Computational Design of Electro-Thermally Constrained Ultra-Fast Charging Schemes for High-Energy-Density Li-Ion Batteries

Extremely fast charging (XFC) of high-energy-density lithium-ion batteries is fundamentally constrained by the intrinsic waveform characteristics of conventional variable-current profiles (VCPs), limiting further reductions in charging time while maintaining electro-thermal safety. In the present study, a computational electro-thermally constrained optimization framework is developed in which a square-wave VCP is reformulated using a finite Fourier series to improve XFC performance. An electro-thermal numerical model is employed to evaluate the charging behavior of the resulting Fourier series-based square wave (F-square wave) with the number of harmonic terms ranging from N = 1 to 100. The optimal charging performance is achieved at N = 10, reducing the charging time from 940 to 878 s (6.6%) and satisfying the U.S. DOE 15-min XFC target (900 s). The performance enhancement originates from two complementary effects: the Gibbs overshoot, which locally increases the charging current near the allowable current limit, and the finite-series approximation, which smooths the current transition before and after the waveform discontinuity. Rather than treating the Gibbs overshoot associated with Fourier approximation as an undesirable numerical artifact, this study demonstrates that it can be computationally exploited as a controlled perturbation to accelerate charging while maintaining electro-thermal safety. Although the Fourier perturbation slightly increases the terminal voltage risk near the waveform discontinuity, all electrical and thermal constraints remain satisfied throughout the charging process. These findings demonstrate that finite Fourier perturbation provides an effective computational design strategy for overcoming the intrinsic waveform limitations of discontinuous charging profiles and advancing electro-thermally constrained XFC of lithium-ion batteries.