LPV continuous fractional modeling applied to ultracapacitor impedance identification

• Ultracapacitor impedance is identified thanks to fractional modeling.
• The fractional model parameters voltage dependence is experimentally evidenced.
• LPV modeling allows to synthesize a set of LTI fractional models.
• The fractional LPV model estimates properly non-linear high level voltage dynamics.

This paper deals with the non-linear behavior of an ultracapacitor in relation to the operating voltage. The ultracapacitor impedance identification is then performed using a fractional continuous LPV model according to a local approach composed of two steps. First, the local LTI fractional impedance model is identified in the time domain at various bias voltages thanks to an output-error technique assuming a linear fractional impedance model issued from the physical description of the porous nature of the electrodes. Therefore, the excitation current is designed so as to induce low level voltage variation, compared with the considered operating voltage. Secondly, the model parameter dependence with respect to the operating voltage is obtained by using a cubic spline interpolation technique. The resulting LPV fractional model allows to synthesize a set of LTI models able to build low level voltage variation around different initial bias voltage. Furthermore, when using charging or discharging current sequence generating high level voltage, the LPV model allows to take into account the non-linear effects due to the fractional model parameters voltage dependence. The fractional LPV model is validated on an experimental ultracapacitor test bed and its advantages compared with the fractional LTI model is evidenced.