Fractal analysis of streamer patterns in transformer oil under lightning impulse voltage

The insulation of dielectric liquids is of great importance for safe operation of transformers. It is generally recognized that the breakdown happens when streamers completely bridge two conductors inside the transformer, leading to insulation failure. The propagation shapes of streamers can be obtained with the help of optical technology and be analyzed qualitatively. Fractal dimension has been increasingly used to quantitatively describe the complexity of a pre-breakdown phenomenon, i.e. electrical treeing in solid insulating materials. In transformer oil, there is a great need for accurate quantitative analysis on streamer propagation patterns by using fractal dimension in consideration of the deviation of visual judgment, which is commonly used at present. In this paper, fractal dimension analysis was introduced to quantitatively study the denseness of streamer propagation patterns in transformer oil under lightning impulse voltage. The fractal dimensions of streamer patterns at different stages and voltage levels were calculated based on box counting method. Results indicate that the fractal dimension is closely related to propagation time and applied voltage. With the propagation time, streamer length increases firstly and then decreases. Different from that, the curve of fractal dimension with time shows two peaks, which is the embodiment of the transformation of streamer patterns. In addition, the fractal dimension increases with the applied voltage. The relation between streamer propagation characteristic and fractal dimension is proposed.