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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Differential arc models with various length of plasma column have been described. They were modified to obtain electrical processes in plasmatrons with periodic gliding arc discharge. The models were also transformed into integral forms. Macromodels of arcs have been created and simulations of electrical processes in plasmatrons have been carried out. Comparisons of results obtained with experiments known from literature have shown usefulness of the developed mathematical models to simulate gliding arc discharges. Streszczenie. Opisano modele różniczkowe łuku elektrycznego o zmiennej długości kolumny plazmowej. Dokonano ich modyfikacji w celu odwzorowania procesów elektrycznych w plazmotronach z wyładowaniem ślizgowym powtarzającym się (gliding arc). Przekształcono te modele do postaci całkowej. Utworzono makromodele łuków i wykonano symulacje procesów elektrycznych w plazmotronach. Z porównania uzyskanych wyników ze znanymi z literatury przebiegami eksperymentalnymi wynikła przydatność opracowanych modeli matematycznych do symulowania wyładowań gliding arc. (Modele matematyczne łuku elektrycznego o zmiennej długości kolumny do symulowania procesów w plazmotronach gliding arc).

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Properties of the universal Pentegov arc model of electric arc plasma column and its particular cases in form of simple electric arc models (i.a. Cassie, Mayr, Zarudi) have been presented. Identification of electric arc model was made by the criterion of minimum variations of voltage arc time series, calculated with the least squares method. Authors pointed out the usefulness of presented method for computer aided design of electrotechnological devices. (Use of the identified electric arc models for computer aided design of electric devices).