The article presents universal functions approximating quasi-static characteristics of electric arc with undefined and defined ignition voltage. The above named approximations take into consideration the effect of disturbances on an arc column. The approximations were used to create a modified mathematical Pentegov model of arc characterised by high and low rate of disturbance changes. The simulation of processes in a circuit with electric arc involved the use of the modified Pentegov model with one and two-parameter rapid disturbances. The authors demonstrated the efficiency of the developed modifications of the Pentegov model.