An electrical submersible well pump assembly includes a pump driven by an electrical motor. A string of tubing connects to the well pump assembly and extends to an upper end of a well. A power cable installed in the tubing has three insulated electrical conductors embedded within an elastomeric jacket. A metal strip has turns wrapped helically around the jacket. The metal strip is compressed between the jacket and the tubing to cause the power cable to frictionally grip the tubing.