The Peculiarities of Transient Recovery Voltage in Presence Of

XXIVth Int. Symp. on Discharges and Electrical Insulation in Vacuum - Braunschweig - 2010 The Peculiarities of Transient Recovery Voltage in Presence of Post Arc Current in Vacuum Circuit Breakers Amir Hayati Soloot1, Edris Agheb1, Jouya Jadidian2, Hans Kristian Hoidalen1 1 Department of Electrical Power Eng., Norwegian Uni. of Sci. and Tech. (NTNU), O.S. Bragstadspl. 2F, Trondheim N-7491, Norway. 2 Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology Cambridge, MA 02142, USA

Abstract- The post arc phase is a critical part in the current interruption [1]. The role of metal vapor, gas and molten interruption process of Vacuum Circuit Breakers (VCB). electrode surfaces [2]-[3], cathode material [4]-[5], During this step, the dielectric strength of VCB has to be plasma density [6]-[9], interrupted current amplitude [9], recovered. In order to improve the performance of VCB, and arcing time [1], [9], [11] is discussed in relation to investigation of Post Arc Current (PAC) in the presence of post arc phenomenon of VCBs. The impact of PAC on Transient Recovery Voltage (TRV) is presented in this breakdown strength after current zero is discussed and paper. evaluated in [10]. The equations of ion sheath length and PAC are solved Since the VCBs are operated for various applications together with network equations, which describe the TRV like capacitive switching [12] and the switching of high and PAC interrelation. In order to solve nonlinear ion voltage high power inductive motors [13], the sheath equations simultaneously with PAC and TRV investigation of post arc phenomenon for these equations, a Gauss-Seidel method is applied. The applications are of vital importance. simulation results for PAC and TRV properly are in an In this paper, the impact of PAC on the form and acceptable accordance with the previous studies and amplitude of Transient Recovery Voltage (TRV) for available experimental records. different cases is investigated with applying two The simulation results indicate that in the case of Short different calculation methods. The numerical method Circuit (SC) current interruption, there is no considerable applied in both methods is based on Gauss-Seidel influence between PAC and TRV. In the case of capacitive method. The calculated TRV and PAC from proposed current interruption, TRV waveform in the first methods are verified by measurement results from [14]. microseconds is highly influenced by the PAC. The results specifically demonstrate that the impact of physical II. POST ARC MODELING parameters of VCB like diffusion time constant and initial The theory of an ion sheath growing in front of post PAC is much more significant than that of circuit arc cathode (former anode) is often used to model the parameters like capacitance of capacitor bank and PAC. This theory relates the sheath thickness, PAC, and equivalent network inductance. the TRV, by means of Child’s law, the Ion-Matrix model, or the Continuous Transition model of Andrews I. INTRODUCTION and Varey [15]-[17]. Although these models are based Current interruption in Vacuum Circuit Breaker), is on assumptions that do not always apply to the situation strongly related - especially in the initial several after a VCB short-circuit interruption, they can be used microseconds - to the capability of the interrupter to for low value PAC assessments [18]. change its conductivity from very large (in the arcing The velocity of the sheath edge usually lies phase) to almost zero (in the isolating position) in an somewhere between child's law and ion matrix model, extremely short time period [1]. which is known as continuous transition model [17]. When the metal vapor arc in VCB extinguishes, it Continuous transition model is based on the following leaves metal ions and electrons in the vacuum gap, assumptions [17]: making a current flow after Current Zero (CZ), known 1. There are no collisions and ionization inside the as Post Arc Current (PAC) possible. In VCBs, the sheath. characteristics of PACs are particularly distinctive. 2. There is no secondary emission or ion reflection at Since it might indicate the performance of the breaker, it the new cathode. has been investigated thoroughly in previous studies 3. It is supposed that no electron exists in the sheath. [1]-[11].In this way, it would be greatly of interest to These assumptions are taken into account in this derive characteristics (from measurements) of PAC paper and simulation results are compared and verified having the potential to indicate the "quality" of the with [14]. Nevertheless, the consideration of the

production of ions via ionization and the effect of TABLE 1. APPLIED PROPERTIES IN (1)-(5) [14] secondary electron emissions is analytically investigated in [19] and resulted in describing the PAC in more Parameter Symbol Description details. Value The continuous transition model has analytical explanation for one dimensional sheath expansion in D PA equivalent diameter 1(mm) presence of TRV [14], [17]: vi Ion velocity at the sheath edge 2250(m/s)  3  4ε U (t)  u(t) 2 3u(t) gap Inter electrode distance 10 (mm) l(t) = 0 0 1+  + −1 (1)    9eZN(t)  U0 (t)  U0 (t) τ Diffusion time constant 10 (µs)   Amp Ion density distribution coefficient 5

