Abstract
A simple fractional order nonlinear supercapacitors (SCs) electrical model has been established, taking into account the parameter variation, diffusion control and Faraday process. Frequency responses resulting from impedance spectroscopies around various operating voltages demonstrated that a SC exhibits a nonlinear behaviour in relation to the operating voltage. The model parameters are identified using fractional vector fitting and then a nonlinear model taking voltage dependency into account is obtained. Through building fractional order differential operator module in Simulink, the numerical solution of fractional order nonlinear calculus equation can be obtained directly. The model accuracy is verified through a comparison with the charging and discharing experimental results.
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