Partial discharge poses a serious threat to the insulation performance of electrical equipment，with streamer discharge being the main form of gas discharge in high-voltage fields and a key issue in the study of gas gap discharge. Due to the influence of external factors such as humidity and air pressure during the operation of electrical equipment，studying the effects of different external conditions on insulation defect discharge is of great significance for the design and operation of transmission lines and substations in high-altitude （low-pressure） and high-humidity areas. The current research status of the impact of external conditions on the discharge process at home and abroad is analyzed in this paper. Based on the fluid dynamics model，a simulation model of streamer discharge at sharp defects is established in the COMSOL environment. Using this model，the influence of external conditions on the streamer discharge process of sharp defects with a gap distance of 3 mm is studied. The research results indicate that a decrease in air pressure accelerates the propagation speed of the streamer，slightly reduces the maximum electric field intensity at the streamer head，and exacerbates the ionization degree of the streamer discharge. An increase in humidity accelerates the propagation speed of the streamer，with little impact on the maximum electric field intensity at the streamer head but exacerbates the ionization degree of the streamer discharge. Taking the example of a streamer head distance of 1.5 mm from the cathode，a decrease in air pressure from 101.325 kPa to 81.060 kPa results in an acceleration of streamer propagation speed by 0.56$ \text{×}{\text{10}}^{\text{6}} $ m/s，a decrease in head electric field intensity by 0.633$ \text{×}{\text{10}}^{\text{6}} $ V/m，and an increase in head luminosity by 1.675$ \text{×}{\text{10}}^{\text{28}}\;{\text{m}}^{{-3}}/\text{s} $. An increase in humidity from 3.04 g$ \text{/}{\text{m}}^{\text{3}} $ to 13.04 g$ \text{/}{\text{m}}^{\text{3}} $ results in an acceleration of streamer propagation speed by 0.08$ \text{×}{\text{10}}^{\text{6}\text{}} $ m/s，a decrease in head electric field intensity by 0.015$ \text{×}{\text{10}}^{\text{6}} $ V/m，and an increase in head luminosity by 0.865$ \text{×}{\text{10}}^{\text{28}}\;{\text{m}}^{{-3}}/\text{s} $.