It is important to control layer current distributions of coaxial multi-layer HTS cables, because a homogeneous layer current distribution decreases AC loss and can supply the largest operational current. We have extended the theory that treat the operational current more than the critical current by considering V-I nonlinear characteristics of HTS tapes including flux flow resistance and contacting resistance between the cable and terminals. It is important to investigate the current distribution under the condition of operational current more than the critical current of cable, because the cable has experiences of fault current. In order to verify the extended theory, we have fabricated a two layers cable with the same twisting layer pitch. It was observed that almost all the operational current less than the critical current flowed on the outer layer because of its lower inductance. In case of operational current more than critical currents of layers, the flux flow resistances affect strongly current waveform and thereby the currents of layers were determined by the flux flow resistances. And we investigated breakdown characteristics in $LN_{2}$/paper composite insulation system for the application to a HTS cable. In this experiment, we got some information out of that the electrical characteristics of the insulation materials depends on the condition of butt gap.