Role of number of consecutive voltage zero-crossings in propagation of water trees in polyethylene

Effects of superposition of a low-frequency (0.1 to 50 Hz) voltage and a high-frequency 2 kHz voltage on the growth of water trees in polyethylene are examined. It has become clear that both the number of total voltage zero-crossings during the whole voltage application period and the number of consecutive voltage zero-crossings in the instant of the polarity reversal of the low-frequency voltage play important roles in the length and shape of water trees. Namely, the water tree length becomes longer as the number of total zero-crossings increases. Furthermore, among the voltages with the same number of total zero-crossings, the length becomes even longer with a prolonged shape in the direction of electric field as the number of consecutive zero-crossings increases. Effects of superposition of a high-frequency voltage onto a dc voltage are also examined. In this case, the dc voltage seems not to have any influence to the tree growth. By assuming the presence of space charge around the water-tree tip, the effective zero-crossings become only sensitive to the high-frequency component. Therefore, this result also indicates that the number of voltage reversals at the tree tip plays a crucial role in the growth of water trees.