The electrical discharge and breakdown characteristics of a triple junction (TJ) in high voltage (HV) electrical insulation are becoming an important issue in recent industrial applications. In this paper, a comparative study is conducted between three insulation materials used in HV: silicone, porcelain, and heat tempered glass, with electrode shape parameters such as inter-electrode distance (d), applied voltage (V), and geometry investigated for positive polarity, using an experimental approach. For optimum test organization to support our research and highlight the parameters and their interactions, we have established a mathematical regression model of the discharge current. It is polynomial, with good performance and a high level of precision. Besides, this yields one monovariable and another two-variable quadratic model. The latter can simulate the electric discharge simultaneously with two variables: V and d, and an adjusted determination coefficient () of nearly 0.99. Consequently, the two-variable quadratic model has been adapted to V and d ranges of 10 to 50 kV and 1.9 to 8 cm, respectively. Finally, this study provides us with new applicable knowledge about the TJ effect on electrical insulation with recommendations to optimize the design for higher performance.