Static breakdown threshold modeling of quasi-uniform gas gaps with a focus on the PDIV of contacting enameled wire pairs
Raphael Färber, Yang Lu, Michelangelo Balmelli, Ondřej Šefl, Christian M. Franck
Abstract
Abstract This paper provides a theoretical and conceptual framework for the determination of static breakdown inception thresholds in quasi-uniform gas gaps bounded by dielectric layers of thickness s and relative permittivity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>ε</mml:mi> <mml:mrow> <mml:mtext>r</mml:mtext> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">′</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> . The special case of uncoated metallic electrodes is included in the limit <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>s</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msubsup> <mml:mi>ε</mml:mi> <mml:mrow> <mml:mtext>r</mml:mtext> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">′</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">→</mml:mo> <mml:mn>0</mml:mn> </mml:math> . Moreover, a review of breakdown mechanisms and the underlying physical processes in quasi-uniform gas gaps is provided, and the applicability of the associated breakdown criteria is discussed. The results include a parametrization of the partial discharge inception voltage of wedge-shaped air gaps at atmospheric pressure as a function of the reduced coating thickness <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>s</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msubsup> <mml:mi>ε</mml:mi> <mml:mrow> <mml:mtext>r</mml:mtext> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">′</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> . The predicted results for this prototypical insulation geometry agree well with a broad array of literature data and own measurements. Finally, a physically motivated parametrization of the ionization threshold K ( d ) is suggested for atmospheric pressure air in terms of secondary electron feedback by energetic photons and ion-enhanced field emission. This contrasts with the ad hoc introduction of modified ‘streamer constants’ often found in literature to explain breakdown voltages that deviate from the predictions of the classical Raether–Meek–Loeb criterion.