A physics-based fractional order model and state of energy estimation for lithium ion batteries. Part I: Model development and observability analysis

The design of a lumped parameter battery model preserving physical meaning is especially desired by the automotive researchers and engineers due to the strong demand for battery system control, estimation, diagnosis and prognostics. In light of this, a novel simplified fractional order electrochemical model is developed for electric vehicle (EV) applications in this paper. In the model, a general fractional order transfer function is designed for the solid phase lithium ion diffusion approximation. The dynamic characteristics of the electrolyte concentration overpotential are approximated by a first-order resistance-capacitor transfer function in the electrolyte phase. The Ohmic resistances and electrochemical reaction kinetics resistance are simplified to a lumped Ohmic resistance parameter. Overall, the number of model parameters is reduced from 30 to 9, yet the accuracy of the model is still guaranteed. In order to address the dynamics of phase-change phenomenon in the active particle during charging and discharging, variable solid-state diffusivity is taken into consideration in the model. Also, the observability of the model is analyzed on two types of lithium ion batteries subsequently. Results show the fractional order model with variable solid-state diffusivity agrees very well with experimental data at various current input conditions and is suitable for electric vehicle applications.