Calculation of pressure and temperature in medium-voltage electrical installations due to fault arcs

In order to determine the pressure rise due to arc faults in electrical installations, the portion of energy heating the surrounding gas of fault arcs has to be known. The ratio of the portion of energy to the electric energy, the thermal transfer coefficient, is adopted as the kp factor. This paper presents a theoretical approach for the determination of the thermal transfer coefficient and the pressure rise in electrical installations. It is based on the fundamental hydro- and thermodynamic conservation equations and the equation of gas state taking into account melting and evaporation of metals as well as chemical reactions with the surrounding gas. In order to consider the dependence of the arc energy on the gas density, the radiative effect of fault arcs on the energy balance is introduced into the arc model by using the net emission coefficient as a function of gas density, arc temperature and arc radius. The results for a test container show that factors such as the kinds of insulating gases and of electrode materials, the size of test vessels and the gas density considerably influence the thermal transfer coefficient and thus the pressure rise. Furthermore, it is demonstrated, for an example of the arc fault in a compact medium-voltage station with pressure relief openings and a pressure relief channel, that the arc energy and the arc temperature can be simulated based on the changing gas density.

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