# The Modelling of Electric Arc with Stochastic Disturbances Part 1. The Mapping of Stochastic Disturbances in Mathematical Models of Electric Arc

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 operation of disturbances and thereby interfering in the input equation of energy balance it was possible to obtain noisy Mayr-Voronin and Cassie-Voronin models of arc characterized by variable geometrical dimensions. 2. By assuming specific systems of the mathematical operation of parameter disturbances and thereby interfering in previously developed deterministic mathematical models it was possible to obtain 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 operation 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.

DOI: 10.17729/ebis.2022.6/5

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