21st

International Symposium on Plasma Chemistry (ISPC 21) Sunday 4 August – Friday 9 August 2013

Cairns Convention Centre, Queensland, Australia

3D modeling and simulation of arc deflection behavior in vacuum interrupters with consideration of external circuits

Lijun Wang, Xiaolong Huang, Zhonghao Qian, Shenli Jia, Zongqian Shi

State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an, 710049, China

Abstract: Vacuum circuit breakers (VCBs) always are used in the power distribution system,

vacuum interrupters (VIs) are the key component of VCBs, vacuum arc (VA) behaviors in

VIs is very critical for successful interruption. For commercial VIs, VA is always controlled

by axial magnetic fields (AMFs) technology. When VIs are connected to power system, VA

characteristics will be influenced not only AMFs generated by itself coil, but also by magnetic

field generated by external bus bar or neighboring phases. In this paper, the deflection effect

of VAs subjected to global magnetic field, including AMFs and TMF along different direc-

tions is modeled and simulated. The VA is modeled by MHD method and simulated by

FLUENT software. Simulation results show that external TMF will lead to deflection of VA,

and plasma parameters also exist deflection. The delfected direction of plasma parameters in

vacuum arc obeys left hand rule. When external TMF is along minus x direction, arc plasma

deflects toward y direction. And when external TMF is along y direction, arc plasma delfects

toward x direction. When external composite TMFs include Bxext = -20mT and Byext = 20mT,

the vacuum arc is deflected toward center line between x and y positive directions.

Keywords: Vacuum arc, 3D model, deflection, TMF, AMF.

1. Introduction

Vacuum arcs widely appear in many fields, such as

coating and depositions, vacuum interrupters (VIs), vac-

uum ion sources and pulsed power technology, and so on

[1]. Axial magnetic fields (AMFs) always are used to

make VAs keep in the diffuse status [2], which also makes

AMFs become the most popular technolgy in commercial

VIs. However, actual VIs are connected in the power sys-

tem through external circuits, which will generate trans-

verse magnetic field (TMF),which is vertical to VAs. So,

actual VAs always are not only subjected to AMFs, but

also external TMFs. This kind of TMFs will lead to de-

flected VAs and electrode erosion. Many interruption

failure of VIs is related to the deflected eorosion of elec-

trode. I. N. Poluyanova and V. A. Bugayov’s research

results showed that interrupting capability of the AMF

electrodes in the external TMF can reduce about 20% [3].

Modeling and simulation are becoming one of the im-

portant methods to undersand vacuum arc mechnism, and

has widely been adopted by many researchers [4]-[12].

Because the external bus bars and neighboring phases

have different current directions, the TMFs generated by

which will be a composite magnetic fields, which include

at least two components. In this case, two dimensional

vacuum arc model is not enough to describe this kind of

phenomena. In our previous work[11], 2D deflected mod-

el has been modeled. In this paper, deflected VAs with

AMFs and TMFs of external circuit will be modeled and

simulated with 3D configuration.

2. 3D model of VA deflection behaviors under global

magnetic fields

2.1 Physical model

3D physical model of deflection behavior of vacuum

arc subjected to global magnetic fields by AMF and

magnetic field generated by external bus bar or

nearboring phase is shown in Fig.1.

Fig.1 3D physical model of deflection behavior of vacuum arc

subjected to global magnetic fields by AMF and magnetic field

generated by external bus bar or nearboring phases

In Fig.1, Bz means AMF generated by the cup-shaped

electrode system, Bxext and Byext mean magnetic fields

generated by the external bus bar or neighboring phases,

whose directions is perpendicular to arc column, which is

called TMF. AMF distribution in this paper is shown in

Fig.2, this AMF distribtion is generated by the coil behind

contact plate, and calculated by Ansys software. AMF

distribution is from midway(z = 5mm), the axial gradient

of AMF is not considered. Electrode diameter is 41mm,

gap distance is 10mm, arc current is 25kA. Copper mate-

21st

International Symposium on Plasma Chemistry (ISPC 21) Sunday 4 August – Friday 9 August 2013

Cairns Convention Centre, Queensland, Australia

rial is selected in the simulation. In the simulation, exter-

nal TMFs include two components, y direction and –x

direction. External TMFs are considered as unifrom dis-

tribution in arc column.

