This paper discusses electrical insulation characteristics at cryogenic temperature, especially focusing on partial discharge (PD) inception characteristics, for high temperature superconducting cables. In liquid nitrogen (L$N_2$) / polypropylene (PP) laminated paper composite insulation system, PD inception strength (PDIE) was evaluated in terms of volume effect and V-t characteristics. Different kinds of butt gap condition were applied in the experiments, using parallel plane and coaxial cylindrical cable samples. Experimental results revealed that the volume effect on PDIE could be evaluated by the statistical stressed liquid volume (SSLV) taking account the discharge probability not only in the butt gap but also in the other thin layers between PP laminated papers. Furthermore, the indices n of V-t characteristics at PD inception were estimated to be 80∼110, irrespective of the butt gap condition.