Dynamic Characteristics of SF 6 -N 2 -CO 2 Gas Mixtures in DC Discharge Process

Transcription

1 Plasma Science and Technology, Vol.16, No.9, Sep Dynamic Characteristics of SF 6 -N 2 -CO 2 Gas Mixtures in DC Discharge Process ZHENG Dianchun ( ), WANG Jia ( ), CHEN Chuntian ( ), ZHAO Dawei ( ), ZHANG Chunxi ( ), YANG Jiaxiang ( ) Key Laboratory of Engineering Dielectrics and Its Application, Ministry of Education, Harbin University of Science and Technology, Harbin , China Abstract Dynamic characteristics of discharge particles are described within the framework of a two-dimensional photoionization-hydrodynamic numerical model for the discharge process of SF 6-N 2-CO 2 gas mixtures at atmospheric pressure, under a uniform DC applied field. The finite difference flux corrected transport (FD-FCT) algorithm is used in the numerical implementation for improving the accuracy and efficiency. Then the tempo-spatial distributions of the gap space electric field and electron velocity are calculated from the microscopic mechanism, and the dynamic behaviors of charged particles are obtained in detail. Meanwhile, the tempo spatial critical point of the avalanche-to-streamer in this model is discovered, and several microscopic parameters are also investigated. The results showed that the entire gap discharge process can be divided into two phases of avalanche and streamer according to Raether-Meek criterion; the electron density within the discharge channel is lower compared to that of positive and negative ions; space charge effect is a dominant factor for the distortion of spatial electric field, making the discharge channel expand toward both electrodes faster; photoionization provides seed electrons for a secondary electron avalanche, promoting the formation and development speed of the streamer. Keywords: hydrodynamic model, photoionization, short gap, streamer discharge, ternary mixture PACS: y, Vp DOI: / /16/9/08 (Some figures may appear in colour only in the online journal) 1 Introduction In recent years, cubicle gas insulated switchgear (C-GIS) has been widely used in the power system, which is filled with SF 6 gas, N 2, compressed air or mixed gas at low pressure (generally less than 0.25 MPa). Among the above gaseous mediums, SF 6 deserves special attention because of its stable chemical properties, high dielectric strength, as well as excellent arc interruption properties [1 3]. However, due to such factors as the discharge characteristics defects and greenhouse effects [4,5], people proceeded to search for new alternative media. Based upon the current research results, there is no single gas that meets all the requirements for power systems, thus the low SF 6 content gas mixtures seem to be an appropriate alternative. Investigations on SF 6 gas mixture are of longstanding interest [6], and most of the relevant studies are reported in the literature of simple binary gas mixtures such as SF 6 -N 2 or SF 6 -CO [7 17] 2. Fundamentally, the dielectric strength of SF 6 -N 2 gas mixture is still not ideal for C-GIS, therefore, how to improve the insulation performance of SF 6 -N 2 gas mixture becomes a new hotspot in the field of gas discharges. Ohtsuka et al. [18,19] came to the conclusion that insulation performance of the SF 6 -N 2 gas can be significantly improved by adding 1% of CO 2. Nevertheless, the above results cannot clearly reveal the physical nature of the discharge phenomenon, thus it is necessary to devote further study to the micro discharge characteristics of 50%SF 6-49%N 2-1%CO 2 mixed gas for the purpose of developing a new insulation medium to replace SF 6 gas. In this work, we investigate micro discharge dynamic characteristics of streamers based on simulation results of the discharge process of SF 6 -N 2 -CO 2 gas mixtures composed of 50%SF 6, 49%N 2 and 1%CO 2, in short gap under atmospheric pressure. The aim of this work is to provide necessary reference for design and manufacture of new types of C-GIS, and promote the development of SF 6 mixed gas applications. 2 The hybrid computing model 2.1 Mathematical model of gas discharge Using hydrodynamic theory to analyze the physical process of gas discharge in an electrode gap, in essence, it translates the charged particle continuity equations supported by National Natural Science Foundation of China (No ) 848

