Equivalent circuit modeling of a supercapacitor bank with variable capacitance and lossless dynamic balancing

There are several equivalent circuit models for supercapacitors (SCs). Although series RC models are often considered insufficient, more advanced models, such as the single-branch variable capacitance model, offer excellent accuracy in fast charge and discharge cycles. However, the complexity of associating cells with variable capacitance has limited their use in SC banks, where the constant capacitance model is typically used. This article addresses this limitation by presenting, for the first time, the necessary conditions and formulas for associating variable capacitance SCs, so that the equivalent circuit maintains the same modeling. The most relevant conclusion of the study is the demonstration that, when a large number of variable-capacitance SCs are connected in series, the assembly converges to the behavior of a constant capacitance SC.