M i dl(t) 2 U (t) = (v + ) (2) I0 Initial PAC -2(A) 0 2e i dt ion charge Z 1.8 The sheath length (l(t)) in (1) is related to TRV e Electron charge 1.6×10-19 (u(t)) and the time variation of sheath length influences on U0(t) in (2). Because copper vapor was inserted in the gap before CZ, the mass of ions (Mi) is taken A. Simultaneous PAC and TRV calculation method 1.06×10-25 kg which equals to copper ions [14]. The In this method, (1)-(4) as PAC equations and network value of ion velocity at sheath edge (v ) is considered i equation considered as TRV equation are numerically constant and independent to sheath location. The coded based on Gauss-Seidel method and TRV and amount of v for simulations in this paper and other i PAC are calculated for each time step with sufficient parameters in (1) and (2) are mentioned in table I. iterations. The basic circuit which is used for the In (1), ion density at the sheath edge is expressed simultaneous PAC and TRV calculation method is with N(t). Whereas the ion density is affected by the illustrated in Fig. 1. location of the sheath between cathode and anode and This circuit is considered for short circuit interruption the plasma diffuses due to the pressure gradient, the and the values of the network parameters and the RC dependency of the ion density with time is expressed branch are taken from [14] and shown in table II. with (3) TABLE II. Applied Properties in Fig. (1) [14] 4I lt2 () Nt( )=+−0 ( Amp . 1)exp( t /τ ). (3) π 22 Symbol Description Parameter Value D Zevi gap

Parameters in (3) and their values are defined in table R Equivalent network resistance 0.1(Ω) I. Amp and τ can be adjusted to match the experimental results as long as it has some physical justification. L Equivalent network inductance 2(mH) The PAC consists of the flow of ions into the sheath Rp Resistance of RC branch 200(Ω) in front of the new cathode and the sheath development toward the new anode. Hence, the PAC is defined as, Cp Capacitance of RC branch 85 (nF)

2 πD eZN (t) dl (t) Vmax Maximum phase voltage 33(kV) I (t) = − (v + ) (4) 4 i dt f Network frequency 50(Hz) Due to the inverse direction of the PAC in comparison with current before CZ, the minus is inserted in (4).

III. PAC AND TRV NUMERICAL CALCULATION

METHODS

(1)- (4) consists of five unknowns l(t), U0(t), u(t), N(t) and I(t) while there are four equations. The fifth one is the relation between PAC (I(t)) and TRV (u(t)) 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, Fig. 1. The considered circuit for PAC and TRV computation in two methods are proposed. SC interruption [14], [20],[21].

Analyzing the circuit in Fig. 1 with Laplace 10 transformation, we achieve (5) which relates TRV to TRV calculated from simultaneous method PAC and system voltage. 0 TRV from [14] +−+ -10 (RppCs 1)[ E sys () s ( R LsIs )()] Us()= (5) 2 ++ + -20 LCppp s()1 R R C s TRV (kV) TRV Value of parameters in (5) are defined and given in -30 table II. In the simultaneous method, numerical -40 techniques such as averaging in the definition of first -50 and second derivatives are applied to support 0 20 40 60 80 100 convergence of solutions by avoiding sharp numerical Time(us) oscillations in results. Equations (6) and (7) show the applied definition of first and second derivatives of I(t) Fig. 3. The verification of the TRV calculated from simultaneous method with TRV in [14] for SC respectively. interruption. Ii(1)(1)+− Ii − Ii′(1)+= (6) As mentioned in introduction, PAC amplitude is 2dt function of amplitude of interrupted current, current +− −+ − interruption mechanism (Axial Magnetic Field or Radial ′′ +=Ii(1)2(1)(3) Ii Ii Magnetic Field) as well as arcing time. Ii(1) 2 (7) 4dt Increasing arcing time results in higher PAC. The The PAC computed via this method is compared importance of arcing time can be identified from the with the measurement results PAC in [14]. As it can measurement results in [1]. It was there shown that be observed from Fig. 2, there is a good agreement although the typical value for PAC in short circuit between PAC from simultaneous method and PAC from interruption is some Amperes, PAC with 10-20 A measurement in [14]. Besides, the comparison of TRV occurs for short circuit interruption (25-35 kA) for from simultaneous method and measurements [14] is arcing time > 7ms. Furthermore, it is likely to witness depicted in Fig. 3 and a good match between proposed PAC with 1-2 A for interruption of nominal current and method and measurement results is obtained. capacitor banks for large arcing time. Since the verification of simultaneous PAC and TRV B. Sequential PAC and TRV calculation method numerical method is done with measurement results, we can apply this numerical technique for capacitive The second method to calculate PAC and TRV is current interruption. based on an iterative process considering an initial TRV In case of inductive load interruption, the interrupted found from (5) assuming PAC equal to zero. Secondly, current is in the order of some ten Ampere or hundred PAC is calculated with this initial TRV and by means of Ampere. Thus, PAC rarely happens in inductive (1)-(4). TRV is going to be modified with this PAC as switching. Nevertheless, the effect of network the third step. This sequential PAC and TRV calculation parameters and RC branch on TRV characteristics for continues until the error of PAC and TRV in two inductive load and short circuit interruption is adjacent iterations becomes lower than a convergance investigated deeply in previous work [22]. criterion. As discussed in [23], in case of capacitive switching, the initial TRV is considered as (8), 0

