Differential evolution based regression algorithm for mathematical representation of electrical parameters in lithium-ion battery model

Accurate equivalent electric circuit models of a lithium-ion battery, generally consisting of lumped electrical parameters, are of utmost importance for implementing various algorithms in Battery Management System (BMS). The low-cost Electronic Control Unit for BMS application prompts for an accurate representation of these parameters with a reduced memory footprint is significant. This prompted the representation of SoC dependant parameters as polynomial, Gaussian, sum of sine and exponential equations through regression algorithms instead of a lookup table. This article proposes Differential Evolution (DE) based Regression algorithm to represent the experimentally pre-identified parameters as a function of SoC through the aforementioned equations. Based on the experimental test, data points representing the SoC dependency of battery parameters such as average open-circuit voltage, hysteresis, internal resistances, and capacitance have been obtained. These data points are subjected to a proposed algorithm to establish the mathematical relationship between the parameters and SoC. The flexibility of the algorithm has been verified by considering the aforesaid equations. The DE based regression algorithm's performance was compared with various other algorithms in terms of statistical parameters such as RMSE, Mean Average, and Variance. Based on the analysis of the obtained results for various algorithms, the equations developed by DE based regression algorithm have the best fit with experimental data for all the aforementioned equations. The analysis depicts that the eighth order polynomial equation fitted by the proposed algorithm is highly accurate. Various battery models have been validated with the experimental data based on the developed equations for all parameters.

Automated summary

Accurate equivalent electric circuit models of lithium-ion batteries are essential for Battery Management System algorithms, and representing parameters as polynomial, Gaussian, sum of sine, and exponential equations through regression algorithms instead of lookup tables can reduce memory footprint. The proposed Differential Evolution-based Regression algorithm successfully establishes mathematical relationships between battery parameters and State of Charge, with superior performance compared to other algorithms in terms of statistical parameters.