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The preliminary assumptions necessary to create a known mathematical model of an electric arc with a radius as a state variable are described. Besides the differential form, the integral form of this model is also presented. A hybrid model of an arc in the differential and integral forms has also been created. Weighting functions depending either on the current or on the resultant conductance were used. The presented mathematical models' performance in mapping the voltage-current characteristics of an electric arc in various current change ranges was examined in simulation.
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