Extensive Validation of the Three-Branch Model in Simulating the Static and the Dynamic Behavior of EDLC Supercapacitors

This study demonstrates the response of the three-branch equivalent circuit model in reproducing the terminal voltage of a supercapacitor that undergoes dynamic galvanostatic pulse trains for frequencies from 0.1 Hz to 100 Hz and signal amplitudes of 1 A, significantly wider than the sinusoidal signals used in impedance spectroscopy. Clean and accurate pulse trains were generated at different frequencies using a transconductance power amplifier, and the voltages at the supercapacitor terminals of three different sizes of supercapacitors were successfully compared with the model. The latter was also utilized to check its ability to accurately reproduce charging and self-discharging processes and the ability to simulate voltammetric cycles. This was verified for six supercapacitor sizes from 1 F (rated 1 mWh, 10 W) up to a large 130 F module (rated 70 Wh, 144 kW). In all cases, the relative difference, with respect to the rated voltage, between the terminal voltage provided by the measurements and that yielded by the model simulations did not exceed 3.5%. This extensive multi-level validation demonstrates how the identified three-branch model based on state equations can provide an accurate electrical design tool and a reference for standards.