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Summary form only given. Mineral transformer oil is the most often used dielectric for electrical insulation and cooling in high power electrical equipment. As a result, transformer oil is widely researched and tested to better understand its electrical, chemical and thermal behavior in power transmission equipment. A large portion of this research is focused on understanding the mechanisms and steps that lead to electrical breakdown, as failure often has disastrous consequences. Previous studies have developed an electro-thermal hydrodynamic model which describes the formation and propagation of streamers leading to electrical breakdown in a needle-sphere electrode geometry. The focus of this paper is to evaluate the effect of applied lightning impulse voltage parameters, such as polarity, magnitude, duration, and rise and fall times on the streamers column diameter, head curvature and head velocity. Modeling results indicate that by increasing the applied voltage magnitude, the streamer velocity slowly increases until a critical voltage is reached, where an order of magnitude velocity increase is observed and the streamer transitions to a higher mode. Moreover, the results indicate that negative streamers initiate at almost twice the applied voltage magnitude and propagate slower than positive streamers at the same applied voltage magnitude and rise-time. These results are in agreement with experiments. In addition, this paper systematically investigates the influence of the applied voltage rise-time on streamer dynamics in transformer oil. From numerical studies, we found that in transformer oil at the same peak voltage, short rise-times create large diameter slow streamers, while a longer rise-time creates thinner streamers propagating faster.