Supercapacitors are becoming increasingly important storage system components. To effectively control their terminal voltage, even in real time, numerous circuit models capable of faithfully simulating their behavior in energy systems and various applications are being explored. The three-branch supercapacitor model appears to be a good compromise between simplicity and accuracy. Typically, this model lacks accuracy in dynamic cycling and long stand-by periods. In this study, a new model identification method based on the state equations of the circuit is described and tested on a 400 F supercapacitor, and the obtained results are validated by measurements. Such an approach, suitably optimized, provides good agreement with the measurements, with discrepancies below 50 mV even in repeated cycles. In the static identification, after 90 minutes of self-discharge, the discrepancy was approximately 5 mV. The study also discusses the sensitivity of the model output to the circuit parameters, which is useful for choosing the appropriate timespan for parameter optimization and introduces variable leakage resistance and a method for its determination. Through this parameter, good agreement with the measurements is observed during the long self-discharging phases. A discrepancy of less than 50 mV between the measured and computed results is observed after one week. The union of the circuit state equations based model and the nonlinear leakage resistance determination allows the three-branch circuit model to achieve a high accuracy both in real-time simulation and in the presence of long stand-by phases.

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.