The converter transformer, as the core equipment of the high-voltage direct current transmission system, plays a crucial role in the energy conversion and transmission within the electrical power system. Its operational state directly affects the safety and stability of the power system. Under the influence of an uneven electric field, partial discharge phenomena may occur inside the converter transformer. This process can be simulated and studied using the rod-plate electrode model. This research aims to investigate the partial discharge characteristics of the rod-plane electrode oil gap in transformer oil. Based on the theory of fluid dynamics drift-diffusion, a two-dimensional axisymmetric simulation model was established. By applying different voltage amplitudes, the microscopic discharge images under direct current electric field conditions, as well as the changing process of space charge and electric field strength distribution, were calculated. The simulation results indicate that with the increase of applied voltage amplitude, the generation number of charged particles in the discharge channel significantly grows, and the diffusion speed of space charge accelerates, causing it to move closer to the grounded electrode. This study holds significant theoretical value for a deeper understanding of the discharge mechanism in transformer oil.