Fig.2 AMF distribution between anode and cathode (z = 5mm)

2.2 Mathematical model

Based on two-fluid theory and Maxwell equations,

the mathematical model of VA subjected to global mag-

netic field can be obtained:

0i yi x i z

n un u n u

x y z (1)

( )

( )

x x xi i x y z y z z y yext

i i e ei x

u u um n u u u j B j B B

x y z

n kT n kT

x x

(2)

( )

( )

y y y

i i x y z z x xext x z

i i e ei y

u u um n u u u j B B j B

x y z

n kT n kT

y y

(3)

( ) ( )

( )

z z zi i x y z x y yext y x xext

i i e ei z

u u um n u u u j B B j B B

x y z

n kT n kT

z z

(4)

( ( )) ( ) ( )

3( )

i i i i i i i i

e e ei ee i T e e

i

u m n E p T u Zen u E

km n n eT T u j g n k T

m

(5)

2 2 2

3( ( )) ( )

2

3( )

ee e e e e e

x y ze e eie i radiation

i

kTv n m E p j T

e

j j jkm nT T P

m

(6)

( )ej en u v (7)

0

1( ) ( )

( )

x x y yext y x xext

z x xext x z

B v B B v B By

v B B v Bz

(8)

0

1( )

( ) ( )

y y z z y yext

x y yext y x xext

B v B v B Bz

v B B v B Bx

(9)

0

0

0

1( )

1( )

1( )

y zx

xzy

yxz

B Bj

z y

BBj

x z

BBj

y x

(10)

Here, ni, ne are ion and electron number density, respec-

tively. ux, uy, and uz are ion velocities along x, y, and z

directions, respectively. vx, vy, and vz are electron veloci-

ties along x, y, and z directions, respectively. mi is the

copper ion mass, jx, jy, and jz are current density along x, y,

and z directions, respectively. Bx, By, and Bz are magnetic

fields along x, y, and z directions, respectively,which are

generated by AMFs electrode system and vacuum arc.

Bxext, Byext, are external magnetic fields along x and y di-

rections, respectively, which are generated by external bus

bar and neighboring phases. k is Boltzmann constant, Ti

and Te are ion and electron temperature. pi and pe are ion

and electron pressure; ki and ke are ion and electron ther-

mal conductivity. μ0 is vacuum permittivity. μi is ion vis-

cosity coefficient. Ei, Ee are total energy of ion and elec-

tron, respectively. u is ion velocity vector; and νei is

electron-ion collision frequency. v is electron velocity

vector; σ is electrical conductivity; gT is a coefficient. is

current density vector; e is electron charge. i is viscos-

ity stress tensor. Pradiation means plasma radiation, in this

paper, we consider vacuum arc radiation by net emmision

coefficient (NEC) method.

3. Simulation results and discussions

3.1 Ion velocityof vacuum arc

The simulation results of vacuum arc deflection behav-

ior along xoy, xoz or the center between xoy and xoz

cross-section are shown in Fig.3. From Fig.3, it can be

seen that the deflection position of vacuum arc center is

mainly influenced by the external TMF. The deflection

position will be incresed with the increase of external

TMF. The Mach number distribution is very similar to

plasma velocity distribution. So, Mach number distribu-

tion is not listed in the simulation results.

Fig. 3 Contours of plasma velocity of vacuum arc subjected to

global magnetic fields along some cross-sections plane (a) Bxext

= Byext = 0; (b) Bxext = -20mT, Byext = 0mT; (c) Bxext = 0mT, Byext =

20mT; (d) Bxext = -20mT, Byext = 20mT

21st

International Symposium on Plasma Chemistry (ISPC 21) Sunday 4 August – Friday 9 August 2013

Cairns Convention Centre, Queensland, Australia

Fig. 4 Contours of plasma velocity of vacuum arc subjected to

global magnetic fields on z = 5mm plane (a) Bxext = Byext = 0; (b)

Bxext = -20mT, Byext = 0mT; (c) Bxext = 0mT, Byext = 20mT; (d)

Bxext = -20mT, Byext = 20mT

3.2 Plasma pressure

Plasma pressure distribution along xoy, xoz or the center

between xoy and xoz cross-section are shown in Fig.5.

The plasma pressure distribution along z = 5mm plane is

shown in Fig.6. From Fig.5 and Fig.6, it can be seen that

the vacuum arc plasma will be deflected by the Ampere

force generated by the action of TMF arc current. From

Fig.6. (b), it can be seen that when TMF along negative

direction of x Bxext exists, the arc center will be deflected

along positive direction of y. In Fig.6. (c), it can be seen

that when TMF along positive direction of y Byext exists,

the arc center will be deflected along positive direction of

x. When the two TMFs with the same intensity (20mT)

are acted on vacuum arc, the arc center will move toward

the center between xoy and xoz cross-section, that is to

say, the angle between x axis and deflection center is 45

degree. If the TMF intensity along x and y direction is

different, this angle should be changed.

