On the order reduction of the radiative heat transfer model for the simulation of plasma arcs in switchgear devices

Abstract

An approach to derive low-complexity models describing thermal radiation, employed to simulate the behavior of electric arcs in switchgear systems, is presented. The idea is to approximate the (high dimensional) full-order equations, describing the propagation of the radiated heat intensity in space, with a model of much lower dimension, whose parameters are identified by means of nonlinear system identification techniques. The proposed order reduction approach is able to systematically compute the partitioning of the electromagnetic spectrum in frequency bands, and the related absorption coefficients, that yield the best matching with respect to the finely resolved absorption spectrum of the considered gaseous medium. In addition to the order reduction approach and the related computational aspects, an analysis by means of Laplace transform is presented, providing a justification to the use of very low orders in the reduction procedure as compared with the full-order model. Finally, comparisons between the full-order model and the reduced-order one are presented.