Jinder Jow

A water treeing model

A new model for water treeing is introduced. It assumes that when the field-induced stress applied on nano cavities filled with a liquid is larger than the yield strength of the polymer, bonds will be broken and the nano cavity will expand. The growth of the water trees is enhanced by the fatigue induced by the alternating electric field. The diffusion of the liquid is also a parameter affecting the water tree length. A simple equation relating the water tree length with field, time, frequency, and the nature of the solution is presented. A very good agreement between theory and experiments for a wide variety of results obtained with low density polyethylene (LDPE) tested under various fields, frequencies and ionic solutions is observed. This model also predicts the growth of water trees under DC fields after very long times or after many polarity reversals. Some aspects of this model requiring further refinements or experimental data are also pointed out.

Influence of frequency on water tree growth in various test cells

It is well known that water treeing in polyethylene (PE) is sensitive to frequency, but there is not yet a reliable analytic model describing this empirical observation. We show from existing published data that the length L of water trees grown in the laboratory under one given ionic solution varies linearly when plotted as log L vs. log N/sub 1/ where N is the number of field cycles. This relation is nearly independent of the applied field, suggesting a fatigue-like process. Ion concentration has only a slight influence on watertree length, especially after long aging. It was observed also that field aging and thermal aging reduce the watertree length. Some authors have suggested that there is an upper frequency limit above which water treeing would be independent of frequency. We have observed that the relationship log L vs. log N deviates from its linear behavior between 30 and 445 kHz. More work is needed to define more precisely the upper frequency limit. This means that accelerated aging for watertree degradation could be done at high frequency and results could then be translated reliably to power frequency. Finally, the fact that all experimental data obtained with one given ion obey the same relation regardless of types of the test cells indicates that results obtained with one given cell can be compared directly to those obtained with any other cell. Practical considerations also are discussed briefly.

Influence of frequency on water treeing in polyethylene

Water treeing depends on many parameters, especially frequency. We have reviewed the literature for water trees grown in polyethylene soaked at room temperature in distilled water and various NaCl solutions. All existing data obtained with water needle electrodes (Ascraft cells) obey one single relationship between water-tree length and the number of field cycles, i.e. the frequency/spl times/time. The upper frequency limit of this process appears to be in the 30 kHz range. The effect of ion concentration is more influential for a large number of field cycles (above 10/sup 8/ cycles), but is not as significant as the frequency effect. The field calculated at water needle defect, ranging from 80 to 600 kV/mm, has little influence on water tree length. The practical impact of these observations is briefly discussed.

Material differentiation by water treeing tests

Because of the importance of water treeing in underground medium voltage cables and the interest in preventing it, many accelerated material test methods and tree retardant materials have been developed. In this paper, several accelerated material water tree tests are reviewed. Three commercially introduced tree retardant materials were evaluated by the ASTM D6097 water treeing test under various conditions. The test parameters included aging time, temperature, water conductivity, applied voltage level, and frequency. As expected, the length of water tree increases with these factors, except temperature. Temperatures, higher than end use conditions should not be used as an acceleration factor. Not all tree retardant materials have the same water tree retardance, since each tree retardant material shows different response to the test parameters. A good tree retardant material should be very effective at various aging conditions. A higher water conductivity or longer aging time is recommended for better material differentiation in the ASTM D6097 test.

A new model for water tree propagation

A quantitative, physical model for water tree formation based on Zellers concept is presented. The water tree is assumed to be composed of cavities filled with aqueous salts connected by narrow cylindrical conducting links. This structure is formed in the amorphous region of a polymer. The difference in conductivity between the links and cavities and the un-treed polymer, introduces an electrical contribution to the free energy difference between these two regions under an ac electric field. Consequently, there is a pressure difference that acts to force aqueous sails into the un-treed polymer and to establish, first, a conducting link capable of transporting the salt under pressure, and second, a new cavity when the pressure builds up suitably at the end of the link. At all times the pressure gradient is directed away from the pre-existing tree structure. Our model suggests that there is no need to deform the polymer to form the link, and that the pressure difference is sufficient to force enough aqueous salts into the free volume to form a percolation system along the link cylinder. Expressions have been derived for the time required to form a link or a cavity in terms of the flow rate of aqueous salt into and through the link. This physically based model is suitable for computer simulation by defining a matrix of incipient links with nodes acting as incipient.

Stochastic simulation of water treeing in heterogeneous media using a field enhancement equation

Water treeing simulation using a field enhancement equation is performed in this study. Tree shape and growth time are stochastically governed by growth probability directly proportional to the enhanced local stress when it is greater than tree inception strength. Trees grow only if a growth criterion (a dimensionless treeing number /spl ges/1) is met. The heterogeneous media are composed of one of four heterogeneous inclusions randomly distributed in a homogeneous matrix. A tree can grow into type I and II, toward but not into type III, and always around type IV inclusions. The treeing number is less than 1 for type II but not for type I. Of course, it is irrelevant to type III and IV. The effects of the presence of each inclusion type at various percentages and sizes on tree shape and growth time are studied. Some of the simulated tree shapes are close to those observed in our laboratory studies. In general, the order from long to short growth time is from type III, II, I, to IV. The physical implication for each inclusion type is also given.