Knowledge of electric fields is necessary in numerous high voltage applications. Electrode geometries that are encountered in practice or under laboratory experimental condition are very many but the rodplane arrangement with rod tip of various shapes (cone, needle, sphere, coaxial cylinder etc) are more common (Onal, 2004). These gaps are subjected to several types of voltage shape so that breakdown and withstand voltage have to be ascertained.
Several models for explaining the observed characteristics of the fifty percent breakdown of long gaps have been put forward by many researchers. Some theories or models used experimental data to obtain numerical estimates for some factors. Even with the varying assumptions the results were similar because they were based on the same avalanche and streamer theories.
Based on the critical flashover (CFO) voltage of long gap put forward by Paris (Begamudre, 2008) there was need to relate this study to small gaps. This was particularly necessary since calculation of small gap field distribution is easier because the controlling factors could be checked.
The most important factors by which engineers describe the breakdown voltage of various gaps are the critical flashover and the withstand voltages. The critical flashover (CFO) voltage is the voltage that yields flashover of 50 percent of the number of shots given probability of voltage flashover (V50%).
The withstand voltage which is critical to the designer could be determined in various statistical form.
Due to large number of variables involved in insulation design especially the use of long gaps tends towards a statistical procedure because each of these variables has its own characteristics probability of occurrence either alone or in conjunction with other variables.
Also the probability of most events occurring simultaneously is also remote. Therefore a flashover once in many operations is allowed. The most usual case is to allow one flashover in 100 switching operations. This could form the basis for design of airgap insulation.
Some designers use 0.2% probability of flashover (1 in 500 operations). In insulation design and operation, the withstand voltage is of outmost importance. Thus, the low probability region of flashover, 0.1% or 0.2% must be obtained from flashover probabilities of higher values .
It is necessary to note that the flashover probability of a given gap distance with voltage follow a nearly Gaussian or normal distribution.
TABLE OF CONTENT
1.0 Introduction
2.0 Background of Theory Stages of the High Voltage Equipment
2.1 A.C. Stage
2.2 D.C. Stage
2.3 Impulse Stage
3.0 Materials and Methods
4.0 Results Analysis
5.0 Discussion
6.0 Recommendation
7.0 Conclusion
8.0 Reference
CRITICAL FLASHOVER AND WITHSTAND VOLTAGE (STATISTICAL APPROACH)
1.0 INTRODUCTION
Knowledge of electric fields is necessary in numerous high voltage applications. Electrode geometries that are encountered in practice or under laboratory experimental condition are very many but the rodplane arrangement with rod tip of various shapes (cone, needle, sphere, coaxial cylinder etc) are more common (Onal, 2004). These gaps are subjected to several types of voltage shape so that breakdown and withstand voltage have to be ascertained.
Several models for explaining the observed characteristics of the fifty percent breakdown of long gaps have been put forward by many researchers (Begamudre, 2008). Some theories or models used experimental data to obtain numerical estimates for some factors. Even with the varying assumptions the results were similar because they were based on the same avalanche and streamer theories.
Based on the critical flashover (CFO) voltage of long gap put forward by Paris (Begamudre, 2008) there was need to relate this study to small gaps. This was particularly necessary since calculation of small gap field distribution is easier because the controlling factors could be checked.
The most important factors by which engineers describe the breakdown voltage of various gaps are the critical flashover and the withstand voltages. The critical flashover (CFO) voltage is the voltage that yields flashover of 50 percent of the number of shots given probability of voltage flashover (V50%).
The withstand voltage which is critical to the designer could be determined in various statistical form.
Due to large number of variables involved in insulation design especially the use of long gaps tends towards a statistical procedure because each of these variables has its own characteristics probability of occurrence either alone or in conjunction with other variables.
Also the probability of most events occurring simultaneously is also remote. Therefore a flashover once in many operations is allowed. The most usual case is to allow one flashover in 100 switching operations. This could form the basis for design of airgap insulation.
