How to Measure and Calculate Equivalent Series Resistance of Electric Double-Layer Capacitors

Electric double-layer capacitors (EDLCs) are energy storage devices that have attracted attention from the scientific community due to their high specific power storage capabilities. The standard method for determining the maximum power (P_max) of these devices uses the relation P_max = U²/4R_ESR, where U stands for the cell voltage and R_ESR for the equivalent series resistance. Despite the relevance of R_ESR, one can observe a lack of consensus in the literature regarding the determination of this parameter from the galvanostatic charge-discharge findings. In addition, a literature survey revealed that roughly half of the scientific papers have calculated the R_ESR values using the electrochemical impedance spectroscopy (EIS) technique, while the other half used the galvanostatic charge discharge (GCD) method. R_ESR values extracted from EIS at high frequencies (>10 kHz) do not depend on the particular equivalent circuit model. However, the conventional GCD method better resembles the real situation of the device operation, and thus its use is of paramount importance for practical purposes. In the latter case, the voltage drop (ΔU) verified at the charge-discharge transition for a given applied current (I) is used in conjunction with Ohm's law to obtain the R_ESR (e.g., R_ESR = ΔU/ΔI). However, several papers have caused a great confusion in the literature considering only applied current (I). In order to shed light on this important subject, we report in this work a rational analysis regarding the GCD method in order to prove that to obtain reliable R_ESR values the voltage drop must be normalized by a factor of two (e.g., R_ESR = ΔU/2I).