Optimized fractional order resonant model of supercapacitors based in error dominant frequency mitigation

A fractional order model for supercapacitors and a method for obtaining its parameters were proposed based in the association between a simplified model of one integer order capacitor (RC) with a fractional order parallel RLC impedance. Like all parallel RLC impedances, the fractional order parallel RLC impedance has a resonance frequency, however its response depends substantially on the fractional order, making it an important parameter for fitting the model to experimental data. Through the analysis of experimental galvanostatic charge and discharge curve and the application of a heuristic optimization algorithm, the parameters of the proposed model were obtained, pursuing to remove the main frequency component of the error between the data and the RC simplified model. The results demonstrated that the model obtained actually minimized the dominant frequency of the error and also resulted in a decrease in components at other frequencies, highlighting the advantage of the fractional order applied in the RLC proposed model.