Simulating electron-avalanche-driven positive streamers in dielectric liquids

Summary of thesis: The thesis presents a novel predictive model for simulating positive streamers in dielectric liquids. Such liquids are commonly used for electrical insulation of high-power equipment, for example power transformers, which are essential parts of the electrical distribution network. A ``streamer'' is the phenomenon leading to electrical breakdown in dielectric liquids. Modeling and simulating streamers to better understand the phenomenon is crucial to improve the performance of electrical insulation and electrical equipment alike. Streamer propagation is modeled in a needle--plane electrode gap, with cyclohexane as a model for the insulating liquid. The needle and the extremities of the streamer (streamer heads) are modeled by hyperboloids. In the strong electric field, close to the needle or the streamer, electrons detach from anions and form electron avalanches. The streamer grows when the size of an avalanche exceeds the Townsend--Meek criterion. Each streamer head is modeled as an RC-circuit to calculate its potential. Resistance in the channel and capacitance in the gap towards the planar electrode are taken into consideration. A high electric field within a channel can give a breakdown, a reillumination of the channel, equalizing the potential of the needle and the streamer head. The streamer transitions into a fast mode of propagation when radiation from the streamer head causes photoionization. This occurs when the field-dependent ionization potential is reduced below the energy of this radiation. The streamer conductivity regulates the propagation speed, and reilluminations increase the average conductivity. Simulated streamers can change from fast to slow mode if the conductivity of the channel is low. Conversely, the streamer can change to a fast mode during propagation if the conductivity is high. This change can be triggered by a reillumination. The work demonstrates that an avalanche-driven streamer breakdown is possible. However, the propagation voltage is high compared to experiments. The limitations of the model are discussed and several possible improvements are suggested. The software developed to simulate the model is published as open-source software