Optimal variable estimation of a Li-ion battery model by fractional calculus and bio-inspired algorithms

To optimal manage of lithium-ion (Li-ion) batteries, different features like the state of charge (SOC), state of health (SOH) should be considered. This consideration should also consider good reliability and precision for the battery modeling. This study introduces a new fractional model for a Lithium-ion battery by considering several operating conditions, temperatures, and SOCs. To achieve a suitable model, the parameters of the fractional model were optimized based on a newly developed design of the Krill Herd (DKH) optimizer. After verifying and comparing the capability of the algorithm with several different metaheuristics, it has been applied to the model and the best values have been obtained. The optimized fractional-order model is then validated by various characteristics regarding precision and reliability. The test data was considered under different SOC ranges, working conditions, and temperatures. The results showed that the ability of the proposed DKH method based on dynamic stress test (DST), test of hybrid pulse power characteristic (HPPC), and FUDS simulated condition in the ambient temperature is 7.18 mV, 8.75 mV, and 6.83 mV that are small RMSE values and shows higher reliability of the in different performing condition. The small value of RMDE was also proved in temperature and SOC which show its proper efficiency in different condition vales. Finally, the model has been compared with an RC integer equivalent circuit model. The comparison results showed that the proposed DKH method with 0.040 % relative mean error provides higher accuracy than the Second-order RC model with 0.045 % relative mean error which displays its excellence toward that model.