With the increase of grid voltage and system capacity

internal faults like discharge phenomenon frequently occur in gas insulated switchgears（GIS）. Based on virtual boundary and multi-layer boundary

the finite element method was used to establish an analytical model of three-phase compact GIS with metal protrusions at different positions. Moreover

the distribution of the internal potential and electric field intensity was calculated

and a new concept of second-order sensitivity coefficient α was proposed to analyze the sensitivity of regional field intensity distortion to the change of metal protrusion’s height and radius. It is found that the electric field generated by metal protrusions on high voltage conductor is 2～9 times greater than that by protrusions on the enclosure under same conditions. Besides

it is found that the sensitivity of field strength in high voltage conductor to the radius and height of metal protrusion is basically identical

while

for protrusions on enclosure

the electric field distortion is about twice as high as the sensitivity of the radius. Finally

the calculated maximum electric field strength value is compared with the critical breakdown field strength value of SF6

and the security domain is obtained for metal protrusions at different positions. The study is of great significance to the actual operation and maintenance of GISs in the power system.