The use of the arc furnace and its influence on the power system is being studied. A set of models that allows for the evaluation of the electrical behavior during steady state is presented in this paper. The results are presented and used to validate them. Detection of steady-state voltage instabilities is performed through certain mathematical criteria. Among those arc furnace load criteria (dEs /dVp) criterion, L-indicator criterion, and (ZTh /ZLoad) criterion. The result of those criteria has been checked using the critical voltage value of arc furnace load node, which represents criterion quantities.