11.1

Calculation of the Short-time Withstand Current forAir Circuit Breaker

Honggang Xiang, Degui Chen, Xingwen Li, Liang Ji, Weixiong TongState Key Laboratory of Electrical Insulation and Power Equipment

Xi'an Jiaotong UniversityXi'an, China

dgchengmail.xjtu.edu.cn

Abstract-In the optimization design of contact system for the aircircuit breaker (ACB), it is important to calculate the short-timewithstand current. Introducing the contact bridges to describecontact spots between movable and fixed contacts, transientanalysis is carried out by coupling electromagnetic field andthermal field to parallel contact systems, where nonlinear offerromagnetic splitter plates and properties of conduct materialvarying with temperature are under consideration. In each timestep of calculation, the cross-sectional areas of the contact bridgesare changed with the contact forces by Holm formula. Theproposed method could be used to analyze the short-timewithstand current of ACB.

Keywords- short-time withstand current; ACB; contact bridge

I. INTRODUCTION

According to IEC standard of 60947, the Air CircuitBreaker (ACB) belongs to B type in low voltage circuitbreakers, and the short-time withstand current (ICW) must besatisfied due to selective protection. ICW represents the abilityof ACB enduring mechanical effects and thermal effects ofshort-circuit current. It is important and significant to calcualteIJW ofACB.Many works have been carried out in the field of electric

contacts phenomena. Holm studied the relationship betweenradius of contact spots and contact force[1]. In literature [2],using Holm formula to calculate the radius of contact spot andtheoretical formula to describe the relationship betweenelectromagnetic force and current, the influence of vapourpressure on the dynamics of repulsion by contact blow-off wasinvestigated. In literature [3], numerical analysis wasperformed to study the heating transient of electric contactsunder short circuit conditions. Belbel investigated theelectrodynamic force experimentally [4], on the other hand, Itoand Kawase calculated the electrodynamic forces in stationaryelectric contacts and low voltage circuit breakers using 3-Dfinite element method [5] [6]. In our previous paper, using thecontact bridge to describe contact spots between contacts, theinfluences of the configuration of the current-carryingconductors on the electromagnetic repulsion force wereinvestigated [7].

In this paper, a new type of double-breakers ACB whose IJWis much higher than traditional single-breaker ACB is studied,and its conduct loop can make over compensation of the

electromagnetic repulsion force. In the calculation model, thecylindrical contact bridges are introduced to describe thedispersive contact spots between movable and fixed contacts.Usually, in order to reduce electromagnetic repulsion force,the configuration of parallel contacts is applied to ACB, so theHolm force included in electromagnetic repulsion force can'tbe got directly by Holm formula because the current flowingthrough each parallel contact is unknown. By nonlinear 3-Dfinite element method, taking into account properties ofconductor material varying with temperature, the coupledtransient analysis of electromagnetic field and thermal field isdone for the calculation model. After each time step ofsolution, the cross-sectional areas of contact bridges arechanged with the electromagnetic repulsion force by Holmformula.

II. CALCULATION METHOD

A. Basic AssumptionsIt is known that the temperature variation of conductors in

ACB under short-circuit current is a very complexphenomenon, which involves the coupled interactions betweenthermal and electromagnetic processes. In order to simplifythe analysis, the following assumptions about contact bridgeare made:(1) The dispersive contact spots between the movable and

fixed contacts concentrate on the cylindrical contactbridge.

(2) By Holm formula, the cross-sectional area of contactbridge varies with the contact force.

Figure 1 shows the model of contact bridge. The length h ofcontact bridge has much influence on contact resistance. TableI shows the calculation value and the measurement value ofconduct loop resistance including contact resistance for ACB1and ACB2 with contact bridge built between contacts whenh=0.05mm. In the solution of the calculation model, h is set to0.05mm.

In Fig.2, a calculation model whose configurationassociated with the contact system of a double-breaker ACB isbuilt. Due to its symmetrical structure, only a quarter of themodel is constructed with xoz and yoz being the symmetricplanes. The contact system of this model is in closed positionas shown in Fig.2, the movable contact is fixed by the

1-4244-0838-5/07/$25.00 02007 IEEE 251

operation mechanism, and the contact springs are put on thefixed contacts which can be separated by electromagneticrepulsion force. The fixed contacts consist of total six piecesin parallel, No.1 and No.3 represent the most inner and themost outer fixed contact respectively, and No.2 represent thefixed contact between them. In the calculation model, theclamps are designed to connect fixed conductors and terminalby the clamp force of 1 OON instead of copper braid, and thecylindrical contact bridges are built in these connections aswell.

