Precise Sizing of Supercapacitor Packs by Accurate Prediction of Energy Using Fractional Order Model

Designing a supercapacitor (SC) pack for any application involves choosing the optimum value of capacitance that meets the energy and power demands of the application. However, this is not straight forward due to the nonlinear variation of the value of capacitance with operating conditions. The conventional sizing methodology determines the capacitance value by equating the energy demand with the energy predicted using the RC model. It assumes a constant capacitance value, which results in over sizing of the SC pack. To overcome this drawback, this article proposes a fractional order (FO) model (FOM) based method to accurately predict the stored energy in SC pack. Although FOM accounts for the nonlinear capacitance variation due to the charge redistribution in the porous SC electrodes, there are certain shortcomings. First, the identification of the FOM parameters is cumbersome due to their dependence on the charge/discharge history. Second, the scaling of the FOM parameters from cell to pack level for the performance analysis of SC systems is not clearly addressed so far. Considering these, a predictor-corrector methodology for SC pack sizing is proposed. A rough estimate of the number of SC modules for meeting the specified energy and power demand is determined in the prediction stage. The correction stage evaluates the power, energy and efficiency of the selected module with FOM parameters and adjusts the sizing. The proposed methodology is then validated with a case study on a supercapacitor-based city bus, where a 27% reduction in sizing is observed.