Near-Real-Time Parameter Estimation of an Electrical Battery Model With Multiple Time Constants and SOC-Dependent Capacitance

A modified particle swarm optimization algorithm for conducting near-real-time parameter estimation of an electrical model for lithium batteries is presented. The model comprises a dynamic capacitance for characterizing the nonlinear relationship between the battery electromotive force and the state-of-charge, and a resistor-capacitor network for characterizing the static and transient responses. The algorithm is confirmed by successfully determining all parameters in a predefined simulation model. It is also evaluated on a hardware test bed with two samples of 3.3-V, 40-Ah, Lithium Iron Phosphate (LiFePO₄ ) battery driven under six different loading patterns. The intrinsic parameters are estimated by first processing 15-min samples of the battery terminal voltage and current. The whole process takes 2 min. Then, the voltage-current characteristics in the following 15 min are predicted. Results show that the extracted parameters can fit the first 15-min voltage samples with a maximum error of 16 mV and an average error of 3.8 mV. With the extracted parameters, the electrical model can predict voltage-current characteristics in the following 15 min with a maximum error of 31 mV and an average error of 15 mV. The algorithm is further verified by successfully determining the emulated variation of the output resistance.