Toward the practical applications, on operation of conduction-cooled HTS SMES at temperatures well below 77 K should be investigated, in order to take advantage of a greater critical current density of HTS and considerably reduce the size and weight of the system. Recently, research and development concerning application of the conduction-cooled HTS SMES that is easily movement are actively progressing in Korea. Electrical insulation under cryogenic temperature is a key and an important element in the application of this apparatus. Using multi wrapped copper by Polyimide film for HTS SMES, the breakdown characteristics of models for turn-to-turn, that is surface contact model, were investigated under ac and impulse voltage at 77 K. A material that is Polyimide film (Kapton) 0.025 mm thickness is used for multi wrapping of the electrode. Statistical analysis of the results using Weibull distribution to examine the wrapping number effects on breakdown voltage under at and impulse voltage in $LN_2$ was carried.