New method for solving the energy-balance equation for moving-boundary a.c.arcs

The characteristics of moving-boundary a.c. electric arcs are derived using a new mathematical approach. The solutions, although approximate, are found in specific cases to give close agreement with results obtained by exhaustive numerical calculations based on finite-difference methods1 and by experiments.2 The main advantage of the new method, which is based on variational calculus, is a greatly simplified calculation procedure, obtained with no evident loss of accuracy. The results can be expressed analytically in similar terms to those of the Mayr model, and the model lends itself to general predictions of current-interruption behaviour, allowing for interaction with the external circuit.