2013 2nd International Conference on Electric Power Equipment - Matsue, Japan

Analysis of Arc Plasma During Small Capacitive Current Interruption

in SF 6 Circuit Breaker WANG Liangl, LIN Xinl, WANG Feimingl, Terry Yan2, XU Jianyuanl

ISchool of Electrical Engineering, Shenyang University of Technology, Shenyang 110870, Liaoning Province, China. 2Department of Mechanical Engineering, Southern Illinois University Edwardsville, IL 62026 USA

Abstract- This paper establishes a model for the

conductivity of non-equilibrium dual temperature arc

plasma during small capacitive current interruption in a

SF6 circuit breaker. Considering the contributions of

electron-ion-neutral particle collision frequency and

collision cross-section, we obtain the conductivity of SF 6

plasma as a function of temperature and pressure and

establish a dynamic arc model for small capacity currents.

Based on the model, a numerical simulation is performed

on the flow field with a load of small current of 1600 A for

a 126 kV SF6 circuit breaker. Density, pressure and

temperature distributions inside the circuit breaker

chamber are obtained. With the electric field inside the

same interrupter, dielectric recovery characteristic curves

are described. In addition, the effect of arc duration on the

dielectric recovery characteristics for small capacitive

current is studied and the influence mechanism is

discussed.

I. INTRODUCTION

Arc mathematical model study is the basis and prereqUisIte of computer modeling, numerical calculation for load flow field of SF 6 circuit breaker. Over a long-term, continuous research, international and domestic academics have proposed different arc model theory. Electric arc theory under high pressure in the past was focused on the steady arc breaking process during large current, for example, the arc mathematical model based on the theory of energy balance was put forward by Cassie; arc mathematical model considering the heat conduction and diffusion was proposed by Mayr. Numerical analysis using the finite volume method was proposed by Chevrier P (1993)[1], J. C. Verite (1995P], Trepanier J. Y. (1995)[3]. Gauster E (1997)[4], Frank Karetta (1998P], Van, J. D. (1999)[

6] have studied the nonlinear numerical calculation method of electromagnetic transient process, these arc mathematical models were based on fluid dynamics equations (Navier-storkes), the energy equation, momentum equation, ampere's law, mass continuity equation and the magnetic induction intensity equation. In recent years, Xi'an Jiaotong University carried out the study of the arc plasma generation mechanism;

Fund project: Project Supported by National Natural Science

Foundation of China (51277123) and National Natural Science

Foundation of Liaoning Province (201102169)

Tsinghua University carried out a comprehensive study on the three cathode high temperature arc plasma jet formation and particle coupling. Above researches of scholars at home and abroad were aimed at arc In a stable burning phase, whose models were established based on steady-state, high current conditions and local thermodynamic equilibrium.

Due to capacitive current breaking is very small and arc duration is very short, electrons and heavy ion did not reach uniform temperature in the development stage of plasma arc, plasma arc will be in a state of imbalance. In some occasions, where electron number density lower than or the temperature and concentration gradient much larger, electron diffusion has become obvious, temperature of plasma electron is significantly higher than that of heavy particles, thus, dual temperature models are often used to describe the plasma.

Based on the non-equilibrium dual temperature arc plasma model, numerical terms include chemical composition of SF 6 gas arc, thermodynamics, transport parameters, etc of state parameters. The plasma composition and particle density are obtained through calculation, and the dual temperature conductivity model is determined further. On this basis, the load flow field of 126kV SF6 circuit breakers breaking the 1600A current different arcing time was calculated by the numerical analysis methods, the arcing chamber density, pressure and temperature distribution are acquired, with the electric field distribution, its critical breakdown voltage is calculated.

II. BASIC EQUATIONS

Calculation of plasma chemical composition, is not only plasma thermodynamic parameters and transport the necessary first step, but also an important part of understanding micro plasma process. Calculation of plasma components, involving the main theoretical basis and basic equations, are as follows.

