A mathematical model of heterogeneous electrochemical supercapacitors (HES) is proposed which makes it possible to develop capacitors with optimal designs and make calculations of their energy, capacity, and power parameters. Special attention is paid to the processes which occur in electrodes with double electric layer (DEL) of HES capacitors during their charge and discharge by different currents. It is demonstrated theoretically that in the efficiency of HES capacitors' operation, an important role is played by distribution of the potential along the thickness of electrodes with DEL. In order to build capacitors with improved parameters and optimal design, it is of paramount importance to take account of the type and value of conductivity of the material of the electrode with DEL and conductivity of the electrolyte in its pores. Analysis is performed to determine the efficiency of PbO2 parallel to H2SO4 parallel to C system capacitors' operation subject to thickness, conductivity, and specific capacitance of the electrode with DEL. It is established that energy and capacity parameters of the capacitors depend to a great extent on conductivity of their negative electrodes and electrolytes. It is demonstrated that there are different mechanisms of losses of energy and charge of the capacitors during their charge, discharge, and storage.