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Abstract

This paper describes modifications of the Mayr and Cassie models of the electric arc. They include the phenomena of increased heat dissipation and non-zero residual conductance when the current passes through zero. The modified models are combined into a new hybrid model connecting them in parallel and activated by a weight function. Two cases of functional dependence of models on current intensity and instantaneous conductance are considered. Mathematical models in differential and integral forms are presented. On their basis, computer macromodels are created and simulations of processes in circuits with arc models are performed. The families of static and dynamic arc voltage and current characteristics are presented.
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Bibliography

[1] King-Jet Tseng,YaomingWang D., MahindaVilathgamuwa, An experimentally verified hybrid Cassie- Mayr electric arc model for power electronics simulations, IEEE Transactions on Power Electronics, vol. 12, no. 3, pp. 429–436 (1997), DOI: 10.1109/63.575670.
[2] Sawicki A., Haltof M., Spectral and integral methods of determining parameters in selected electric arc models with a forced sinusoid current circuit, Archives of Electrical Engineering, vol. 65, no. 1, pp. 87–103 (2016), DOI: 10.1515/aee-2016-0007.
[3] Pentegov I.V., Sidorec V.N., Comparative analysis of models of dynamic welding arc, The Paton Welding Journal, no. 12, pp. 45–48 (2015), DOI: 10.15407/tpwj2015.12.09.
[4] Kalasek V., Measurements of time constants on cascade d.c. arc in nitrogen, TH-Report 71-E18, Eindhoven, pp. 1–30 (1971).
[5] Sawicki A., The universal Mayr–Pentegov model of the electric arc, Przegl˛ad Elektrotechniczny (Electrical Review), vol. 94, no. 12, pp. 208–211 (2019), DOI: 10.15199/48.2019.12.47.
[6] Katsaounis A., Heat flow and arc efficiency at high pressures in argon and helium tungsten arcs, Welding Research Supplement I, September, pp. 447-s–454-s (1993).
[7] Maximov S., Venegas V., Guardado J.L., Melgoza E., Torres D., Asymptotic methods for calculating electric arc model parameters, Electrical Engineering, vol. 94, no. 2, pp. 89–96 (2012), DOI: 10.1007/s00202-011-0214-6.
[8] Sawicki A., Arc models for simulating processes in circuits with a SF6 circuit breaker, Archives of Electrical Engineering, vol. 68, no. 1, pp. 147–159 (2019), DOI: 10.24425/aee.2019.125986.
[9] Sawicki A., Classical and Modified Mathematical Models of Electric Arc, Institute ofWelding Bulletin, no. 4, pp. 67–73 (2019), DOI: 10.17729/ebis.2019.4/7.
[10] Janowski T., Jaroszynski L., Stryczewska H.D., Modification of the Mayr’s electric arc model for gliding Arc Analysis, XXVI International Conference on Phenomena in Ionized Gases, Nagoya, Japan 2001/7/17, pp. 341–342 (2001).
[11] Ziani A., Moulai H., Hybrid model of electric arcs in high voltage circuit breakers, Electric Power Systems Research, vol. 92, pp. 37–42 (2012), DOI: 10.1016/j.epsr.2012.04.021.
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Authors and Affiliations

Antoni Sawicki
1
ORCID: ORCID

  1. Association of Polish Electrical Engineers (NOT-SEP), Czestochowa Division, Poland
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Abstract

Mathematical models of electric an arc with disturbed geometric sizes were created based on initial assumptions adopted from theMayr and Cassie models. Two cases of approximation of arc characteristics were considered separately. The Mayr–Voronin model was created in the low-current range with an exponential dependence of conductance on plasma enthalpy. However, the Cassie–Voronin model created is valid in the high-current range with a linear dependence of conductance on plasma enthalpy. In addition, the effect of two different assumptions about the method of energy dissipation, proportional to the lateral surface of the column or proportional to the volume of the column, on the parameters of both mathematical models was compared. It has been shown that under constant geometrical parameter values, created models can be reduced to classic Mayr and Cassie models. Then, these modelswere modified by taking into account the additional increase in heat dissipation as the current increases. Increasing voltage and current characteristics correspond to such an arc. Using the computer simulations, the effectiveness of using developed mathematical models in mapping the dynamic characteristics of the electric arc has been shown.
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Bibliography

