This paper presents an evaluation of commercial supercapacitors performance (ESR, C, self-discharge, Pmax, Emax, coulumbic efficiency, etc), under different conditions. Characterization of supercapacitor performances as a function of current, voltage, frequency and thermal constraints, is carried out by constant current test, electrochemical impedance spectroscopy, and voltamperometry. A comparative study of measurement techniques is conducted in detail in this work. The supercapacitor self-discharge amplitude is determined by measuring the decline of open-circuit voltage. The mechanisms of the self-discharge, leakage current and diffusion of ions at the electrode-electrolyte interfaces are modelled by a new electrical equivalent circuit. In addition, we model the electrochemical impedance of self-discharge with diffusion-controlled in frequency domain. Supercapacitor is represented by two complementary electrical equivalent circuits: two branches and non-homogeny pores. The first represents the supercapacitor time behaviour. The second represents supercapacitor dynamic behaviour. Finally, the origin and a new model of pseudoinductance are described.