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 978-1-4244-8365-5/10/$26.00 ©2010 IEEE 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].

Load more