Quantitative modeling of factors determining Ragone plots for batteries and electrochemical capacitors

Ragone plots relating power-density to achievable energy-density have been used for many years as an empirical basis for comparative performance evaluation of various battery systems. However, their theoretical basis, and the relative contributions of ohmic and activation (Tafel) polarization effects to the dependence of energy-density on operating power-density have been little studied. Quantitative modeling calculations for various selected values of ohmic resistance, and Tafel exchange-current densities and polarization slopes, b, provide rationalizations for the shape of Ragone diagrams and their positions in the log-log plane of energy-density versus power-density plots. Separate evaluations of the ohmic and Tafel polarization 'components' of the Ragone relations are of practical value in the evaluation of the battery performance. The Tafel value b is of special importance. Complications which arise in trying to represent electrochemical capacitor behaviour in terms of Ragone-type plots are analysed; they are important for the design and operation of hybrid capacitor/battery systems for electric-vehicle drive trains.