DETERMINATION OF PARAMETERS OF THE ELECTRIC DISCHARGE MODEL

Transcription

1 I E E E Lubl in University of Technology 4 th International Conference ELMECO Nałęczów, Poland September 2003 DETERMINATION OF PARAMETERS OF THE ELECTRIC DISCHARGE MODEL Leszek JAROSZYŃSKI Institute of Electrical Engineering and Electrotechnologies, Lublin University of Technology, Nadbystrzycka 38A, Lublin, Poland leszekj@weber.pol.lublin.pl Abstract In this paper, the Mayr s electric arc model modified by the author has been described. Modification allows computer simulation of the supply circuit of the GlidArc non-thermal plasma reactor. The method of the determination of numerical model parameters based on experimental data has been presented. The comparison of the numerical simulation with laboratory results has also been shown. Keywords: gliding arc numerical model, analogue behavioural modelling, PSpice. 1. INTRODUCTION Numerical analysis of the plasma reactor supply system performed with the aid of an electric circuit simulator is a valuable method for evaluating operation of a supply and a non-linear load. However, computer simulation of the gliding arc plasma reactor (GlidArc) requires a specific model of the electric discharge. Many conceptions of electric arc mathematical modelling have already been elaborated. They can be divided into two major categories: physical/mathematical models (arc channel models) and adaptive models (so-called black-box models). Solving simulation problem with the help of a computer application such as PSpice imposes the use of a black-box electric discharge model. Supply circuit electric waveforms may be calculated with proper accuracy, though detailed analysis of plasma channel parameters is unachievable. The following models are among well-known concepts of adaptive modelling: Cassie s model, Mayr s model, Schwartz s model, Urbanek s model. However, none of them directly satisfies the needs of the numerical simulation of the gliding arc plasma reactor [1]. It takes place because GlidArc reactor is a non-linear load which is characterized by cyclic discharge expansion: starting from high voltage ignition, through rapid elongation, until its fading due to cooling caused by the working gas stream

2 2. GLIDING ARC DISCHARGE The gliding electric discharge has already been successfully utilised for the gas purification in many environment protection technologies [1]. The chemical reactions are conducted with the help of free radicals generated by the non-thermal plasma. These processes take place in the plasma generator, which general idea has been shown in figure 1 (so called GlidArc I plasma reactor). Fig. 1. Idea of the GlidArc I plasma reactor: A processing chamber, B working electrodes, C striking electrode, D gas flow, E gliding arc discharge, Z supply circuit [2]. In this apparatus, the electric discharge is initiated in the region where the distance between two (or more) knife-shaped working electrodes is the smallest. Central striking electrode provides high voltage for discharge ignition. After the ignition, the discharge is forced to glide along working electrodes by the fast moving flow of the treated gas. The discharge is extinguished when its power consumption exceeds possibilities of the supply circuit. Then the whole process is starting anew. The period of the single cycle of the reactor operation depends mainly on electrode shape and dimensions, thermal parameters of a treated gas, gas velocity and can be equal up to several periods of 50 Hz supply network voltage. 3. GLIDING ARC MODEL The use of the well-known black-box electric arc models for the computer simulation of gliding electric discharge produces some problems. It gives improper static u-i characteristic of the electric arc in the low current range. The dynamic behaviour of the discharge described by so-called arc time-constant is unsuitable. The simulation of cyclic operation of the GlidArc plasma reactor is impossible. It doesn't permit the simulation of electric ignition (high voltage breakdown). That is why, the modification of Mayr s electric arc model (1) has been made. 1 dg 1 Ei 1 G dt M P 0 where: G - unitary arc conductance, E - arc electric field strength, i - arc current, P 0 - unitary power dissipated from discharge, M - Mayr s arc time-constant (1)

