Analytical description of a series fault on a dc bus

The solution of the equations of a dc circuit containing an arc is given and compared with experimental data. The arc is modeled according to its classical equivalent circuit and the adequacy of this model is discussed. The analytical solution for the circuit with an opening gap is given for the case of a constant gap and the results are extended to the cases of a gap opening with uniform velocity and a gap opening with constant acceleration, under the assumption of a quasi-static approximation for which the limits of applicability are estimated. Voltage and current evolutions in time are derived, including an estimate of the arc duration and quenching time. The results are compared to experimental data. Also provided is a generalized view of the transient behavior of an arc in a circuit that extends the description commonly used, in terms of only a voltage-current relationship, by also including inductive effects.