr M. Aslaninejhad for his helpful comments and advices.

[19]

S. M. Borghei, J. Mahdavi, A. Hojabri and M. Ghoranneviss: J. Plasma Fusion Res. SERIES 5 (2002) 471-473.

[20]

L. R. Orama and B. Rodriguez: Int. Conf.on power syst. Trans. (IPST) New orlean USA 2003.

current changes its direction. Thus electric arc power falls down and finally circuit breaker performs a successful interruption of the current. Conclusion

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