PAC calculated from = ω − TRV 1 (t) Vmax [cos( t) 1] (8) -0.5 simultaneous method PAC in [14] Numerical calculation of (1)-(4) considering (8) results in PAC with dashed curve in Fig. 4. PAC has a -1 decreasing exponential waveform. The initial value (I0)

PAC(A) is mentioned in Table I. The time constant of PAC is the same as diffusion time constant (τ) due to weak effect of -1.5 capacitive TRV on sheath velocity (dl/dt) and the dominant effect of ion diffusion, described in (4), on

-2 PAC. In second step, TRV is computed by considering 0 20 40 60 80 100 120 the calculated PAC in previous step. Due to Time(us) aforementioned reason, an analytical exponential expression is defined for PAC as, Fig. 2. The verification of the PAC calculated from simultaneous method with measured PAC in [14] for SC interruption. = − τ I PA (t) I 0 exp( t / ) (9) It can be assumed that a current source parallel with

VCB is the model of PAC. Since PAC is in the reverse Time (ms) 0 5 10 15 direction of vacuum arc before CZ, current source is 0.05 10 paralleled inversely (Fig. 5). 0 0

0.4 -0.05 -10 TRV after CZ

-0.1 -20 0

-0.15 -30 ) kV -0.4 ( -0.2 -40 PAC with TRV1(t)=Vmax[cos(wt)-1] TRV

PAC with TRV2(t) CZ(kV) after TRV -0.8 -0.25 -50 PAC(A) -0.3 -60 -1.2 -0.35 -70

-1.6 -0.4 -80 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time(us) -2 0 20 40 60 80 100 Time(us) Fig. 6. TRV2, illustrated in dotted line, for the first 150 µs after CZ which has inappreciable effect in the waveform of Fig. 4. Comparison of PACs calculated from TRV1(t), shown in TRV in the range of 150 ms (solid line) [20]-[21]. dashed line, and TRV2(t), shown in solid line.

50 AC current source (PAC model) 0

Network Impedance -50

-100 TRV in simultaneous method Vacuum Circuit Breaker -150 TRV in sequential method

AC Voltage Source TRV(V) -200 Capacitor Bank -250

-300

-350

-400 Fig. 5. Modeling PAC with a current source parallel to VCB 0 5 10 15 20 25 30 35 40 Time(microsecond) [20]-[21].

Now, the modified TRV can be analytically Fig. 7. TRV calculated by simultaneous method, illustrated in dotted line, comparing to TRV [20]-][21]. calculated by applying KVL in the network shown in 2 Fig. 5 and considering current source described in (9). The dotted line in Fig. 8 is TRV2 obtained from The modified TRV is defined as TRV2(t) in (10). sequential method and the solid line is the result of ATP L τ − t I τ software. There is a good agreement and proves the TRV() t=+−−+− V cos (ω t ) I ( R ) eτ 0 V (10) 2max0τ CC max accuracy of methods proposed in this paper.

