| Summary: | A variable fractional-order equivalent circuit model is proposed to accurately describe the dynamic characteristics of lithium-ion batteries (LIBs). Firstly, a fractional impedance model (FIM) is established, such that the fractional-order (FO) is a polynomial function of the LIB state of charge (<i>SOC</i>). Then, a chaotic adaptive fractional particle swarm optimization (CAFPSO) method is derived to identify the parameters of the FIM. Experiments reveal the reliability of the novel approach through the root-mean-squared error (RMSE) and the mean absolute error (MAE) of the LIB terminals voltage, yielding the values 8.99 mV and 4.56 mV, respectively. This translates into accuracy improvements of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>22.5</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>34.4</mn><mo>%</mo></mrow></semantics></math></inline-formula> for the particle swarm optimization (PSO) algorithm and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>57.9</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>72.8</mn><mo>%</mo></mrow></semantics></math></inline-formula> for the adaptive fractional particle swarm optimization (AFPSO) algorithm, respectively.
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