TABLE I. THE EXPERIMENTAL RESULTS AND CALCULATION RESULTS OFTHE CONDUCT LOOP RESISTANCE INCLUDING CONTACT RESISTANCE

h=0.05mm

ACB1

ACB2

Experimentalresult20pf32PQ

Calculationresult19.8p&33 Q

cont act

Fig.1 model of contact bridge: Top view and front view

movabi econductor

splitter

L fixed conductor

clirapsclamp force

t erminal

Fig. 2 Calculation model

B. Calculation ofShort-time Withstand CurrentIn the aspect of electric circuit, the short-circuit current

passing through ACB can be written as

i = NEI (sin (I1 OO)zt + gvf )-sin (Vv-f() e L )( I )

i: instantaneous value of short-circuit currentI: effective value of short-circuit currentql: phase angle of voltagey: phase angle difference between voltage and currentR: equivalent resistance ofnetworkL: equivalent inductance ofnetworkWith the electric-field intensity distribution of short-circuit

current, the electromagnetic equation can be written as

I= u(T)KVVv+aJ, fiVXA (2)((at)(2J: current density of the short-circuit currentv: conductivity of current-carrying conductorT: temperaturet: timeV: electric potential

A: magnetic vector potentialB: magnetic flux densityConsequently, the heat generation and electromagnetic

repulsion force due to short-circuit current can be obtained by1 j2 F JJXB dv (3)

a(T)Q. heat generation of short-circuit currentF: electromagnetic repulsion force acting on contactsAfter contact bridges built between contacts, the

electromagnetic repulsion force including Holm force andLorentz force can be combined to calculate in equation (3).

In the aspect of thermal analysis, the temperature rise ofcurrent-carrying conductors can be calculated with the heatgeneration calculated in equation (3) to be loaded as thethermal source, that is

dH=pcdT, a +V.q=Q (4)a9t

where H is the enthalpy of current-carrying conductors, q isheat flux through boundaries of the conductors, p is density ofconductor, c is specific heat. In the calculation model, the heattransfer between conductors and air is heat convection, and thefilm coefficient is assigned to 2.5 (W.m-2 * -1).The key for temperature rise calculation of current-carrying

conductors is the treatment of dispersive contact spots betweenthe movable and fixed contacts. According to assumption (1),a contact bridge is introduced to describe the contact spots inthis paper, where the cross-sectional area of the contact bridgerelates with the contact force.

According to assumption (2), the cross-sectional area ofcontact bridge can be determined by Holm formula:

2 F _F F F2 K -K p

~Hb F H F F A0 (5)Where the total contact force FK= F - F, FP is the force

of contact spring, F is the electromagnetic force includingHolm force and Lorentz force, d is the surface conditioningcoefficient, Hb is the Brinell hardness, Ao is the initial cross-sectional area of contact bridge when F=O.

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In the paper, the following assumption is made: at the end ofcalculation, if the highest temperature in the current carryingconductors is near to the melting temperature of contacts, theloaded short-circuit current I is considered as the short-timewithstand current ICW. That is

0< (Tm Tmax)1Tm<10%where Tmax is the highest temperature of current carryingconductor include the contact bridges, Tm is the meltingtemperature of contact material.

Summarily, the calculation process of temperature riseunder short-circuit current is concluded in Fig.3. According tothe IEC standard, one second is taken as the calculationduration.

start

t=O

el ect r onagnet c<f el d anal ysi s

2i F-fJJxB -dvQoa(T) A=~H

V CHb (T)therrral fi el d t=t+At

anal ysi s

t= econd N

IY

end

Fig. 3 Flow process of temperature rise calculation under short-circuit current

C. Boundary ConditionsFor the temperature rise calculation of current-carrying

conductors under the short-time withstand current, thetraditional way is to consider the heat generation of conductorsas an adiabatic process. However, the temperature rise of thecontact bridge is very high due to high current density, so theheat transfer between exterior surfaces of conductors and aircan't be ignored. In this paper, the following boundaryconditions are considered:

(1) The film coefficient of heat convection is 2.5 W-m.2. K-' and the environment temperature was 20°C .

(2) The heat flux through symmetric planes is zero.

III. CALCULATION RESULTS

During the calculation process, the load short-circuit currentis applied to electromagnetic field analysis as excitation source.In equation (1), according to IEC standard, qf-y should beassigned to -z/2 and RIL should be assigned to 20.4z if wetake I=80KA. Then, the instantaneous value of short-circuitcurrent isi = XI (- cos( OOzt) + e 204) (I=80KA) (8)

With the method presented in section II, the analysis of theshort-time withstand current calculation are carried out to themodel as shown in fig.2.

