A stress cone for reducing electrical stresses is disclosed for use on terminated ends of tubing encapsulated power cable used in surface applications in a subsurface well power system employing electric submersible pumps (ESPs). The stress cone comprises an annular section about a longitudinal axis for receiving a terminated end of the TEPC in its first end and for abutting the terminated metal TEPC end against a metal shoulder at its second end therein, and an insulation chamber axially aligned with and connected to the annular section. The chamber comprises a metal interior surface symmetrical about the axis. The insulated TEPC core (without outer metal sheath) passes through the insulation chamber along the axis and then exits. The ID of the TEPC metal sheath and the inside metal surface of the chamber form a smooth ground plane transition surface. Insulation material surrounds the TEPC insulation layer within the insulation chamber.