Stoichiometric conservation elements:

�>\ln:l =c (1) I

Dalton law of partial pressures:

P+Op = L P; (2) I

Charge quasi-neutral conditions:

L Ztn; -n� = 0 (3) I

The above fonnula, n�1 is the amount of substance related to the s kind of element and the I kind of particles in the plasma; c,z is the amount of substance s atoms of I seed particles in the plasma in units moles; C is constant; Pi is the partial pressure of the i particle composition in the plasma; 0" is the pressure correction value considering the presence of plasma internal charge in the plasma; n; is the charged particles number density of the t particle in the plasma; 2, is electric charge of the t particle in the plasma; Positive ions are positive and negative ions are negative; n; is electron number density.

Saha (ionization) equation:

Electron temperature 'Fe and heavy particle temperature Th are no longer equal in non-equilibrium plasma. With the dual temperature model, the electron temperature and heavy particle temperature unified respectively, the ratio of both 1;, / � = (). At this point, the partition function Zr is no longer a function of the electron and heavy particle uniform temperature, but the function of electronic temperature Te and the heavy particle temperature Tz,. In the formula (4), 1;,x is Ar particle excitation temperature, its value determines the way of the particle collisions in transport process. For ionization reactions involving atoms and ions, particle excitation particles is the largest contribution to the calculation of partition function, while particle excitation temperature and electron temperature is approximately equal in most cases, assuming that Zr ('4,1;,) � Zr ('4). In the formula (5), t is plasma Debye length and formula for calculation:

(6)

In the formula (6), So is the permittivity of vacuum; 2,

is the t kind of charged particles charge; V is the species number of particles in the plasma.

The Guldberg-Wagge (dissociation) equation:

nAnR = ZAZR (2mAmH�kTh J3/2 . exp (- �J (7)

nAB ZAB mARh k�x

In the formula (7), n" m" Z, express particle number density, particle quality and the distribution function of particles respectively (i = A, B, AB) .

2

TABLE 1 DOUBLE ATOMIC PARTICLE TYPE PARTITION FUNCTION VALUE

T(K) 1000 2000 4000 6000

F2 5.55' 102 1.79'103 6.92'103 1.5'104 S2 5.54·10' 1.83.104 7.46.104 1.86.105 SF 5.72'103 2.02. 104 7.79'104 1.78'105 F/ 7.51'103 2.24'103 7.88'103 1.75'104 SF' 5.43·10' 1.71.104 6.42.104 1.53.105 SF 2.95·10' 9.66·10' 3.74.104 8.41.104

III. NONE-QUILIBRIUM COMPONENTS AND

THERMODYNAMICS PROPERTIES

A. The Partition Function

The internal partition functions (IPF) of each species were determined differently according to the structure of each species. For atomic species, we used the values given by Drawin and Felenbok[7lin addition to our own calculations allowing extrapolation to low temperatures. The ionization potential lowering had been taken into account:

M =_l_ �

, 47rEo An (8)

� = EokT

e2L k (Z;nk ) (9)

For diatomic species, the IPF were calculated using the Morse potential minimalization method[8land were reported in table 1 for various temperatures. For polyatomic species, we used the formula proposed by Herzberg[9l. For diatomic and polyatomic species the required data were taken from the lanaf tables [IOl.

B. Non- equilibrium Composition Computing

To study the thermodynamic and transport properties of SF 6 arc plasma, the distribution of particle number density changing with the arc temperature and arc chamber pressure in every composition need to be obtained first. Taking the arc plasma generated during the interruption of high-voltage SF 6 circuit breakers as the research object, it can be seen from the literature that pure SF6 gas may produce dissociation equilibrium in the arc generated during the interrupting course as shown in Table 2.

