The Peculiarities of Transient Recovery Voltage in Presence of Post Arc Current in Vacuum Circuit Breakers

XXIVth Int. Symp. on Discharges and Electrical Insulation in Vacuum - Braunschweig - 1 The Peculiarities of Transient Recovery Voltage in Presence of Post Arc Current in Vacuum Circuit Breakers Amir Hayati Soloot 1, Edris Agheb 1, Jouya Jadidian, Hans Kristian Hoidalen 1 1 Department of Electrical Power Eng., Norwegian Uni. of Sci. and Tech. (NTNU), O.S. Bragstadspl. F, Trondheim N-7491, Norway. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology Cambridge, MA 14, USA Abstract- The post arc phase is a critical part in the current interruption process of Vacuum Circuit Breakers (VCB). During this step, the dielectric strength of VCB has to be recovered. In order to improve the performance of VCB, investigation of Post Arc Current (PAC) in the presence of Transient Recovery Voltage (TRV) is presented in this paper. The equations of ion sheath length and PAC are solved together with network equations, which describe the TRV and PAC interrelation. In order to solve nonlinear ion sheath equations simultaneously with PAC and TRV equations, a Gauss-Seidel method is applied. The simulation results for PAC and TRV properly are in an acceptable accordance with the previous studies and available experimental records. The simulation results indicate that in the case of Short Circuit (SC) current interruption, there is no considerable influence between PAC and TRV. In the case of capacitive current interruption, TRV waveform in the first microseconds is highly influenced by the PAC. The results specifically demonstrate that the impact of physical parameters of VCB like diffusion time constant and initial PAC is much more significant than that of circuit parameters like capacitance of capacitor bank and equivalent network inductance. I. INTRODUCTION Current interruption in Vacuum Circuit Breaker), is strongly related - especially in the initial several microseconds - to the capability of the interrupter to change its conductivity from very large (in the arcing phase) to almost zero (in the isolating position) in an extremely short time period [1]. When the metal vapor arc in VCB extinguishes, it leaves metal ions and electrons in the vacuum gap, making a current flow after Current Zero (CZ), known as Post Arc Current (PAC) possible. In VCBs, the characteristics of PACs are particularly distinctive. Since it might indicate the performance of the breaker, it has been investigated thoroughly in previous studies [1]-[11].In this way, it would be greatly of interest to derive characteristics (from measurements) of PAC having the potential to indicate the "quality" of the interruption [1]. The role of metal vapor, gas and molten electrode surfaces []-[3], cathode material [4]-[5], plasma density [6]-[9], interrupted current amplitude [9], and arcing time [1], [9], [11] is discussed in relation to post arc phenomenon of VCBs. The impact of PAC on breakdown strength after current zero is discussed and evaluated in [1]. Since the VCBs are operated for various applications like capacitive switching [1] and the switching of high voltage high power inductive motors [13], the investigation of post arc phenomenon for these applications are of vital importance. In this paper, the impact of PAC on the form and amplitude of Transient Recovery Voltage (TRV) for different cases is investigated with applying two different calculation methods. The numerical method applied in both methods is based on Gauss-Seidel method. The calculated TRV and PAC from proposed methods are verified by measurement results from [14]. II. POST ARC MODELING The theory of an ion sheath growing in front of post arc cathode (former anode) is often used to model the PAC. This theory relates the sheath thickness, PAC, and the TRV, by means of Child s law, the Ion-Matrix model, or the Continuous Transition model of Andrews and Varey [15]-[17]. Although these models are based on assumptions that do not always apply to the situation after a VCB short-circuit interruption, they can be used for low value PAC assessments [18]. The velocity of the sheath edge usually lies somewhere between child's law and ion matrix model, which is known as continuous transition model [17]. Continuous transition model is based on the following assumptions [17]: 1. There are no collisions and ionization inside the sheath.. There is no secondary emission or ion reflection at the new cathode. 3. It is supposed that no electron exists in the sheath. These assumptions are taken into account in this paper and simulation results are compared and verified with [14]. Nevertheless, the consideration of the 978-1-444-8365-5/1/$6. 1 IEEE

