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, 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.