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Streamer branching in liquid dielectrics is driven by stochastic and deterministic factors. The presence of stochastic causes of streamer branching such as inhomogeneities inherited from noisy initial states, impurities, or charge carrier density fluctuations is inevitable in any dielectric. A fully three-dimensional streamer model presented in this paper indicates that deterministic origins of branching are intrinsic attributes of streamers, which in some cases make the branching inevitable depending on shape and velocity of the volume charge at the streamer frontier. Specifically, any given inhomogeneous perturbation can result in streamer branching if the volume charge layer at the original streamer head is relatively thin and slow enough. Furthermore, discrete nature of electrons at the leading edge of an ionization front always guarantees the existence of a non-zero inhomogeneous perturbation ahead of the streamer head propagating even in perfectly homogeneous dielectric. Based on the modeling results for streamers propagating in a liquid dielectric, a gauge on the streamer head geometry is introduced that determines whether the branching occurs under particular inhomogeneous circumstances. Estimated number, diameter, and velocity of the born branches agree qualitatively with experimental images of the streamer branching. V

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Theoretical images of streamers, revealing the mechanisms behind impulse breakdown in liquid dielectrics, are presented. Streamers form paths that are capable of carrying large current amplitudes through the electrode gap, leading to electrical breakdown. Breakdown delays are calculated for different electrode geometries (40 µm needle and 6.35 mm sphere) and gap distances (up to 10 mm) as well as time dependent currents through the gap. Modeling results indicate that the breakdown within needle-needle electrodes requires higher impulse voltage magnitudes than within needle-sphere electrodes for the same gap distances. Streamers in needlesphere geometries are about 50 percent thicker than streamers propagating in needle-needle geometries under similar impulse voltage amplitudes. A three-carrier continuum model 1 is utilized to account for the charge generation, recombination and transport mechanisms, which are critical in the study of streamers emanating from a needle electrode, with 40µm radius of curvature, propagating through a transformer oil based liquid dielectric volume and eventually reaching either grounded needle electrode (with the same radius of curvature) or sphere grounded electrode, with 6.35 mm radii of curvature. The governing equations that contain the physics to model streamer development are based on drift-dominated charge continuity equations for positive ion, negative ion and electron charge densities, coupled through Gauss' law. The thermal diffusion equation is included to model temperature variations and gas formation in oil. 2,3 The mobility dependencies on electric field intensity 4 (due to electron velocity saturation at extremely high electric fields) and temperature (due to lower viscosity of the fluid at high temperature) have been taken into account.Formation of streamers in transformer oil is mainly due to the field-dependent molecular ionization of hydrocarbon molecules at intense electric fields. 1 The field ionization is modeled using the Zener electron-tunneling function improved by Density Functional Theory (DFT). 1 Appropriate boundary conditions on electrode surfaces have also been assigned. 1,5 The electric field intensity just close to the electrode surface is higher around the points with smaller radius of curvature which is particularly true for a needle electrode defined by the IEC 60897. 6 This does not necessarily mean that the streamer breakdown occurs at lower voltages in a needle-needle gap rather than the needle-sphere electrode geometry. A sharp needle shape of the positive electrode assists the streamer initiation. However, if both electrodes are needles, the electric field in the middle of the gap will be relatively lower than what would be the case for the corresponding needle-sphere electrode geometry. This is caused by the fact that the a)