Fractal index of streamer patterns in insulating liquids under lightning impulse voltages

In insulating liquids, a breakdown event is the consequence of streamer initiation and propagation. A number of parameters such as stopping length, propagation velocity, and current and light pulses can be used to characterize the streamer phenomenon. In addition, it is recognized that the geometric patterns of streamers in insulating liquids are with a fractal nature and the shape complexity of streamer patterns can be analyzed by using fractal index, i.e. fractal dimension. This paper described the fractal features of streamer patterns in a synthetic ester insulating liquid under lightning impulse voltages. The fractal dimensions of streamer patterns at different propagation times and voltage levels were calculated by using box-counting method. Relationships between fractal index and other parameters such as stopping length and streamer area were finally presented. Results indicate that fractal dimension with propagation time and applied voltage follows the similar trend to streamer length and area. All of them generally increase with the increase of propagation time and applied voltage level.