Two-dimensional (2D) porous materials with high specific surface area and ordered morphology exhibit great potential as supercapacitor electrodes. The fundamental understanding of the charge storage and charging dynamics of 2D porous materials can help the optimal design of supercapacitors. Herein, we investigated the energy storage, including the double layer and quantum capacitances, of supercapacitors with typical 2D porous graphynes in the ionic liquid electrolyte by combining molecular dynamics simulation and density functional theory. Simulations revealed that supercapacitors with porous graphyne electrodes could obtain excellent double-layer capacitances, but their total capacitances are limited by the low quantum capacitances. We further predicted boron-/nitrogen-doped graphynes and found that the new porous graphynes turn into good conductors after doping and could achieve a quite high quantum capacitance. The charging dynamics in nanoscale and capacitive performance in macroscale based on the predicted graphyne electrodes were evaluated by combining molecular simulation and transmission line model. Results demonstrate that both outstanding gravimetric and volumetric energy and power densities could be obtained in doped porous graphyne supercapacitors. These findings pave the way for understanding energy storage mechanisms and designing high-performance supercapacitors.