Static breakdown threshold modeling of quasi-uniform gas gaps with a focus on the PDIV of contacting enameled wire pairs

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 eps'. The special case of uncoated metallic electrodes is included in the limit s/eps' -> 0. 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 s/eps'. 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.

On the influence of humidity on the breakdown strength of air—with a case study on the PDIV of contacting enameled wire pairs

“…It is thus interesting to recall the breakdown electric field values E b of quasi-uniform air gaps (see e.g. [18]) in order to translate the crossover field strength E x into a corresponding crossover gap length d x , below/above which the ionization yield of an electron avalanche traversing the gap is decreased/increased. Figure 2 illustrates the three regimes.…”

“…In a quasi-uniform electrode configuration the breakdown electric field E b is defined by a Townsend-Schumann type criterion [18]:…”

“…The hatched area for d < 10 µm is meant to indicate that the breakdown in these gaps at atmospheric pressure starts to be dominated by field emission of electrons (see e.g. [18]), and hence is outside the scope of this paper.…”

“…Considering the twisted wire pair in the quasi-uniform field approximation has been shown to be a good approximation for PDIV calculations, unless the wire radius R is smaller than about 0.15 mm [18,23]. The voltage across the gas gap at a position x (= ordinate of the field line start/end point) is then given by [18]…”

“…The PDIV is reached when I max reaches the ionization threshold K. For the range 10 µm < d < 1 mm, K = ln(γ −1 ) = − ln(2.5 • 10 −3 ) ≈ 6 may be used as a satisfactory approximate value of the ionization threshold, although there is a decrease towards a value of ∼4 when d changes from ∼25 µm to ∼10 µm [18]. This trend can be taken into account by adding an iterative correction if d = PDIV/E th is smaller than ∼25 µm, where PDIV is the inception voltage calculated using K = 6.…”