Behavioral Models for Lithium Batteries Based on Genetic Programming

This paper proposes a novel methodology based on the Genetic Programming (GP) to derive behavioral models describing the transient evolution of the terminal voltage of a battery. These models analytically relate the battery voltage to its state of charge, charge/discharge rate, and temperature. Compared to the popular equivalent circuit-based models, one of the main advantages is the significant reduction of the effort to produce the experimental dataset required to identify the model parameters. The GP generates a family of optimal "candidate" analytical models, each associated with suitable metrics that quantify performance indicators like simplicity and accuracy. The methodology is applied to describe the transient discharge phase of a Lithium Iron Phosphate (LiFePO4 or LFP) battery under realistic operating conditions, considering the state-of-charge between 20% and 80%, discharge rates comprised between 0.25C and 1C, and temperature ranging from 5°C to 35°C. The GP provides different solutions that can be chosen by imposing the desired trade-off between accuracy and simplicity. Two models are selected and validated against experimental results. The chosen models guarantee a quite low level of the relative root mean square error (maximum 0.31% and 0.22%, respectively) over the range of analysis.