3 The modification consists in the introduction of the linear function p 0 =f(g) (2), which describes power dissipated from the discharge. p0 ( g) a g c (2) where: a, c constants. This approach allows simple and effective control over static discharge u-i characteristic. Additionally, it permits to take into account an expansion of gliding discharge by the introduction of functions a(l) and c(l), where l is a discharge length [3]. The values of constants a and c have been calculated using dynamic u-i characteristic of the discharge (Fig. 2) taken during laboratory tests of the GlidArc plasma reactor. Fig. 2. Dynamic u-i characteristic of the electric discharge during one period of supply voltage. Slopes of the u-i characteristic have been approximated using function derived from equation (2). Approximating curves 1 and 2 (Fig. 3) have enabled the calculation of static u-i characteristic 3 [4]. Fig. 3. Approximation of dynamic and static u-i discharge characteristics

4 The static u-i characteristic has allowed to determine values of the constants a and c (a=5000 V 2, c=75.8 W or unitary values: a 0 =81E6 V 2 /m 2, c 0 =9650 W/m). The usage of Mayr s definition (3) has been the first attempt to calculate the value of discharge time-constant. Q M 0 (3) P 0 where: Q 0 - energy needed for e-times alteration of the arc conductance. Constant value of M =0.13 ms has been evaluated near maximum of the discharge conductance g. Assuming sinusoidal variation of the discharge current, the second attempt to find function (g) has been made. Knowing relation (2), it is possible to transform Mayr s equation (1) to the formula (4). 2 i g ag c ( g) (4) d g dt Figure 4 shows results of the second attempt. Both relations between discharge constant and discharge conductance obtained for dg/dt>0 and dg/dt<0 have been approximated using polynomial (5). Fig. 4. Time-constant vs. discharge conductance ( g) = 37,110 50,2 10 g - 6,23g 304g -5,5310 g (5) -106-

5 4. COMPUTER SIMULATION Electric discharge model described above has been used for simulation with the help of analogue behavioural blocks of the PSpice. Non-linear arc conductance described on the basis of the modified Mayr s equation can be expressed in formula (6). i uer g 2 u g ER 1 dt p ag c Equation (6) leads to the simulation scheme presented in figure 5 (version with constant value of M ). (6) Fig. 5. Analogue behavioural model of the electric discharge (PSpice): ABM1 voltage controlled voltage source, ABM2 integrator (with given initial condition), ABM3 voltage controlled current source. The transient analysis of the circuit presented above and the similar circuit taking into consideration function (5) has been made. The comparison between dynamic discharge u-i characteristics is shown in figure 6. Fig. 6. Comparison of dynamic discharge u-i characteristics

6 5. CONCLUSION The extension of Mayr's switching arc model proposed by the author is possible, therefore this modified equation can be applied in analysis of operation of the GlidArc I plasma reactor and the integrated supply system. Unfortunately, the introduction of time-constant conductance relation to modified Mayr s model seriously lowers stability of the computer simulation (PSpice). However, the introduction of relation =f(g) doesn t improve correspondence between experimental results and computer simulation in the low current range. Proper determination of =const has almost the same effect and it doesn t degrade the simulation performance. Discrepancy between measurement and simulation might be elucidated in two ways: mathematical discharge model based on heat balance doesn t take into consideration high voltage phenomena, which appear to have significant effect on u-i characteristic in low current range. REFERENCES [1] T. Janowski, L. Jaroszyński, H. D. Stryczewska, Modification of the Mayr s electric arc model for gliding arc analysis, XXV ICPIG: International Conference on Phenomena in Ionized Gases: Proceedings, Nagoya, Japan, [2] H. Lesueur, A. Czernichowski, J. Chapelle, Apparatus for the generation of low temperature plasmas by the formation of gliding electrical discharges, Patent application, France, National registration no ; May 20th, [3] L. Jaroszyński; H. D. Stryczewska, Computer simulation of the electric discharge in GlidArc plasma reactor, Electromagnetic devices and processes in environment protection - The Third International Conference ELMECO 2000: Conference Proceedings, Lublin-Nałęczów, Poland, [4] L. Jaroszyński, Parameters of the numerical model of electric discharge (in Polish), Międzynarodowa Konferencja z Podstaw Elektrotechniki i Teorii Obwodów IC-SPETO 2002: Proceedings, Gliwice-Ustroń, Poland,