Fig. 5 Contours of plasma pressure of vacuum arc subjected to

global magnetic fields along some cross-sections plane (a) Bxext

= Byext = 0; (b) Bxext = -20mT, Byext = 0mT; (c) Bxext = 0mT, Byext =

20mT; (d) Bxext = -20mT, Byext = 20mT

Fig. 6 Plasma pressure contours of vacuum arc subjected to

global magnetic fields on z = 5mm plane (a) Bxext = Byext = 0; (b)

Bxext = -20mT, Byext = 0mT; (c) Bxext = 0mT, Byext = 20mT; (d)

Bxext = -20mT, Byext = 20mT

3.3 Ion and electron temperature

Ion temperature along xoy, xoz or the center between

xoy and xoz cross-section are shown in Fig.7. The ion and

electron temperature distribution along z = 5mm plane are

shown in Fig.8 and Fig.9, respectively. In Fig.7, (a), TMF

is not considered, also, in this case, arc radiation is not

considered in the model, that is why the ion temperature

in (a) is higher than (b),(c) and (d). Also, it can be seen

that when external TMF is added on arc column, ion and

electron temperature also are deflected.

Fig. 7 Contours of ion temperature of vacuum arc subjected to

global magnetic fields along some cross-sections plane (a) Bxext

= Byext = 0; (b) Bxext = -20mT, Byext = 0mT; (c) Bxext = 0mT, Byext =

20mT; (d) Bxext = -20mT, Byext = 20mT

21st

International Symposium on Plasma Chemistry (ISPC 21) Sunday 4 August – Friday 9 August 2013

Cairns Convention Centre, Queensland, Australia

Fig. 8 Contours of ion temperature of vacuum arc subjected to

glogal magnetic fields on z = 5mm plane (a) Bxext = Byext = 0; (b)

Bxext = -20mT, Byext = 0mT; (c) Bxext = 0mT, Byext = 20mT; (d)

Bxext = -20mT, Byext =20mT (r is the direction of 45°from x to y

coordinate axis)

Fig. 9 Contours of electron temperature of vacuum arc subjected

to global magnetic fields on z = 5mm plane (a) Bxext = Byext = 0;

(b) Bxext = -20mT, Byext = 0mT; (c) Bxext = 0mT, Byext = 20mT; (d)

Bxext = -20mT, Byext = 20mT

4. Conclusions

In this paper, the deflection effect of VAs subjected

to global magnetic field, including AMFs and TMF along

different directions is modeled and simulated. Simulation

results show that external TMF will lead to deflection of

VA, and plasma parameters also are deflected. The

delfected direction of plasma parameters in vacuum arc

obeys left hand rule. When external TMF is along minus x

direction, arc plasma deflects toward y direction. And

when external TMF is along y direction, arc plasma de-

flects toward x direction. When the above composite

TMFs is added on arc column, the vacuum arc is deflect-

ed toward center line between x and y positive directions.

5. References

[1] R. L. Boxman, P. J. Martin, and D. M. Sanders,

Handbook of Vacuum Arc Science and Technology.

Park Ridge, NJ: Noyes, 1995.

[2] S. Yanabu, S. Souma, T. Tamagava, S. Yamashita,

and T. Tsutsumi, Proc. Inst. Elect. Eng., 126, 313

(1979).

[3] I. N. Poluyanova and V. A. Bugayov, 25th

ISDEIV,

Russia, Tomsk, 224 (2012).

[4] M. Keidar, M. B. Schulman, and E. D. Taylor, IEEE

Trans. Plasma Sci., 32, 783(2004).

[5] E. Schade and D. L. Shmelev, IEEE Trans. on Plasma

Sci., 31, 890 (2003).

[6] N. Wenzel, S. Kosse, A. Lawall, R. Renz and W.

Hartmann, 25th

ISDEIV, Tomsk, Russia, 321 (2012).

[7] Y. I. Londer and K. N. Ulyanov, IEEE Trans. Plasma.

Sci., 35, 897 (2007).

[8] L. Wang, S. Jia, Z. Shi and M. Rong, J. Phys. D: Appl.

Phys., 38, 1034 (2005).

[9] L. Wang, S. Jia, Z. Shi, and M. Rong, J. Appl. Phys.,

100, 113304 (2006).

[10] L. Wang, S. Jia, L. Zhang, D. Yang, Z. Shi, F. Gentils,

B. Jusselin, J. Appl. Phys., 103, 063301 (2008).

[11] L. Wang, S. Jia, K. Liu, L. Wang, Z. Shi, Physics of

Plasmas, 16, 103502 (2009).

[12] L. Wang, S. Jia, X. Zhou, H. Wang, Z. Shi, Physics of

Plasmas, 19, 013507 (2012).

6. Acknowledgements

This work is supported by National Natural Science

Foundation of China (50907045).