Some designers use 0.2% probability of flashover (1 in 500 operations). In insulation design and operation, the withstand voltage is of outmost importance. Thus, the low probability region of flashover, 0.1% or 0.2% must be obtained from flashover probabilities of higher values (Kara et al 2006, Faruk and Rizk 2009).
It is necessary to note that the flashover probability of a given gap distance with voltage follow a nearly Gaussian or normal distribution. The CFO and the withstand voltage could be related as
2.0 BACKGROUND OF THEORY:
Nonuniform fields: The important characteristic of non uniform field is the unequal distribution of field intensity in the space between the electrodes.
If the profile is different the greatest value of field intensity occurs on the surface of the electrode having smaller radius of curvature (Naidu and Kamaraju, 2007) and the region of minimum intensity is shifted to the opposite electrode. The degree of nonuniformity of a field can be characterized by the ratios of maximum intensity of the field to its average value that is,
Nonuniformity of a field can exert considerable influence on the nature of the development of discharge (Afa and Wiri 2010, Marzinoto et al 2005)
In a sharply nonuniform field (positive point), an electron formed in the gap while moving towards the point falls into the region of strong field, ionization takes place near the point but at a distance sufficient to permit ionization and form avalanche. As the electrons of the avalanche reach the anode they move away through the point electrode but the positive charges due to their slow movement will remain in the space, moving slowly towards the cathode. This simulates an extension of the electrode surface (point) and its radius of curvature is increased thereby decreasing the field intensity in the vicinity of the point and slightly increasing the field on the cathode (Naidu and Kamaraju, 2007), Fofana and Beroual 2002).
If the voltage between the electrodes is sufficiently high an avalanche begins on the right hand side of the volume charge which by mixing with the positive ions of the volume charge creates an embryo of the canal (anode streamers). The charges of the plasma of the streamer are situated in an electric field so that there are surplus positive charges. The charges partly compensate the field in the canal of the streamer itself and create increased intensity at its head. Presence of a region of strong field before the head ensures formation of new avalanches, the electrons of which are attracted in the canal of the streamer and ions establish the positive volume charges which lead to further increase of field before the head of the streamer. The newly formed avalanches convert this volume charges into the continuity of the canal of the streamer and this gradually spread to the cathode. The streamer growth for positive point electrode is shown in fig. 1.
illustration not visible in this excerpt
Fig. 1: Streamer Growth for Positive Point Electrode
Effect of humidity on breakdown voltage
Humidity in air exerts some significant influence on the breakdown voltage. According to data of Ritz (Razevig, 2007) an increase of absolute humidity of air from 10 to 25mm of Hg. column at normal atmospheric pressure of gap d = 1cm between electrodes increases the breakdown voltage by 2% in a uniform field. Kuffels investigation (Razevig, 2007, Fengnian 2003) for breakdown of air at normal atmospheric pressure showed that with smaller gap up to 20mm of Hg, the breakdown voltage increases from 4 – 5% in 85% relative humidity than in dry air. Figure 2 shows the effect of humidity on the breakdown voltage of a 25cm diameter spheres with spacing of 1cm when a.c and d.c voltages are applied. The spark over voltage increases with partial pressure of water vapour in air, and or a given humidity condition, the charge in spark over voltage increase with the gap length.
The increase in breakdown voltage with increase of humidity is due to the fact that water vapour is electronegative gas. An increase of content of electronegative gas causes arrest of a large number of electrons with the formation of negative ions, as a result of which, the number of ionizing particles in the gap decreases and the breakdown voltage increases. However, in sharply nonuniform field the effect of humidity is considerably more. Usually, the effect of humidity of air is determined according to deviation from the breakdown voltage of standard humidity.
If the spark over voltage is V under test condition of temperature T and pressure P torr and if the spark over voltage is under standard condition of temperature:
Where k is a function of the air density factor d, which is given by:
The relationship between d and k is given in table 1.
illustration not visible in this excerpt
Fig 2: Humidity on breakdown Voltage for a.c and d.c for 25cm diameter spheres

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