Figure - available from: Journal of Physics D: Applied Physics
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(a) A wedge-shaped gas gap bounded by dielectric electrode coatings representing, for instance, the turn-to-turn insulation in an electric motor winding. Typical wire diameters are on the order of 1 mm, while coating thicknesses range from roughly 20 μm to 100 μm . The coating is typically a polymeric material with a dielectric permittivity εr′ between 2.5 and 5 (at room temperature). (b) Approximate reduction of the geometry in (a) to a parallel connection of uniform discharge cells. (c) Single discharge cell with an electron avalanche and the release of a secondary photo-electron at the cathode boundary. The special case of metallic electrodes is obtained by letting s/εr′→0 .
Source publication
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 mechani...
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Citations
... According to the IEC 60052 standard, rising absolute humidity of air increases the breakdown voltage in uniform (sphere-gap) field by about 0.2% g −1 m 3 . While the field in between the magnet wires is quasi-uniform [Fär+23a], the air gaps are much shorter (µm-range) than those tackled by the standard, making it not directly applicable [FSF23]. Furthermore, the PDIV is also affected by the possible change in the relative permittivity of the magnet wire coating due to ingress of water molecules from the humid air. ...
... Base model. The employed PDIV prediction model, described in detail in [Fär+23a], discretizes the wedge-shaped insulation system (coating + air) of the two samplescontacting electrodes-into into a large number of individual plate-plate discharge cells. For each cell, the voltage in the respective air gap is calculated using the formula: ...
... which is valid under the assumption of quasi-uniformity of the relevant part of the gap electric field, shown to hold true for sample curvatures (magnet wire radii) ⪆150 µm [Fär+23a]. The electrode voltage U el is identical to the test voltage, d is the length of the examined air gap (field line) in meters, x the distance from the contacting point in meters, and s and ε r the thickness (in meters) and complex relative permittivity of the coating, respectively. ...
The partial discharge inception voltage (PDIV) of low-voltage induction motor turn-turn insulation analogy is investigated for variable relative humidity (RH) of the surrounding air (temperature and pressure are kept constant close to their ambient values). Three materials, perfluoralkoxy alkane, sealed and unsealed alumina (UA), are employed as the dielectric coating (insulation) of test samples. Each material’s dielectric properties change differently with RH—of these, relative permittivity is regarded as the most crucial, as it was previously proven to be, along with the coating’s thickness, the key factor in determining the PDIV in dry air conditions. To further vary the value of permittivity and thus provide larger data sets for the verification study, the frequency of the excitation voltage is also varied between 1 Hz and 50 kHz. The obtained experimental data are compared against the PDIV predictions obtained by a breakdown model based on the reduced thickness of the coating (ratio of the coating thickness to its relative permittivity). Satisfying agreement between the measured and predicted PDIV are obtained for the first two materials, whereas significant discrepancies are seen for the UA material. For this case, surface conductivity is introduced into the prediction model and much better fits to the experimental data are obtained for a suitable value of surface resistance. It is hence demonstrated that the model is able to satisfactorily predict the PDIV for three substantially different materials when the RH of the surrounding air is varied between 10% – 80% .
... 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. The indicated associated relative increase, approximate constancy or decrease of the breakdown voltage U b is derived in sections 4.1-4.3, ...
... 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. ...
The partial discharge inception voltage (PDIV) in contacting enameled wire pairs exhibits a marked decrease with increased air humidity. While existing literature mentions several potential mechanisms for this reduction, a comprehensive quantitative assessment of the associated effects is lacking. This research paper addresses this knowledge gap by providing a quantitative estimation of the combined impact of water on the gas's ionization yield (effective ionization coefficient) and the modification of the gap electric field caused by water absorption into the bulk of the insulating coating and the associated microscopic and macroscopic polarization processes (dielectric permittivity). However, a comparison of the theoretical predictions with experimental data reveals that these factors alone cannot fully account for the observed reduction in PDIV. Therefore, the study explores additional mechanisms mentioned in the literature, with particular focus on the development of a semi-conductive layer on the insulation coating in humid atmospheres. The numerical simulations of the surface charge dynamics within this layer suggests that the frequency-dependent decrease in PDIV under high-humidity atmospheres can indeed be attributed to the modification of the gap electric field due to the accumulation of surface charge in the semi-conductive layer.
... Paschen's law for argon with account of nonuniform DC electric field, the loss of electrons due to radial diffusion, and the applied axial magnetic field has been derived in [14]. Evaluation of inception voltages for quasiuniform air gaps bounded by dielectric layers is performed in [15]. One can hope that the mathematical validation and evaluation of the accuracy of the classical Townsend criterion, proposed in this paper, will be a useful addition to these and other works and will contribute to a wider use of their results. ...
... Equation (15) was obtained by partial integration, under certain assumptions, of the eigenvalue problem (1)-(4), governing the ignition of self-sustained drift-dominated discharges and describing ion and electron transport in the applied electric field. However, equation (15) only requires knowledge of the input parameters of the problem: the Townsend ionization and attachment coefficients α and η and the secondary electron emission coefficient γ ′ , specified as functions of the reduced electric field, and the spatial distribution of the applied electric field. Thus, equation (15) represents a necessary condition for the problem (1)-(4) to be solvable, i.e. to admit a nontrivial solution for distributions of the ion and electron densities. ...
... Thus, equation (15) represents a necessary condition for the problem (1)-(4) to be solvable, i.e. to admit a nontrivial solution for distributions of the ion and electron densities. In mathematical terms, (15) is an equation for the eigenvalue parameter. From the point of view of gas discharge physics, equation (15) represents the multidimensional Townsend ignition criterion. ...
An eigenvalue problem governing ignition of volume discharges is formulated in the drift approximation with account of photoionization and the presence of multiple ion species with various reactions. The Townsend ignition (self-sustainment) criterion is deduced by partial integration of this eigenvalue problem neglecting the photoionization, and, in the case of electronegative gases, also the detachment. The Townsend criterion is applied to three examples of discharge ignition in high-pressure air, two of them referring to negative coronas in concentric-cylinder and point-to-plane configurations and one to a configuration with weakly nonuniform electric field. The comparison of the results obtained from different forms of the Townsend criterion with those given by the accurate numerical solution of the full eigenvalue problem shows that the neglect of the diffusion of the charged particles produces an error in the ignition voltage of the order of 1% or less. The effect of photoionization for these configurations is also weak as expected. The lower and upper estimates of the effect of negative ions over the ignition voltage are obtained from different forms of the Townsend criterion. A form of the Townsend criterion, which employs an effective attachment coefficient in air and takes into account, in an approximate way, also the detachment, gives a virtually exact value of the inception voltage in all the cases considered. Practical recommendations are given on when one can use the Townsend self-sustainment criterion, and when one should resort to a numerical solution of the general eigenvalue problem governing discharge inception.