[1] Krouchinin A.M., Sawicki A., Modelling of the constricted arc in plasma generators, Monographs series, no. 109, The Publishing Office of Częstochowa University of Technology, Częstochowa (2005).
[2] Solonenko O.P., Thermal Plasma Torches and Technologies, Cambridge International Science Publishing, vol. 1 (2000).
[3] Jaroszynski L., Stryczewska H.D., Computer simulation of the electric discharge in GlidArc plasma reactor, 3rd International Conference: Electromagnetic devices and processes in environment protection ELMECO-3, pp. 31–36 (2000).
[4] Schavemaker P.H., van der Sluis L., An Improved Mayr-Type Arc Model Based on Current-Zero Measurements, IEEE Trans. Power Delivery, vol. 15, no. 2, pp. 580–584 (2000).
[5] Kopersak V.M., The theory of welding processes – 1, KPI (in Ukrainian), Kiev (2011).
[6] Zalessky A.M., Fundamentals of the theory of electrical apparatus, Higher School Publishing House (in Russian), Moscow (1974).
[7] Taev I.S., Electrical contacts and arcing devices of low voltage devices, Energy Publishing House (in Russian), Moscow (1973).
[8] Marciniak L., Dynamic models of short-circuit arc for networks with low ground fault current, Energy Archive (in Polish), vol. 37, pp. 357–67 (2007).
[9] Ziani A., Moulai H., Hybrid model of electric arcs in high voltage circuit breakers, Electric Power Systems Research, vol. 92, pp. 37–42 (2012).
[10] Voronin A.A., Improving the efficiency of contact-extinguishing systems of high-current switching devices with an extending arc, Abstract of thesis (in Russian), Samara (2009).
[11] Ciok Z., Mathematical models of connecting arc,Warsaw University of Technology (in Polish),Warsaw (1995).
[12] Sawicki A., Models of adjustable length electric arc,Wiadomosci Elektrotechniczne (in Polish), no. 7, pp. 15–19 (2012).
[13] Berger S., Mathematical approach to model rapidly elongated free-burning arcs in air in electric power circuits, ICEC 2006, 6–9 June 2006, Sendai, Japan (2006).
[14] Pentegov I.V., Sydorets V.N., Comparative analysis of models of dynamic welding arc, The Paton Welding Journal, no. 12, pp. 45–48 (2015).
[15] Sawicki A., The universal Mayr–Pentegov model of the electric arc, Electrical Review, vol. 94, no. 12, pp. 208–211 (2019), DOI: 10.15199/48.2019.12.47.
[16] Krouchinin A.M., Sawicki A., A theory of electrical arc heating, The Publishing Office of Technical University of Częstochowa, Częstochowa (2003).
[17] Sawicki A., Arc models for simulating processes in circuits with a SF6 circuit breaker, Archives of Electrical Engineering, vol. 68, no. 1, pp. 147–159 (2019), DOI: 10.24425/aee.2019.125986.
[18] Katsaounis A., Heat flow and arc efficiency at high pressures in argon and helium tungsten arcs, Welding Research Supplement I, pp. 447-s- 454-s (1993).
[19] Kalasek V., Measurements of time constants on cascade d.c. arc in nitrogen, TH-Report 71-E18, Eindhoven, pp. 1–30 (1971).
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Authors and Affiliations

Antoni Sawicki
1
ORCID: ORCID

  1. Association of Polish Electrical Engineers (NOT-SEP), Czestochowa Division, Poland
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Abstract

The paper discusses problems arising in attempts to accurately represent dynamic processes of an electric arc by means of simple mathematical models. It describes the properties of the universal Pentegov model, employing any shape of static voltagecurrent characteristics of an arc. Next, it presents spectral and integral measuring methods for determining arc parameters in the Mayr, Cassie and Pentegov models of the electric arc with a forced sinusoid current circuit, with the raising static characteristics of hyperbolic-flat and hyperbolic-linear shape. The influence is discussed of the random power supply disturbances on errors of determining the mathematical model parameters.
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Authors and Affiliations

Antoni Sawicki
Maciej Haltof

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