The modelling of electric arc with stochastic disturbances. Part 1, The mapping of stochastic disturbances in mathematical models of electric arc

• Autorzy: Sawicki Antoni

Identyfikatory

DOI

10.17729/ebis.2022.6/5

Warianty tytułu

PL

Modelowanie łuku elektrycznego z zaburzeniami stochastycznymi. Cz. 1, Odwzorowanie zaburzeń stochastycznych w modelach matematycznych łuku elektrycznego

• Języki publikacji: EN

Abstrakty

EN

The heterogeneous physical structure of electric arc inspired a proposal to consider separately the generation of random disturbances of electric waveforms in the plasma column and in near-electrode areas. The article presents selected mathematical correlations which could be used to assess parameters of noisy signals in arc devices. Depending on the type of generated noise (white, pink, red), it is necessary to apply appropriate filters (which can be modelled using the ordinary differential equations presented in the article). The article discusses in detail the methods enabling the mapping of stochastic disturbances affecting the electric arc column. 1. By assuming specific systems of the physical effect of disturbances and thereby interfering in the input equation of energy balance it was possible to obtain the noisy Mayr-Voronin and Cassie-Voronin models of arc characterised by variable geometrical dimensions. 2. By assuming specific systems of the mathematical effect of parameter disturbances and thereby interfering in previously developed deterministic mathematical models it was possible to obtain the modified noisy Mayr, Cassie and Schwarz models as well as a model with the radius of a cylindrical column as a state variable. 3. The assumption of specific systems of the mathematical effect of disturbances on the deterministic load of the circuit with electric arc made it possible to consider macro-models with current or voltage noise generating sources additionally connected to arc.

Słowa kluczowe

EN

electric arc; stochastic disturbances of electric waveform; mapping

PL

łuk elektryczny; zaburzenia stochastyczne przebiegu elektrycznego; mapowanie

• Wydawca: Sieć Badawcza Łukasiewicz - Górnośląski Instytut Technologiczny
• Czasopismo: Biuletyn Instytutu Spawalnictwa w Gliwicach
• Rocznik: 2022
• Tom: Vol. 66, No. 6
• Strony: 47--64
• Opis fizyczny: Bibliogr. 24 poz., rys.

Twórcy

autor

Sawicki Antoni

• Association of Polish Electrical Engineers (NOT-SEP), Czestochowa Division, Poland

