Nonlinear function of the heat processes damping factor in thermal column plasma have been introduced to modified mathematical models of the AC electric arc. This way, universal arc models with moderate cooling and constant geometric sizes, using static characteristics, have been created. Similar method has been used to hybrid arc models with variable column length connecting Berger and Kulakov models. It has been proposed the introduction of nonlinear damping factor function to modified Voronin model using static characteristics. Thereby the extended range of current for application of these models has been achieved.