The presence of bubbles and impurities, influenced by various external factors, has a significant impact on the operational condition of the transformer. In this study, a two-phase flow model with rod-plate electrodes was constructed based on the phase-field method to characterize the spatial distribution of non-uniform electric fields under the coupled effects of electric, thermal, and fluid fields. Numerical simulations were performed to analyze the effects of bubble size, number, and different voltage levels on bubble deformation, motion trajectory, and the extent of internal electric field distortion. The results indicate that during the vertical ascent phase, the bubbles undergo deformation perpendicular to the electric field direction, and during the slope ascent phase, they deform along the electric field direction. With an increase in voltage level, the stretching and repulsion of the bubbles by the electric field force also increase. There is a positive correlation between bubble size, voltage level, and the degree of distortion of the maximum electric field strength inside the bubbles. Coalescence of multiple bubbles leads to irregular shape changes and non-uniform distribution of polarized charge on their surface. However, the internal maximum electric field strength tends to increase with an increasing number of bubbles.