50 TRV2 is computed using the network values in table II and is depicted with dotted line in Fig. 6. The initial 0 -50 TRV2 value equals to 0.4 kV which is not recognizable in the range of millisecond and the form of TRV1 is -100 TRV calculated in ATP TRV from sequential method dominant in this range. -150 In the third step, the PAC is calculated with TRV2 to -200 TRV(V) find out whether there are modifications in PAC. The -250 comparison of PAC derived from TRV2 with the one -300 calculated with TRV1 demonstrates a good agreement -350 and convergence (Fig. 4). -400 TRV for capacitive interruption is also performed by -450 means of simultaneous method and is compared with 10 20 30 40 50 60 70 80 90 100 Time(microsecond) TRV2 from in Fig. 7. Besides, TRV is computed with Alternative Transient Program (ATP) in Fig. 8. ATP is Fig. 8. TRV simulated by ATP, illustrated in solid line, an Electromagnetic Transient Program (EMTP), which comparing to TRV2 in dotted line [20]-[21]. is based on step by step method [24]. Although the sequential method matches perfectly with ATP simulations due to the advantage of its these two physical parameters and result in both positive analytical part, it encounters some limitations when we and negative TRV amplitude increment (Fig. 11). intend to consider the impacts of ionization and Both the negative and positive peaks of TRV are secondary electron emission on PAC. The simultaneous proportional to I0. As mentioned for network parameters, method brings better results in this case and due to the impact on negative value is more remarkable than aforementioned numerical techniques, the risk of PAC on positive one. divergence is lower [20]-[21]. 100

0 IV. PARAMETERS EFFECT ON CAPACITIVE TRV -100 CHARACTERISTICS -200 In this section, the impact of physical parameters and -300 L=1 mH network parameters on TRV waveform is discussed in L=2 mH TRV(V) L=3 mH detail. Main physical parameters are diffusion time -400 constant (τ) and initial PAC (I0).The prominent network parameter is the capacitance of CB. The impact of -500 capacitance increase is a slight decrease of positive -600 amplitude of TRV which is explainable by analyzing -700 (10) and is depicted in Fig. 9. The capacitance of CB 0 20 40 60 80 100 120 140 160 180 200 Time(microsecond) approximately has no effect on TRV value in the first ten microseconds. It is observable that a 20% increment Fig. 10. The Effect of equivalent network inductance on TRV in capacitance value from 0.5 nF to 0.6 nF causes waveform [20]-[21]. approximately 20% decrease in positive amplitude of TRV. 100 50 0

-100 0

-200 I0=2 A -50 I0=3 A I0=4 A -300 -100 -400

-150 C=0.5 uF TRV(V) C=0.6 uF -500 C=0.7 uF

TRV(V) -200 -600

-250 -700

-300 -800

-900 -350 0 20 40 60 80 100 120 140 160 180 200 Time(microsecond) -400 0 20 40 60 80 100 120 140 160 180 200 Time (microsecond) Fig. 11. The Effect of initial PAC on TRV waveform [20]-[21]. Fig. 9. The Effect of capacitance value of CB on TRV The effect of τ is illustrated in Fig. 11. Since τ exists waveform [20]-[21]. in both exponential term and I0τ/C term in (10), it has The other network parameter which depends on the diverse effects on negative part (t<4τ) and positive part characteristics of network is the equivalent network (t>4τ) of TRV. According to (11), τ directly affects the inductance which its modifications affect on the positive amplitude of TRV and has inverse impact on exponential amplitude of (10). The initial value of TRV initial negative TRV amplitude. is proportional to the inductance as shown in Fig. 10 100 while the positive amplitude is not influenced. Besides, 50 100% increment in equivalent inductance value results 0 -50 in 100% rise of TRV negative amplitude. Consequently tav=10 us -100 tav=15 us TRV amplitude has the same sensitivity to these two tav=20 us tav=25 us parameters. But, the higher value of negative part of -150 TRV in comparison to positive part causes more TRV(V) -200 -250 consideration in negative part. Initial PAC value (I0) and diffusion time constant (τ) are the two physical -300 parameters which have influence on the TRV waveform -350 -400 in the first ten microseconds in capacitive switching by 0 20 40 60 80 100 120 140 160 180 200 Time (microsecond) VCB. According to (4), I0 is directly related to initial ion Fig. 12. The Effect of diffusion time constant on TRV density and vi. It means that the rises in I0 are due to waveform [20]-[21].

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