Validation and Sensitivity Analysis of a Fractional Order Model of a Lithium Ion Battery via Impedance Spectra and Temporal Duty Cycles

In this paper, a lumped fractional order model (FOM) is developed for a lithiumion battery (LIB). Electrochemical impedance spectroscopy (EIS) is used to obtain the cell impedance at different temperatures and SOCs, and at a wide range of frequencies. This data is used for the model parameterization which is a complex nonlinear least squares problem. A modified Levenberg-Marquardt algorithm is adopted to solve this problem. Two statistical measures, including sum of squares of residual and coefficient of determination are employed to incrementally build up on the integer order model (IOM) and obtain the final FOM. A derivative-based parameter sensitivity analysis is performed to study the influence of parameters on the model by considering their interactions. The terminal voltage of the FOM is simulated by mathematical approximation of the fractional derivative to study the model accuracy under temporal duty cycles. A comparative analysis between the fractional and integer order models is performed to gain insight on pros and cons of each model.