Accurate Parameters Identification of a Supercapacitor Three-Branch Model

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 have been 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 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. Using 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.