Comparison of two LPV fractional models used for ultracapacitor identification

This paper deals with the comparison of two LTI fractional models allowing the identification of an ultracapacitor impedance using input current data and output induced low level voltage variation measurements around an initial bias voltage in the time domain. Both models are issued from the analysis of the porous nature of the electrodes. The first one, based on a 1-pore model structure has already been developped in previous works and will be used as a reference model. The second one, based on a multipore model, leads to a new more complex fractional model based on the sum of two fractional integrators of non integer order. The interest of this new modeling is discussed. For both models, the double layer capacitance depends on the voltage. So, in order to explicitly take into account the dependence of the system dynamics on the operating voltage, fractional continuous LPV models are used and determined thanks to a local approach composed of two steps. First, the local LTI fractional model parameters are estimated thanks to an output-error technique at different bias voltages. Secondly, the parameter estimates dependence with respect to the operating voltage is obtained by using cubic spline interpolation. The resulting LPV fractional models performances are compared on an experimental ultracapacitor bench.