#### Title:

Quadratic Polynomial Form of Electric Arc Furnace Equation

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#### Abstract:

Purpose – Electric arc furnaces are very often modelled using combined models which cover separately deterministic and stochastic phenomena taking place in the furnace. The deterministic part is expressed by nonlinear differential equations. A closed form of the solution to one of the most popular nonlinear differential equations used for the AC electric arc modelling does not exist for some values of the parameters. The paper goal was to convert electric arc furnace equation for these parameters to the quadratic polynomial form which significantly simplifies solution. Design/methodology/approach – The solution has been obtained in the time domain by a sequence of transformations of the original nonlinear equation which lead to a system of quadratic equations, for which a periodic solution can be found easily using harmonic balance method (HBM). Findings – Quadratic polynomial form of electric arc furnace nonlinear equation in the case for which the solution to the nonlinear differential equation describing e

#### Keywords:

electric arc furnace ; nonlinear differential equations ; quadratic polynomial form ; nonlinear loads

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#### Resource Identifier:

#### Source:

COMPEL 2014 vol. 33 no. 6, s. 2030-2042

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#### Relation:

Wydział Elektryczny. Politechnika Śląska