An ultracapacitor model derived using time-dependent current profiles

A linear model of an ultracapacitor cell has been determined using time-domain identification techniques. A third-order transfer function consistent in form with an RC ladder circuit model is assumed. The transfer function coefficients are identified from experimental data consisting of time-varying current excitations and the first differences of the resulting terminal voltage responses. The model accurately matches the transient response of the cell over time intervals of about an hour. A longer charge-redistribution time constant (on the order of days) was also observed; however, this time constant has no significant effect in the one-hour timeframe, and is included in the model only as a dissipative term.