Variable fractional-order model for lithium-ion battery based on a hybrid fractional particle swarm optimization method with crisscross learning strategy

A variable fractional-order (FO) equivalent circuit model with order related to the state of charge (SOC) of Lithiumion batteries (LIBs) is addressed in this paper. A hybrid fractional particle swarm optimization with crisscross learning strategy (FOPSO-CL) algorithm is proposed to identify the parameters of the FO equivalent circuit model. In order to well balance the global exploration and local exploitation capabilities of PSO, a search direction adjustment mechanism based on subpopu-lation division operation is proposed. Meantime, to avoid the premature convergence and enhance the global search ability, a crossover-based comprehensive learning strategy (CCL) is adopted. Additionally, a stochastic example learning strategy (SEL) is introduced, which can assist collective information to be spread among separate sub-swarms, improve the local exploitation ability of the algorithm. The effectiveness of the proposed algorithm is verified by experimental data.