Development of a Coupled Electrical, Thermal and Degradation Supercapacitor Model for Automotive Applications

Despite the fact that supercapacitors are less complex than lithium ion batteries, they are less well understood. Although supercapacitors do not possess sufficient energy density to make them suitable as the only source of energy storage in the majority of applications, they are ideal as a buffer for the primary energy source. Applied to hybrid and electric cars, supercapacitors can be used to reduce the degradation and power requirements of the primary energy source, typically lithium ion batteries.  

To the best of the author’s knowledge, currently, no unified, high fidelity, electrical, thermal and degradation model exists of a supercapacitor that meets automotive requirements. This is because the electrical and thermal models must re-create both short term and long term cell behavior over a large range of temperatures, frequencies, and currents. They must also include degradation models that are valid under complex cycling conditions and not simply under constant current cycling.

The state-of-the-art electrical models of a supercapacitor are equivalent circuit models, which utilize a de-Levie transmission line. The length of the transmission line is analogous to the path length of an ion from its initial location to forming part of the electrical double layer, or pore depth penetration. Thus, the transmission line can be utilised to either model the available electrode surface for ion adsorption, and hence capacitance variation with frequency, or model the charge distribution throughout the porous structure, and hence determine voltage hysteresis as a result of charge re-distribution. The standard de-Levie transmission line cannot be used to characterize both of these effects simultaneously, (which is necessary for automotive requirements) without being adapted.

The majority of supercapacitor thermal models are either lumped models or axi-symmetric models utilizing an assumption of uniform heat generation. Although these models are suitable for determining thermal management strategies, and degradation under steady state conditions, they are unsuitable for determining degradation in highly dynamic systems. They are unable to predict localized hotspots at the electrode/electrolyte interface, which are caused by the entropy effects of the generation or breakdown of the electrical double layer. Furthermore, they are unable to predict the temperature difference between the positive and negative terminals. 

This talk will outline the development and validation of a new equivalent circuit model of a supercapacitor for automotive use. The electrical model is capable of reproducing cell behavior, including power limits, variation of capacitance and resistance with operating temperature and frequency, charge re-distribution and self-discharge. The coupled thermal model is capable of predicting reversible and irreversible heat generation and its spatial distribution throughout the cell, and the resultant degradation.