| Breakdown Voltage Characteristics in Weakly Non-Uniform Fields |
- The breakdown mechanism in weakly nonuniform fields is similar to uniform fields. Like in uniform fields the PB inception, Ui , and the breakdown voltages in weakly nonuniform fields are equal, the breakdown voltage can be estimated from the following relationship given by Schwaiger,
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 (11.1) |
- At breakdown the 'maximum breakdown field intensity', Ebmax in an electrode system or equipment having gaseous dielectric is always higher than the intrinsic 'electric strength', Eb' of the gas in uniform fields. The breakdown characteristics in weakly nonuniform fields mainly depend upon the geometrical factor of uniformity η of the electrode configuration. Breakdown characteristic for different gap lengths between two spheres in air having diameters of 10 cm each is shown in Fig. 11.1 for ac power frequency voltage. Knowing the dimensions, the factor η can be found out. It can be seen that as the gap distance d between the spheres is increased, the Schwaiger factor decreases, i.e. the field becomes more nonuniform. If the measured values of Ub- d characteristic are known, Ebmax - d characteristic can be plotted. From these curves it is evident that Ebmax does not change much within a certain range of gap distance d, as also shown by the straight-line part of the Ub- d curve. For this particular electrode configuration, it is limited upto a gap distance nearly equal to the radius of the sphere. For a rough estimation of breakdown voltage, one may take, therefore, a mean value of Ebmax from the curve in Fig. 11.1. It works out to be equal to 34.5 kV/cm.
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Fig 11.1 ac Breakdown voltage in air, maximum breakdown field intensity at the electrode and factor of uniformity for different gap distances in weakly nonuniform field |
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| Limiting value of η, the ηlim |
| The value of η at which the transition from a weakly nonuniform to extremely nonuniform filed configuration takes place is termed as ηlim . The exact value of ηlim in gaseous dielectrics depends not only upon the field nonuniformity but also upon the gas pressure and the type and polarity of the voltage since it is related with the inception of PB (Lecture 2). |
| The distinction between breakdown with and without stable PB can be made in terms of the value of degree of uniformity, η of the field. Consider a positive sphere-plane electrode configuration. As the gap distance 'd' between these two electrodes is increased, the filed becomes more nonuniform, resulting in decrease in the value of η. |
| For small gap distances, a weakly nonuniform field exists in the gap. On applying a sufficient magnitude of the voltage to the sphere, the required maximum field intensity for breakdown Ebmax is achieved. An abrupt breakdown without any stable PB takes place, region A in Fig. 11.2 . |
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Fig 11.2 Threshold curves showing breakdown with stable streamer for positive sphere-plane electrode configuration. |
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| On increasing the gap distance d, the field becomes more nonuniform. In the region B, in contrast to region A, stable PB takes place below the breakdown voltage. The borderline between these two regions is described in terms of η limit or ηlim , the threshold degree of uniformity. As illustrated in this figure, stable PB take place only in the shaded area in region B. As explained, the breakdown voltage in the region A and the PB inception voltage in the region B can be estimated with the knowledge of Ebmax and the electrode geometry determining the value of η. The boderline between the two regions A and B, represented by ηlim , represents the transition from the weakly to the extremely non uniform fields. |
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