production of ions via ionization and the effect of secondary electron emissions is analytically investigated in [19] and resulted in describing the PAC in more details. The continuous transition model has analytical explanation for one dimensional sheath expansion in presence of TRV [14], [17]: 3 4ε ( ) ( ) = U t u t 3u( l( + 1 + 1 9eZN( U( U( U i ( ( vi + ) (1) M dl( = () e dt The sheath length (l() in (1) is related to TRV (u() and the time variation of sheath length influences on U ( in (). Because copper vapor was inserted in the gap before CZ, the mass of ions (M i ) is taken 1.6 1-5 kg which equals to copper ions [14]. The value of ion velocity at sheath edge (v i ) is considered constant and independent to sheath location. The amount of v i for simulations in this paper and other parameters in (1) and () are mentioned in table I. In (1), ion density at the sheath edge is expressed with N(. Whereas the ion density is affected by the location of the sheath between cathode and anode and the plasma diffuses due to the pressure gradient, the dependency of the ion density with time is expressed with (3) 4 I l () t i gap Nt ( ) = ( Amp. 1)exp( t/ τ ). π D Zev + (3) Parameters in (3) and their values are defined in table I. Amp and τ can be adjusted to match the experimental results as long as it has some physical justification. The PAC consists of the flow of ions into the sheath in front of the new cathode and the sheath development toward the new anode. Hence, the PAC is defined as, π D ezn ( dl ( I ( = ( vi + ) (4) 4 dt Due to the inverse direction of the PAC in comparison with current before CZ, the minus is inserted in (4). Symbol TABLE 1. APPLIED PROPERTIES IN (1)-(5) [14] Description Parameter Value D PA equivalent diameter 1(mm) v i Ion velocity at the sheath edge 5(m/s) gap Inter electrode distance 1 (mm) τ Diffusion time constant 1 (µs) Amp Ion density distribution coefficient 5 I Initial PAC -(A) Z ion charge 1.8 e Electron charge 1.6 1-19 A. Simultaneous PAC and TRV calculation method In this method, (1)-(4) as PAC equations and network equation considered as TRV equation are numerically coded based on Gauss-Seidel method and TRV and PAC are calculated for each time step with sufficient iterations. The basic circuit which is used for the simultaneous PAC and TRV calculation method is illustrated in Fig. 1. This circuit is considered for short circuit interruption and the values of the network parameters and the RC branch are taken from [14] and shown in table II. TABLE II. Applied Properties in Fig. (1) [14] Symbol Description Parameter Value R Equivalent network resistance.1(ω) L Equivalent network inductance (mh) R p Resistance of RC branch (Ω) C p Capacitance of RC branch 85 (nf) V max Maximum phase voltage 33(kV) f Network frequency 5(Hz) III. PAC AND TRV NUMERICAL CALCULATION METHODS (1)- (4) consists of five unknowns l(, U (, u(, N( and I( while there are four equations. The fifth one is the relation between PAC (I() and TRV (u() which depends on the network and load type. In order to calculate PAC and TRV for different kind of load interruptions, (1)-(4) should be solved numerically with a network equation. For these reason, two methods are proposed. Fig. 1. The considered circuit for PAC and TRV computation in SC interruption [14], [],[1].

Analyzing the circuit in Fig. 1 with Laplace transformation, we achieve (5) which relates TRV to PAC and system voltage. ( RpCps+ 1)[ Esys( s) ( R+ Ls) I( s)] U( s) = (5) LC s + ( R + R ) C s + 1 p p p Value of parameters in (5) are defined and given in table II. In the simultaneous method, numerical techniques such as averaging in the definition of first and second derivatives are applied to support convergence of solutions by avoiding sharp numerical oscillations in results. Equations (6) and (7) show the applied definition of first and second derivatives of I( respectively. Ii ( + 1) Ii ( 1) I ( i+ 1) = (6) dt Ii ( + 1) Ii ( 1) + Ii ( 3) I ( i+ 1) = (7) 4dt The PAC computed via this method is compared with the measurement results PAC in [14]. As it can be observed from Fig., there is a good agreement between PAC from simultaneous method and PAC from measurement in [14]. Besides, the comparison of TRV from simultaneous method and measurements [14] is depicted in Fig. 3 and a good match between proposed method and measurement results is obtained. Since the verification of simultaneous PAC and TRV numerical method is done with measurement results, we can apply this numerical technique for capacitive current interruption. In case of inductive load interruption, the interrupted current is in the order of some ten Ampere or hundred Ampere. Thus, PAC rarely happens in inductive switching. Nevertheless, the effect of network parameters and RC branch on TRV characteristics for inductive load and short circuit interruption is investigated deeply in previous work []. PAC(A) -.5-1 -1.5 PAC calculated from simultaneous method PAC in [14] - 4 6 8 1 1 Fig.. The verification of the PAC calculated from simultaneous method with measured PAC in [14] for SC interruption. TRV (kv) 1-1 - -3-4 TRV calculated from simultaneous method TRV from [14] -5 4 6 8 1 Fig. 3. The verification of the TRV calculated from simultaneous method with TRV in [14] for SC interruption. As mentioned in introduction, PAC amplitude is function of amplitude of interrupted current, current interruption mechanism (Axial Magnetic Field or Radial Magnetic Field) as well as arcing time. Increasing arcing time results in higher PAC. The importance of arcing time can be identified from the measurement results in [1]. It was there shown that although the typical value for PAC in short circuit interruption is some Amperes, PAC with 1- A occurs for short circuit interruption (5-35 ka) for arcing time > 7ms. Furthermore, it is likely to witness PAC with 1- A for interruption of nominal current and capacitor banks for large arcing time. B. Sequential PAC and TRV calculation method The second method to calculate PAC and TRV is based on an iterative process considering an initial TRV found from (5) assuming PAC equal to zero. Secondly, PAC is calculated with this initial TRV and by means of (1)-(4). TRV is going to be modified with this PAC as the third step. This sequential PAC and TRV calculation continues until the error of PAC and TRV in two adjacent iterations becomes lower than a convergance criterion. As discussed in [3], in case of capacitive switching, the initial TRV is considered as (8), TRV 1 ( = Vmax [cos( ω 1] (8) Numerical calculation of (1)-(4) considering (8) results in PAC with dashed curve in Fig. 4. PAC has a decreasing exponential waveform. The initial value (I ) is mentioned in Table I. The time constant of PAC is the same as diffusion time constant (τ) due to weak effect of capacitive TRV on sheath velocity (dl/d and the dominant effect of ion diffusion, described in (4), on PAC. In second step, TRV is computed by considering the calculated PAC in previous step. Due to aforementioned reason, an analytical exponential expression is defined for PAC as, I PA ( = I exp( t / τ ) (9) It can be assumed that a current source parallel with

VCB is the model of PAC. Since PAC is in the reverse direction of vacuum arc before CZ, current source is paralleled inversely (Fig. 5). Time (ms).5 5 1 15 1.4 -.5 TRV after CZ -1 PAC(A) -.4 -.8 PAC with TRV1(=Vmax[cos(w-1] PAC with TRV( TRV after CZ(kV) -.1 -.15 -. -.5 - -3-4 -5 TRV(kV) -1. -.3 -.35-6 -7-1.6-4 6 8 1 Fig. 4. Comparison of PACs calculated from TRV 1 (, shown in dashed line, and TRV(, shown in solid line. -.4-8 1 3 4 5 6 7 8 9 1 11 1 13 14 15 Fig. 6. TRV, illustrated in dotted line, for the first 15 µs after CZ which has inappreciable effect in the waveform of TRV in the range of 15 ms (solid line) []-[1]. Network Impedance AC current source (PAC model) 5-5 -1 AC Voltage Source Vacuum Circuit Breaker Capacitor Bank -15 - TRV in simultaneous method TRV in sequential method -5-3 -35 Fig. 5. Modeling PAC with a current source parallel to VCB []-[1]. -4 5 1 15 5 3 35 4 Now, the modified TRV can be analytically calculated by applying KVL in the network shown in Fig. 5 and considering current source described in (9). The modified TRV is defined as TRV ( in (1). t L τ Iτ τ TRV() t = Vmaxcos( ω + I( R ) e + Vmax (1) τ C C TRV is computed using the network values in table II and is depicted with dotted line in Fig. 6. The initial TRV value equals to.4 kv which is not recognizable in the range of millisecond and the form of TRV 1 is dominant in this range. In the third step, the PAC is calculated with TRV to find out whether there are modifications in PAC. The comparison of PAC derived from TRV with the one calculated with TRV 1 demonstrates a good agreement and convergence (Fig. 4). TRV for capacitive interruption is also performed by means of simultaneous method and is compared with TRV from in Fig. 7. Besides, TRV is computed with Alternative Transient Program (ATP) in Fig. 8. ATP is an Electromagnetic Transient Program (EMTP), which is based on step by step method [4]. Fig. 7. TRV calculated by simultaneous method, illustrated in dotted line, comparing to TRV []-][1]. The dotted line in Fig. 8 is TRV obtained from sequential method and the solid line is the result of ATP software. There is a good agreement and proves the accuracy of methods proposed in this paper. 5-5 -1-15 - -5-3 -35-4 -45 TRV calculated in ATP TRV from sequential method 1 3 4 5 6 7 8 9 1 Fig. 8. TRV simulated by ATP, illustrated in solid line, comparing to TRV in dotted line []-[1]. Although the sequential method matches perfectly