2 ZHENG Dianchun et al.: Dynamic Characteristics of SF 6 -N 2 -CO 2 Gas Mixtures in DC Discharge Process and Poisson equation into appropriate partial differential equations, and then solves the equations based on the discrete numerical difference format. The transport properties of charged particles in the gas gap discharge process are governed by the following equation set [20] : n e t = (n ev e )+ 2 (Dn e )+α v e n e η v e n e β ep n e n p + S, (1) n p = (n p v p )+α v e n e β np n p n n β ep n e n p + S, t (2) n n = (n n v n )+n e η v e n p n n β np, (3) t where n e, n p, n n are the densities of electrons, positive ions and negative ions, while v e, v p, v n are the corresponding drift velocities. A total of 18 species ions are considered in this work, 9 species are positive ions (SF + 6,N+ 2,CO+ 2,N+ 4,O+ 2,SF+ 5,O+ 4,N+ 3,N+ ), 9 species are negative ions (SF 4,SF 5,SF 6,O 2,O,F,SOF 5, SO 2 F,CO 3 ). t is the time, β np and β ep are the recombination coefficients for the ion-ion and the electron-ion reactions. The term S stands for the source of electronpositive ion pairs due to photoionization. The α, η and D denote the ionization, attachment and electron diffusion coefficients, respectively. They are entirely determined by the local reduced electric field E/N, wheree is the electric field and N is the neutral gas density. The values that have been used for the transport parameters and rate coefficients in the model are described in Ref. [21]. The collision ionization process between electrons and neutral particles at atmospheric pressure will radiate photons, and these photons are absorbed by molecules according to a certain probability, on this occasion, once photon energy reaches the level of ionization, the photoionization process will occur. Generally speaking, the number of photons is much smaller than the number of electrons generated by impact ionization. However, these photons will result in the formation of a secondary avalanche which moves towards the head, thereby prompting the development of the discharge process. Hence the photoionization process at atmospheric pressure plays a significant role in the gas discharge process. The photoionization model used in this paper is defined by the expression of S(x) d = Ψ(N,x x )NΩ(x x )α(x )N(x ) v(x ) dx, 0 (4) where N, ψ and d are the density of neutral molecules, photoionization coefficient and gap separation, respectively, x is the target point, x isthesourcepoint,and Ω denotes the solid angle subtended at x by the disk charge at x. Taking into account the distortion effects of space charge on the electric field, the Poisson equation is given by: 2 ϕ = q ε 0 (n p n e n n ), (5) where ϕ is the electric potential; q is the electronic charge; ε 0 is the permittivity of free space. The current I in the external circuit due to the motion of electrons and ions between the electrodes is calculated using Stato s equation [22] : I = πr2 q d d 0 (N p v p N n v n N e v e )dx, (6) where r is the radius of the discharge channel. 2.2 Calculation conditions In this paper, the schematic diagram and calculation conditions for parallel-plate electrodes discharge at atmospheric pressure are set in Fig. 1 and the calculation model is converted to a two-dimensional structure by rotating the axis of symmetry. In the present study, the gap distance between the electrodes filled with 50%SF 6-49%N 2-1%CO 2 gas mixture is 5 mm under the pressure of 0.1 MPa, at a temperature of 300 K. The spatial mesh chosen to be uniform with 40,000 mesh points, namely, the longitudinal axis (z-axis) and the radial axis (r-axis) are all uniformly divided into 200grids. ThetimestepisΔt = s, which is much smaller than that required by the stability of the adopted numerical scheme. Fig.1 Discharge calculation model At the initial moment of gas discharge, the quasineutral plasma spot of Gaussian shape in the radial and axial directions is placed at the front of the cathode: [ ( ) 2 ( ) 2 r z z0 ] n e t=0 = n p t=0 = n 0 exp, δ r δ z (7) n n t=0, (8) 849

