Based on the energy theory

this paper proposes an evaluation method for the breakdown failure probability of the tri-post insulator in a gas-insulated metal-enclosed transmission line (GIL). Various internal defects

vector forces and torque forces were considered

along with the application of an AC voltage. Both the simulation and experimental results show that the breakdown channel of the insulator with a GND (ground) defect is a straight line

whereas that of the insulator with a HV defect is bending. As the angle α between the vector force and the axis of the insulator leg increases

the failure probability of the insulator increases

and the effect of the vector force on breakdown transitions from suppression to promotion. When subjected to the gravity of the insulator and the conductor

the insulator in the horizontally laid GIL presents a lower failure probability compared to that in the vertically laid GIL. Moreover

the breakdown failure probability is lowest when the three legs of the insulator are arranged in the 60°

180° and 300° directions. The torque force noticeably deflects the breakdown channel in the direction of the torque due to the asymmetric distribution of the strain energy density along the axis of the insulator leg. This study aims to provide theoretical guidance for evaluating the breakdown failure probability of insulators.