with ATP simulations due to the advantage of its analytical part, it encounters some limitations when we intend to consider the impacts of ionization and secondary electron emission on PAC. The simultaneous method brings better results in this case and due to aforementioned numerical techniques, the risk of PAC divergence is lower []-[1]. IV. PARAMETERS EFFECT ON CAPACITIVE TRV CHARACTERISTICS In this section, the impact of physical parameters and network parameters on TRV waveform is discussed in detail. Main physical parameters are diffusion time constant (τ) and initial PAC (I ).The prominent network parameter is the capacitance of CB. The impact of capacitance increase is a slight decrease of positive amplitude of TRV which is explainable by analyzing (1) and is depicted in Fig. 9. The capacitance of CB approximately has no effect on TRV value in the first ten microseconds. It is observable that a % increment in capacitance value from.5 nf to.6 nf causes approximately % decrease in positive amplitude of TRV. 5 these two physical parameters and result in both positive and negative TRV amplitude increment (Fig. 11). Both the negative and positive peaks of TRV are proportional to I. As mentioned for network parameters, the impact on negative value is more remarkable than on positive one. 1-1 - -3-4 -5-6 -7 4 6 8 1 1 14 16 18 1 L=1 mh L= mh L=3 mh Fig. 1. The Effect of equivalent network inductance on TRV waveform []-[1]. -1-5 -1-15 - C=.5 uf C=.6 uf C=.7 uf - -3-4 -5-6 I= A I=3 A I=4 A -5-7 -3-8 -35-4 4 6 8 1 1 14 16 18 Time (microsecond) Fig. 9. The Effect of capacitance value of CB on TRV waveform []-[1]. The other network parameter which depends on the characteristics of network is the equivalent network inductance which its modifications affect on the exponential amplitude of (1). The initial value of TRV is proportional to the inductance as shown in Fig. 1 while the positive amplitude is not influenced. Besides, 1% increment in equivalent inductance value results in 1% rise of TRV negative amplitude. Consequently TRV amplitude has the same sensitivity to these two parameters. But, the higher value of negative part of TRV in comparison to positive part causes more consideration in negative part. Initial PAC value (I ) and diffusion time constant (τ) are the two physical parameters which have influence on the TRV waveform in the first ten microseconds in capacitive switching by VCB. According to (4), I is directly related to initial ion density and v i. It means that the rises in I are due to -9 4 6 8 1 1 14 16 18 Fig. 11. The Effect of initial PAC on TRV waveform []-[1]. The effect of τ is illustrated in Fig. 11. Since τ exists in both exponential term and I τ/c term in (1), it has diverse effects on negative part (t<4τ) and positive part (t>4τ) of TRV. According to (11), τ directly affects the positive amplitude of TRV and has inverse impact on initial negative TRV amplitude. 1 5-5 -1-15 - -5-3 -35 tav=1 us tav=15 us tav= us tav=5 us -4 4 6 8 1 1 14 16 18 Time (microsecond) Fig. 1. The Effect of diffusion time constant on TRV waveform []-[1].

V. ONCLUSION In this paper, two methods have been introduced to calculate PAC and TRV for different load interruptions with Vacuum circuit breakers. The first method is simultaneous TRV and PAC calculation method. The second one is sequential TRV and PAC calculation method which is a combined numerical and analytical method. Since the impacts of ionization and secondary electron emission on PAC is not assumed in this paper, the sequential method performs better results in capacitive current interruption rather than simultaneous method. The TRV waveform from sequential method matches perfectly with ATP simulations due to the advantage of analytical part in the sequential method. While, the consideration of these two phenomena results in some limitations for sequential method and the simultaneous method is more effective in this case and due to aforementioned numerical techniques, the risk of PAC divergence is lower. The calculated PAC for the cases of capacitive, inductive and short circuit current interruption is not influenced by TRV and RRRV and is in the form of decreasing exponential with the time constant same as ion diffusion time constant. Although RRRV is in the order of 1 kv/µs in the case of short circuit current interruption, the sheath velocity is just achieved in the order of 1 m/s and is not comparable to v i. Therefore, PAC is completely controlled with v i and N( is not affected by RRRV and load type. PAC has no considerable impact on TRV characteristics in short circuit and inductive load interruption while, TRV waveform in capacitive current interruption is affected by PAC especially in the first ten microseconds. Physical parameters of VCB such as diffusion time constant (τ) and initial PAC (I ) have more announced influence on TRV compared with the network parameters like circuit breaker capacitance and equivalent network inductance. 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