Abstract: In order to solve the general calculation of induced voltage in single core cable metal sleeves under the action of power frequency balance current, a detailed derivation and analysis of induced voltage in high-voltage single core cable metal sleeves are carried out. A general calculation formula for induced voltage in high-voltage cable metal sleeves is given. Compared with the scattered calculation formulas given in standard GB 50217-2018, it is more helpful to understand the principle and influencing factors of metal induced voltage, and the derived calculation formula is more universal and applicable to various laying conditions. In addition, the principle of the "3:7" arrangement of the auxiliary ground wire is derived, and it is demonstrated that under normal operating conditions, the " 3:7 " arrangement of the auxiliary ground wire has no effect on the induced voltage of the metal sleeve. Provide theoretical reference for the calculation of induced voltage in the metal sheath of single core cables.