3 Plasma Science and Technology, Vol.16, No.9, Sep where r and z are the radial and axial coordinates, respectively; the origin of coordinates (r = z =0) is positioned at the center of the cathode surface, the peak density of particles (seed electrons and positive ions) n 0 = 10 6 m 3, the position of initial plasma z 0 =10 3 m, characteristic scales δ r = m and δ z = m. The variation of these parameters considerably changes the delay time of the streamer development, but does not affect the main streamer characteristics. Boundary conditions of electrons and positive ions at the electrodes are as follows: n e z = n e n p z=0 z =0, z=d z = n p z=0 z =0. z=d (9) The solution of Poisson s equation is subject to the following boundary conditions: V z=0 = V 0, V z=0 =0, V z r =0, V r=r = V 0 r=0 d, (10) where V 0 is the applied voltage, R is the radius of the computational domain. 2.3 Numerical techniques The steep density gradients of charged particles in spatial and temporal dimensions will inevitably result in spurious oscillation or excessive numerical diffusion, therefore, how to get a more accurate solution of particle continuity equations is especially important for the research of short gas gap discharge phenomena. FD-FCT technique described by Book and Boris [23] introduces an anti-diffusion term to eliminate the numerical diffusion of SHASTA algorithm, and then uses the flux correction procedure to correct the antidiffusion term. This algorithm is the first nonlinear difference method used to deal with the very steep density gradients that appear. Nevertheless, since the proposed calculation method cannot be used to directly deal with a high dimensional case, Zealezak [24] clearly put forward the method of mixed low-level and high-level solution to improve the accuracy and stability of the algorithm. Afterwards, several scientists including Morrow, Williams and Dhali [25 27] used and developed the FD-FCT on the basis of it. Wu and Kunhardt [16] reported a twodimensional simulation study on the streamer development process of SF 6 -N 2 mixed gas, and the results agreed satisfactorily with the relevant experimental values. Thus the continuity equations described in this paper are solved by the FD-FCT method. 2.4 Charged particle species in SF 6 -N 2 - CO 2 discharge process During the gas discharge process, many diverse phenomena can occur when the collision process takes place between charged particles and elementary particles. For example, momentum or energy of particles will change; neutral particles will be ionized; charged particles may become neutralized. The main collision process between electrons and atoms is elastic scattering (change in electron momentum) and inelastic collision (excitation and ionization reaction), and the main collision process between ions and atoms is elastic scattering (momentum and energy exchange) and resonance charge transfer. Meanwhile, there are other important collision processes in the gas discharge process, for instance, decomposition, recombination, and the process involving negative ions (attachment, desorption, charge transfer between positive and negative ions). In this paper, the generating process of charged particles in SF 6 - N 2 -CO 2 gas mixtures is shown in Appendix A [28 30]. 3 Results and discussion Results are presented for the discharge process between parallel-plate electrodes 0.5 cm apart, with a constant applied voltage of 43.3 kv( 5% overvoltage), in 50%SF 6-49%N 2-1%CO 2 under the pressure of 0.1 MPa. The calculation is initiated by the release of 10 6 electron-ion pairs near the cathode at t = 0 ns. The total formative time is 9 ns, of which the first 7.4 ns is avalanche development phase, and the next 1.6 ns is streamer development phase. We analyze the discharge process by combining Townsend s theory with streamer mechanism, based on the discharge characteristics. 3.1 Development of the avalanche and streamer Fig. 2 shows contour plots of electron density at the time moments of 0 ns, 1 ns, 2 ns, 3 ns, 4 ns, 5 ns, 6 ns, 7 ns, 7.4 ns, 8.3 ns, 8.6 ns and 9 ns. It can be seen that, starting from t = 0 ns, the charged particles of the initial plasma obtain sufficient energy from the external electric field, accelerate and collide with the gas molecules in the gap, thereby releasing more electrons, which in turn multiplies exponentially and creates an avalanche. At the moment t = 7.4 ns, the electron density in the avalanche head attains a peak value of approximately m 3 after the avalanche has traveled a distance of 1.3 mm, which accords well with Raether-Meek criterion (10 18 m 3 ). Therefore, this moment is regarded as the tempo-spatial critical point for the avalanche-to-streamer, and then a phase of streamer propagation of ns follows. This streamer phase is characterized by a sharp growth in electron densities as well as a serious distortion in electric field under the combined actions of space charge effect and photoionization effect. As can be seen in Fig. 2, from t = 7.4 ns to 9 ns, the streamer propagates quickly towards both cathode and anode along the axial direction, respectively, and then ultimately forms a high conductance streamer channel between cathode and anode at 9 ns. Furthermore, after an initial slow growth in the avalanche phase, the current rises sharply in the streamer phase, as illustrated in Fig