It can be initially identified from the decomposition and ionization chemical equations of SF6 gas that SF6 arc plasma model mainly contains 20 kinds of particle components, which are: SF6, SFs, SF4, SF3, SF2, SF, SSFb FSSF, Sz, Fz,S, F, e, F-, F+, F2+, S/, S+, S2+, S3+. According to the basic principle of arc gas composition calculation listed in II, and the calculation parameters of SF 6 plasma particles given in tables 2, such as the partition function and the ionization energy, the particle density of the arc plasma in different temperature and pressure can be obtained by solving nonlinear equations

TABLE 2 IONIZATION(Ei) AND DISSOCIATION(Ed) ENERGIES

Reaction r;d(eV) Species r;,(eV) F2=F+ F 1 6 S 104

SF2=S+ F2 59 S+ 234

SFJ=SF2+ F 2 92 S2+ 35 I

SFs=SF4+ F 2 2 7 F 174

SSF2=SF2+ S 39 S2 83

FSSF=SF+ Sf 3 71 SF 10 1

S2=S+ S 437 F+ 35 6

SF=S+ F 3 52 F2 158

SF2=SF+ F 4 01

SF4=SF,+ F 347

SF6=SFs+ F 4

SSF2=SF+ SF 436

using the Newton iteration method. The pressure is 0.1 Mpa, and the calculation results of SF 6 plasma particle density are shown in figure I.

As shown in figure I, SF 6 gas starts to decompose when T=IOOO K, and the decomposition products are SF4 and F. With the increase of temperature, SFs, Fz, SF3, SFz, SF4 and F produce successively. The density of SF 5 and F 2 reaches the maximum when T= 1700 K, then the SF 4, F when T=1800 K. The main decomposition product of SF6 is SF4 and F when T=IOOO K-1800 K, and a part of SF4 are decomposed to SF3, SFz in this stage. SF4 are mainly decomposed to SF3, SF2 and F when T=1800 K-2100 K, and the number of SF3 and SFz particles rises gradually. When T = 2100 K, the particle number density of SF 3, SF z and SF 4 has the same order of magnitude. When T=2000 K, SF2 begins to decompose into SF and F. When T= 2000 K-3000 K, SF is gradually decomposed to S and F. With the progress of decomposition, S atoms generate Sz and SF molecules generate FSSF and SSF2 through composite, So Sz, SF, FSSF and SSF2 particle densities have reached the peak successively first and then declined gradually during this period. Ionization effect starts When T=4000 K and S is ionized to S+ and e first. When T=4000 K-8000 K, a part of e and F are composited to F, and the initial density of S+ is slightly more than that of e. Since T=8000 K, the curves of S+ and e are basically in coincidence because F has a very small order of magnitude and a part of F are ionized to F+ at this time. When T=17000 K, the F+ density reaches the maximum value and then declines gradually.

C. Calculation a/The Conductivity

Ignoring a few runaway electrons, when the electric field E is far less than the critical field intensity, the calculation formula of the conductivity without temperature and density gradient is as follows

= _6_ -2Z-1k3/2T3/2In-l (A) -1/2 (10) (J" 2 � e I e me J[ ,,2

In the formula (10), 21 is plasma average charge; In A is the Coulomb logarithm; Te is electron temperature.

Figure 2 shows the SF6 plasma conductivity curve

3

1, SF,,; 2, SF,; 3, SF4; 4, SF,; 5, SF,; 6, SF; 7, SSF,;

8, FSSF;9, S,; 10, F,; II, S; 12, F; 13, e; 14, F; 15, F ;

16, F' ; 17, S, ; 18, S ; 19, S' ; 20, S3

Fig, 1. P= 0,1 Mpa each particle density changes with the temperature curve

12000 1 aIm _ 1()()()()- - 2 aIm ------+----"--c-,§ 4 aIm � 8000- - �o

a��m ______ +-'--'-�L t5 :J � 6ooo---+-----���---o o � 4000· � W 2000

%�. -=-��-�1--�1�5--�2 Temperalure(K) x 104

Fig, 2, Pure SF6 electrical conductivity changing with pressure and temperature curve

changing with the temperature under different pressure conditions. It can be seen from the figure that, with the increase of the pressure, SF 6 arc plasma conductivity also increases, and it basically indicates an increasing trend with the temperature increasing.

