Embedded Fractional Nonlinear Supercapacitor Model and Its Parametric Estimation Method

This paper deals with a supercapacitor (SC) onboard model and its online identification procedure for embedded applications. To take into account its nonlinear behavior, the strategy used in this paper consists, as the first step, in the application of the porous electrode theory to the SC and the approximation of the resulting model. A set of fractional linear systems which are represented by a differential equation involving fractional derivatives is then obtained. Each element of this set represents the behavior of the SC only around one operating voltage. A global nonlinear model is then deduced through an integration method. An online identification procedure has been developed for this nonlinear model. This time identification is based on the mean least square method. Its time behavior has been compared with that of an SC cell for a specific current profile with different levels.