4 ZHENG Dianchun et al.: Dynamic Characteristics of SF 6 -N 2 -CO 2 Gas Mixtures in DC Discharge Process Fig.2 Contours of the electron density at various times maximum value of electron density is m 3 in the streamer head, whereas it is m 3 in the streamer tail. Meanwhile, it is clear that positive and negative ion densities within the streamer body are greater than the electron density, as depicted in Fig. 4. This is because the recombination process between positive and negative ions is relatively slow. Furthermore, the presence of electronegative gas (SF 6 ) in the mixed gas makes some electrons be adsorbed by gas molecules, inhibiting the increase of electrons so that the peak value of positive charge density is higher than that of the electrons. 3.2 Spatial electric field Fig.3 Computed current in the external circuit vs time In the discharge process, the spatial electric field is a dominant factor in the development of the streamer. Fig. 4 represents the distributions of the ion, electron, Consequently, the dynamics characteristics for the and net space charge density at various moments streamer are mainly determined by temporal and spa- during the discharge process, namely at t = 1 ns, tial characteristics of the spatial electric field. Fig ns, 8.3 ns and 9 ns, respectively. Note that the electron, displays the evolution of spatial electric field distribuing positive and negative ion densities are increastion, as time process. Evidently, the initial uniform gradually as time goes by in the entire discharge process. At the moment t =7.4ns, the peak density electricfieldisgraduallydistortedastimegoesbydue to the space charge effect, the electric field intensities of electron is m 3, the corresponding peak in different regions show different trends. Compared density of positive and negative ions is m 3 and m 3, respectively. When the streamer expands toward both electrodes, namely t =9 ns, the to the electric field within the streamer, the local electric field of the streamer head as well as the tail is significantly enhanced, which is consistent with the basic theory of streamer discharge [31]. 851

5 Plasma Science and Technology, Vol.16, No.9, Sep Fig.4 Spatial distribution of the electron, negative ion, positive ion, and net charge density along the gap axis Fig.5 Spatial distribution of the electric field at different moments 852

6 ZHENG Dianchun et al.: Dynamic Characteristics of SF 6 -N 2 -CO 2 Gas Mixtures in DC Discharge Process 3.3 The influence of photoionization As the main source of secondary electrons, photoionization plays an important role in enhancing electric field distortion as well as promoting streamer development [32,33]. It is clear from Fig. 6 that the position and net charge number of avalanche head are not obviously different in both cases (with or without photoionization). Until the beginning of the stream phase, the difference between the two curves becomes significant. Evidently, the curves which take account of the photoionization process change more drastically. The results clearly demonstrate the fact that the photoionization provides more electrons ahead of the advancing field maxima for the streamer. Additionally, the formation and propagation velocity of the streamer is accelerated, the mean streamer velocity is approximately 0.37 mm/ns from t = 0 ns to 9 ns, 28% higher than that without photoionization. The effective collision ionization coefficient (α η)/p is intimately associated with the variation of the spatial electric field, therefore we can satisfactorily reveal the specific position of photoionization in the discharge process by comparing the effective collision ionization coefficient trends in the cases with and without the photoionization effect. As is clear from Fig. 7, either in the avalanche stage or in the streamer phase, the gradient of the curve that takes into account the photoionization effect varies obviously. This is due to the secondary electrons generated by the photoionization collision with gas molecules under the strong electric field of the streamer head and tail, promoting the rapid growth of the space charge numbers, then the space charge effect leads to more severe distortion of the electric field, resulting in a drastic change in the effective impact ionization coefficient. Fig.6 Time evolution of the net charge number and streamer head position with and without photoionization Fig.7 The effective impact ionization coefficient versus distance for the moments of 5 ns, 7.4 ns, 8.3 ns and 9 ns 853