A. Calculation result ofcurrent density distributionFig.4 shows the current density distribution of conductors at

t=O.00 Is as I being 80KA. It is clear in Fig.5 that the currentdensity of contact bridge is much greater than other parts ofconductors due to constriction of current lines. In addition, theouter contact bridge has greater current density than innerbridge due to the influence of skin effect since dildt. 0.

ANSYS S v?

0X SO 4ZVECTOR

\|7, T IM=' 10 OE+O

at W-MF, ;i; m I=1 Z141+O4

Fig.~~~~~- loL- 4Curn dest ditibto of codcs at 0.0 s whe IS8OEKOAB.Calculation resul,_tof,Shea lgeeraton

, - ':/ .2 N - 2 5S~~~44E+ O Scl ,;R n<W; m 84?E+OS?

: *; *;". \ P; _ 4SD~21aE+ O S

_ 6XlE+O8

-397E+O0

shlgnet ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~~~~~~~~~~~~~~:,Ei c

Fig. 5 Joulrenhet generatiodistribution of contatbigeadfxeuotctsatm.OsweI8K

t 0.O0lswhenl8OKA~~~~~~~~~~~~~~~~~~4,5+

C. Cailculaition result ofhelatrumengnaticfn cBheaouse thea curenertifowingibtonithruheac contactb idgs

adifeet,e thxed eletctromagnethicsanforc acting on each fIxbedn

contact hasdiffeaeren peakevealuaendraphasetanglne. rdg u

to~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. higher curn desiyANSYS 4SvAPR593Ea08

_ _ ELESI~~~~~~~~~~~~~~~~-53ENT S 0L8 IO_ SUBP_~~~~~~~~~~~~~~~~~~~~~,'1 E0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-7 SdHN^E108

and llth fie cotat at the intn of 0. swit I ben80K is shw in Fil5 It i__scla tha the outer-conac

l l l l l l l -1_ ~~~~~~~~A SYS 25-BUFE| | | | | | | __ _~~~~~~~AP 161111120__ 44l l l l l l l ~~~~~~~~~~15_ ZllE+O

0 0 0 i t 0 0 _ _ y42~~~~EEMEN SE+OLUIOl l l l l l l ~~~~~~~~~~STGEP=10 0 2 0 0 0 0 : ~~~~~~~UB 10Eg| | | | | | | ~~~~~~~~T ME _1 OE 0

| | | | | | l ~~~~~~~~~SM \= I-;1l90E+0O

! ! ! ! ! ! ! 3 s. , s :~~~~~~~XV -.448

Fig. 5 Joule heat geeration distributio of contact bridge ndfixVd=contacts at=0.00~~~~~~~~~~~~~~~~~~~2 ls wen I80KC. Calculation result ofelectromagneticforc2e 3

Because the urrent flowig through eah contact5 idifferent,~~ ~~~~~~~~~Ytheetrmgntc oceacig neahfie

contacts has different peak value and phase angle.0526

253

Figure 6 (a) and (b) show the current and electromagneticforce variations with t acting on no.1-no.3 fixed contacts,respectively. It demonstrates that the current flowing throughNo.3 contact and the corresponding electromagnetic forceacting on the No.3 contact are obviously greater than force ofthe other two contacts. In addition, the current phase angle ofNo.3 is ahead of the others. The negative value ofelectromagnetic repulsion forces indicates that the forcedirections are the same as direction of FI7, which means thatthe Lorentz force produced by conductor loop makes overcompensation to Holm force. To No.3 fixed contact, themaximum electromagnetic repulsion force is 275N, so themaximum contact force is 48 IN (F =206N).

40 -

30 -

20 -

10 -

O -

-10 -

-20 -

-3u

No. I

No.2No.3

". ''

0 10 20 30 40t (ms)

(a) Current variation with time of the three fixed contacts

50 -

0-

-50 -

-100 -

-150 -

-200 -

-250 -

-300 -

No. I

No.2------- No.3

iv,\ \'1ft / "\ Ad

\\11/~~~~~~~~~~~~~~~~1k1 1,'I,

It should be noted that in this calculation model, we useAgW(50/50 wt%) as the material of movable contact andAgNi as the material of fixed contact, the meltingtemperatures 1200°C and 1100C, respectively. Therefore, theaverage melting temperature of contact bridge is set to 11 50°C.From the fig. 8, it shows that the maximum value of T

appears at the instant of 12ms, and T is beyond Tm from theinstant 0.01 is to 0.0 13s.

ai

20t (ms)

Fig. 7 Variations of the cross-sectional area of the contact bridge in the No.3fixed contact and temperature with time

E. Calculation result ofthermalfieldFigure 8 shows the temperature distribution of the contact

bridge and fixed contacts at the instant of 0.0 is when i reachesits maximum peak value of 172.8KA. The temperature of thecontact bridge in No.3 fixed contact is obviously higher thanthe else two contact bridges.