Bibliografia

• [1] Sawicki A.: The Mayr-Pentegov model of electric arc involving the use of the exponential function and enabling the approximation of static characteristics Bulletin of the Institute of Welding, 2021, vol. 65, no. 1, pp. 32–37.
• [2] Skowronek K.: Dyssypacja energii w rzeczywistym źródle napięcia obciążonym losowo. Energy dissipation in the real voltage source with random load. Poznan University of Technology Academic Journals. Electrical Engineering 2013, vol. 73, pp. 71–77.
• [3] Âkimov A.V.: Fizika šumov i fluktuacij parametrov. Nižegorodskij gosuniversitet, Nižnij Novgorod, 2013.
• [4] Marat: Osnovy cifrovoj obrabotki signalov: Vidy šumov, otnošenie signal/šum, Statističeskaâ obrabotka signala, Korrelâcionnaâ funkciâ, https://hub.exponenta.ru/post/osnovy-tsifrovoy-obrabotki-signalov-vidy-shumov-otnoshenie-signalshum-statisticheskaya-obrabotka-signala-korrelyatsionnaya-funktsiya843. (15.04.2022)
• [5] Gurarij M.M., Žarov M.M., Rusakov S.G., Ulyanov S.L.: Šumovoj analiz vo vremennoj oblasti avtogeneratornyh shem. Time domain noise analysis of oscillators Žurnal Radioelektroniki, 2020, no. 3. DOI 10.30898/1684-1719.2020.3.6.
• [6] Metody analiza slučajnyh signalov https://studref.com/624661/tehnika/metody_analiza_sluchaynyh_signalov (10.05.2022).
• [7] Aniŝenko V.S., Astahov V.V., Vadivasova T.E. et al.: Nelinejnye èffekty v haotičeskih i stohastičeskih sistemah. Regulâr. i haot. dinamika. Moskva 2003.
• [8] Moss F., McClintock P.V.E.: Noise in nonlinear dynamical systems. Vol. 3 Experiments and Simulations. Cambridge University Press 1989.
• [9] Anishchenko V., Boev Y.I., Vadivasova T.E.: Noise-Induced Parametric Oscillations in Nonlinear Oscillator. February 2011, Technical Physics Letters, 2011, vol. 37, no. 2, pp. 87–94. DOI: 10.1134/S1063785011020180.
• [10] Mironov Û.M.: Èlektričeskaâ duga v èlektrotehnologičeskih ustanovkah. Monograph. Izd. Čuvaš. un-ta, Čeboksary 2013.
• [11] Slezkin D.V., Cvelev R.V., Erofeev V.A. et al.: Izmerenie i rasčët ènergetičeskih harakteristik dugi pri svarke plavâŝimsâ èlektrodom v smesi zaŝitnyh gazov. Izv. Tulgu. Tehničeskie nauki, 2012, pp. 189–201.
• [12] Voronin A.A.: Povyšenie èffektivnosti kontaktno-dugogasitel'nyh sistem sil'notočnyh kommutacionnyh apparatov s udlinâûŝejsâ dugoj. Avtoref. dis. k.t.n. Samara 2009.
• [13] Voronin A.A., Kulakov P.A.: Matematičeskaâ model' èlektričeskoj dugi, pp. 155–162. UDK 621.3.064.43.
• [14] Sawicki A.: Modified Voronin models of electric arc with disturbed geometric dimensions and increased energy dissipation. Archives of Electrical Engineering, 2021, vol. 70, no. 1, pp. 89–102. DOI: 10.24425/aee.2021.136054.
• [15] Kalasek V.: Measurements of time constants on cascade d.c. arc in nitrogen. TH-Report 71 – E – 18, ISBN 90 6144 018 1, Eindhoven University of Technology, 1971.
• [16] Pentegov I.V., Sidorec V.N.: Sravnitel'nyj analiz modelej dinamičeskoj svaročnoj dugi. Avtomat. Svarka, 1989, no. 2, pp. 33–36.
• [17] Ghezzi L., Balestrero A.: Modeling and Simulation of Low Voltage Arcs. Proefschrift 2010.
• [18] Starkloff H.J., Dietz M., Chekhanova G.: On a stochastic arc furnace model. Studia Universitatis Babeş-Bolyai Matematica, 2019, vol. 64, no. 2, pp. 151–160. DOI: 10.24193/subbmath.2019.2.02.
• [19] Sawicki A.: Mathematical Model of an Electric Arc in Differential and Integral Forms With the Plasma Column Radius as a State Variable. Acta Energetica, 2020, no. 2, pp. 57–64. DOI: 10.12736/issn.2330-3022.2020204.
• [20] Winkler R.: Stochastic Differential Algebraic Equations in Transient Noise Analysis. Conference paper, [in:] Anile A.M., Alì G., Mascali G. (eds.) Scientific Computing in Electrical Engineering. Mathematics in Industry, 2006, TECMI, vol. 9, pp. 151–158.
• [21] Römisch W., Winkler R.: Stochastic DAEs in Circuit Simulation. International Series of Numerical Mathematics, vol. 146, pp. 303–318. DOI: 10.1007/978-3-0348-8065-7_19.
• [22] Sickenberger T.: Effiziente transiente Rauschanalyse in der Schaltungssimulation. Humboldt-Universitat zu Berlin, 25. April 2008.
• [23] Weiss L., Mathis W.: Noise equivalent circuit for nonlinear resistors. Conference Paper in Proceedings – IEEE International Symposium on Circuits and Systems, February 1999, DOI: 10.1109/ISCAS.1999.777572, Source: IEEE Xplore.
• [24] Grabowski D., Walczak J., Klimas M.: Electric arc furnace power quality analysis based on a stochastic arc model. 2018 IEEE International Conference on Environment and Electrical Engineering and 2018 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe).

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).