7 4 Conclusions In the present paper, we have briefly presented a two-dimensional numerical model for the microscopic discharge process of SF 6 -N 2 -CO 2 gas mixtures, at a constant voltage in a 5 mm short gap. Furthermore, the FD-FCT algorithm was used to solve steep density gradients that appear in the calculation, and then the microscopic parameters in the discharge development process were obtained. The results show that the number of electrons in the discharge channel body is always Plasma Science and Technology, Vol.16, No.9, Sep lower than that of both positive ions and negative ions, whereas higher than that of negative ions in front of the streamer head and tail. Compared to that in the avalanche phase, the spatial electric field gradient in the streamer phase is larger. Meanwhile, the results also confirm the predominant role of the gas photoionization process in the streamer stage, which is reflected in the tempo-spatial characteristics of such variables as particle density, spatial electric field distribution and other discharge parameters. Appendix: The generating process of charged particles in SF 6 -N 2 -CO 2 gas mixtures Elastic scattering e+sf 6 e+sf 6,e+N 2 e+n 2,e+CO 2 e+co 2,e+O 2 e+o 2 Impact ionization e+sf 6 2e+SF + 6,e+N2 N+ 2 +2e, e+co2 CO+ 2 +2e, e+o2 O+ 2 +2e Dissociative attachment e+sf 6 SF 4 +F2, e+sf6 SF 5 +F, e+sf6 SF5+F,e+CO 2 CO+O, e+o 2 O+O,e+2O 2 O 2 +O2 Attachment processes e+sf 6 SF 6 Charge transfer reaction SF 6 +SF6 SF6+SF 6,F +SF 6 F+SF 6,SF 5 +SF6 SF5+SF 6, SF 6 +SF4 SF5+ SF 5,N+ 2 +2N2 N+ 4 +N2, N+ 4 +O2 O+ 2 +2N2, N + 2 +O2 O+ 2 +N2, SF 6 +SOF4 SOF 5 +SO2, SF 6 +SO2 SO2F +SF 5, SF 6 +SO2 SF 5 +SO2F, SF 6 +SO2 SO2F 2 +SF4, SF 6 +SOF4 SOF 5 +SF5, SO 2F +SOF 4 SOF 5 +SO2, O +O 2 O+O 2 Dissociative ion conversion SF 6 +SF6 SF 5 +F+SF6, SF 5 +SF6 F +SF 4+SF 6, Collision detachment SF 6 +SF6 SF 5 +F+SF6 F +SF 6 F+SF 6+e, SF 5 +SF6 SF5+SF6+e, SF 6 +SF6 SF6+SF6+e Excitation processes SF 6 +SF6 (SF 6 ) +SF 6 Recombination processes SF 5 +SF+ 5 2SF5, SF+ 5 +SF 6 SF5+SF6, SF+ 5 +F SF 6 SF + 5 +SF 4 SF5+SF4, e+n+ 2 2N, O+ 4 +e 2O2, O+ 2 +e 2O Photodetachment Auto-detachment Dissociative ionization Three-body charge transfer reaction O + 4 +O 2 2O2, 2e+N+ 2 N2+e, CO 3 +O+ 2 +N2 O2+O+CO2+N2 SF 6 +hν SF6+e (SF 6 )* SF6+e e+sf 6 SF 5+F+e, e+sf 6 SF 4+2F+e, e+sf 6 SF 2+4F+e e+sf 6 SF + 5 +F+2e, e+co2 CO+O+e, e+co2 C+2O+e O +CO 2+CO 2 CO 3 +CO2, N2+N2+O+ 2 N2O+ 2 +N2, O + 2 +N2+O2 O+ 4 +N2, N+ +N 2+N 2 N + 3 +CO2 Associative ionization O+O 2 O3+e, O +O 2 O 3+e, CO+O CO 2+e References 1 Li Bin. 2003, SF 6 High Voltage Electrical Design. Mechanical Industry Press, Beijing (in Chinese) 2 Qiu Yuchang, 1994, GIS Device and Insulation Technology. Water Power Press, Beijing (in Chinese) 3 Yan Zhang, Zhu Dehuan. 2007, High Voltage and Insulation Technology. China Electric Power Press, Beijing (in Chinese) 4 Wang Feng, Qiu Yuchang. 2003, Power System Technology, 27: 54 5 Tang Jia. 2011, Electric Power, 44: 30 6 Vazquez P A, Georghiou G E, Castellanos A. 2006, Journal of Physics D: Applied Physics, 39: Wang Qi, Qiu Yuchang. 2004, Electric Wire & Cable, 1: 28 8 Zhou Hui, Qiu Yuchan, Tong Yonggang, et al. 2003, High Voltage Apparatus, 39: 13 9 Wang Feng, Qiu Yuchang, Zhang Qiaogen. 2002, Insulating Materials, 35: Qiu Y, Chalmers I D. 1993, Journal of Physics D: Applied Physics, 26: Chen Qingguo, Xao Dengmang, Qiu Yuchang. 2001, Journal of Xi an JiaoTong University, 35: Qiu Y, Kuffel E. 1999, IEEE Trans. Dielectrics and Electrical Insulation, 6:

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