0 10 20 30 40

t (ms)

(b) Force variation with time of the three fixed contactsFig. 6 The current and electromagnetic repulsion forces variations with time Ion No.1-No.3 fixed contacts respectively when I=80KA

D. Variation ofcross-sectional area ofcontact bridge withthe contactforce

Figure 7 shows the variation of the cross-sectional area ofthe contact bridge within 0.04s in the No.3 fixed contact withthe contact force. T is the highest temperature of theconductors including contact bridge in each instant within0.04s. According to equation 5, the cross-sectional area A ofcontact bridge is proportional to contact force, as well as AIAo.

Fig. 8 The temperature distribution of contact bridge and fixed contactors atthe instant of 0.0 s when I=80KA

The solution is not completed until the instant of one second.Figure 9 shows the temperature distribution of conductorsincluding the contact bridges at the instant of one second. Thetemperature in the connection of clamps is much lower thanthe temperature in contact bridges between contacts due topassed half current.

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i l i l |

, S | | i | | | X l__L00 APR 26 aoowf | . l l C v ~~~~~~NODAL S OLUTIONE l | l l 6 g - _ ~~~~~SUB =1

TEMP a1AV)

Powe=Gr aphiC5EFACET-=JL

_~~~~~~~~~~ARa ls 45sm 2 1S 4g

3 1 2284. 945

I=~~~~~~1soslS56-504

-ewAlCB Stlld9 Th rza ll

Fig. 9 Temperature distribution of conductors include the contact bridges atthe instant of one second when I=80KA

IV. CONCLUSIONS AND DISCUSSIONS

(1) In the analyzed double-break ACB, the electromagneticforces acting on fixed contacts have the same direction asthe force of contact spring, it mains that the Lorentz forceproduced by conductor makes over compensation to theHolm force.

(2) Due to skin effect, current passing through the most outerfixed contact is the largest. Though the contact forceacting on the most outer fixed contact is larger than theother two fixed contacts, its temperature rise is the highest.

(3) It shows that the proposed method could be used toanalyze the short-time withstand current of ACB.

(4) In the following works, experiments will be carried out tocheck the calculation results, and phase transition ofcontact bridges will be under consideration further.

(5) In the paper, the criterion for short-time withstand currentof ACB is the maximum temperature of contact spot.However, the short-time withstand current has closerelationship with the duration of high temperature.Therefore, more reasonable criterion should beinvestigated in the future.

REFERENCES

[1] R. Holm: "Electric Contacts, 4th Edition, New York: Springer-Verlag,1967.

[2] M. Bizjak, S. Kharin, H. Nouri: "Influence of vapour pressure on thedynamics of repulsion by contact blow-off" , Proc. 48th IEEE HolmConf On Electrical Contacts, Zurich, Switzerland, 2002. 268-275.

[3] Oriano Bottauscio, Numerical analysis of heating Transient of ElectricContacts Under Short-circuit Conditions. IEEE Trans. on CHMT, 1993,No.5.

[4] E.M. Belbel, M. Lauraire: Behavior of Switching Arc in Low-VoltageLimiter Circuit Breaker, IEEE Trans. on Components, Hybrids, andManufacturing Technology, CHMT-8 No.1, 1985, pp.3-12

[5] S. Ito, Y. Kawase, H. Mory: 3-D Finite Element Analysis of RepulsionForce on Contact System in Low Voltage Circuit Breaker, IEEE Trans.on Magnetics, MAG-32, No 3, 1996, pp. 1677-1680

[6] Y. Kawase, H. Mory, S. Ito: 3-D Finite Element Analysis ofElectrodynamic Repulsion Forces in Stationary Electric Contacts Takinginto Account Asymmetric Shape (invited), IEEE Trans. on Magnetics,MAG-33, No 2, 1997, pp. 1994-1999

[7] X. Li, D. Chen: 3-D Finite Element Analysis and ExperimentalInvestigation of Electrodynamic Repulsion Force in Molded CaseCircuit Breakers, IEEE Trans. on Components and PackagingTechnologies, Vol. 28, No. 4, 2005, pp. 877-883

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