IV ANALYSIS OF CRITICAL BREAKDOWN VOLTAGE

WITH DIFFERENT ARC TIME

Based on the model for the conductivity of dual temperature during small capacitive current interruption established, a numerical simulation was performed on the flow field[lZ-14] with a load of small current of 1600 A for a 126 kV SF6 circuit breaker under different arcing time of 3ms, 4ms and Sms. Electric field, flow field and the calculation method of the critical breakdown voltage were given in reference [11], density, pressure and temperature distribution inside arc were obtained next. With electric field distribution, the critical breakdown voltage is shown as figure 3. Transient recovery voltage (TRV) curve is given by the national standard GB 1984-2003.

By comparing the critical breakdown voltage under three burning arc time of 3ms, 4ms and Sms, we can see that the arc time impacts significantly on the dielectric recovery. In the curve of critical breakdown voltage, its rising rate becomes smaller with arc through zero when arc time is 3ms. There is a downward trend at 3.7ms, at t h i s m o m e n t , d i e l e c t r i c s t r e n g t h b e t w e e n

2000 3mf critical breakdowr voltage

30

:;- 4ms critical bleakdown votage I 25 -'" <D 20 Ol c $ 6> 0 15 � > c

� 1000 10 � � 0 '" 5 � I'! '" [)) I'!

� [))

8 00 0.03 0.04

Fig. 3. Critical breakdown voltage, breakdown margin, and TR V curves with different arc time

contact recovers slow, re-striking is easily happened, but it rises rapidly at 4.2ms. In summary, it can be determined that it is difficult to put out interruption because of arc below zero within 3ms before current going below zero. It rises slowly at O.2ms after arc over zero, and then dielectric strength between contacts recovers rapidly. By curves of 3ms and 4ms, we can conclude that the shortest arcing time is 4.2ms. At the point of 5ms, it rises rapidly after arc extinguishing.

The curve of the breakdown margin (critical breakdown voltage value-TRY value/TRY) changing with time is shown in figure 3, this curve is plotted after comparing the curves of 3ms, 4ms and 5ms respectively with TRY curve. It can be seen that the breakdown margin of breaker is 1.5 when the arc time is 3ms, the value is a litter smaller, its probability to occur heavy breakdown increases. The margin is 3.58 times and 3.84 times respectively with arcing of 4ms and 5ms, which is enough to ensure the safety of interruption for the circuit breaker.

V. CONCLUSION

This paper supposed to the non-thermodynamics equilibrium dual temperature plasma. We obtained the conductivity of SF 6 plasma as a function of temperature and pressure under the condition of different pressure (1 ATM to 10 ATM) of 300�20000 K with the conductivity calculation formula of Spitzer. Before, the calculation of density of particles in the plasma had been finished. The burning arc time was set to 3ms, 4ms and 5ms. Conclusions are as follows:

(1) Conductivity of SF6 plasma arc increases with the pressure, and it shows rising trend when temperature increases.

(2) The effect of arc time on critical breakdown voltage and breakdown margin is obvious. We determine the shortest arc time is 4.2ms by the variation trends of the critical breakdown voltage after arc extinguishing of 3ms and 4ms. This shortest arc time can provide reference for option controls.

(3) The breakdown margin is of 1.5 times with arcing

4

of 3ms, a litter lower. But the margin shows 3.58 times and 3.84 times respectively with arcing of 4ms and 5ms, which is enough to ensure the safety of interruption for the circuit breaker.

ACKNOLEDGMENT

This work was supported by National Natural Science Foundation of China under Grant No.51277123, and National Natural Science Foundation of Liaoning province, CHINA under Grant No. 201102169.

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E-mailofauthors:wangliang13579@126.com