Ultracapacitors experience some level of internal resistance, referred to as "equivalent series resistance (ESR)," which occurs when the materials used in the ultracapacitor resist the passage of the charges from one plate to another. The amount of ESR varies depending on the particular characteristics (materials used, quality, etc.) of the ultracapacitor.
ESR (referred to as Rs in the diagram below) is the main contributor to power loss during ultracapacitor charging and discharging. The other contributing factors are parallel resistance (Rp), capacitance (C), and the series inductor (Ls).
Since Rp is always much larger than Rs, it can be ignored. Also, because of the porous material used on the electrodes of ultracapacitors, they exhibit non-ideal behavior, which causes the capacitance and resistance to be distributed such that the electrical response mimics transmission line behavior. Therefore, it is necessary to use a more general circuit, as shown in the figure below, to represent the real electrical response and ESR effect.