Remaining Discharge Energy Prediction for Lithium-Ion Batteries Over Broad Current Ranges: A Machine Learning Approach

TL;DR

This work defines $E_ ext{RDE}$ as a C-rate–dependent energy remaining in Li-ion cells and develops a hybrid physics–ML framework (NDCTNet) to predict voltage and temperature across broad $C$-rates. Building on this, a real-time RDE predictor uses two ML modules to estimate remaining time to voltage and temperature limits and then forecast $E_ ext{RDE}$, achieving speeds ~0.3–0.4 s per prediction with high accuracy. Experimental validation on NCA and LFP cells shows relative errors below 3% for $E_ ext{RDE}$ predictions and substantial computational savings over forward-model simulations, with application demonstrations for eVTOL scenarios. The approach offers scalable, fast RDE estimation for high-power LiBs and lays groundwork for extension to additional chemistries and uncertainty quantification in future work.

Abstract

Lithium-ion batteries have found their way into myriad sectors of industry to drive electrification, decarbonization, and sustainability. A crucial aspect in ensuring their safe and optimal performance is monitoring their energy levels. In this paper, we present the first study on predicting the remaining energy of a battery cell undergoing discharge over wide current ranges from low to high C-rates. The complexity of the challenge arises from the cell's C-rate-dependent energy availability as well as its intricate electro-thermal dynamics especially at high C-rates. To address this, we introduce a new definition of remaining discharge energy and then undertake a systematic effort in harnessing the power of machine learning to enable its prediction. Our effort includes two parts in cascade. First, we develop an accurate dynamic model based on integration of physics with machine learning to capture a battery's voltage and temperature behaviors. Second, based on the model, we propose a machine learning approach to predict the remaining discharge energy under arbitrary C-rates and pre-specified cut-off limits in voltage and temperature. The experimental validation shows that the proposed approach can predict the remaining discharge energy with a relative error of less than 3% when the current varies between 0~8 C for an NCA cell and 0~15 C for an LFP cell. The approach, by design, is amenable to training and computation.

Figures (13)

• Figure 1: Illustration of the proposed C-rate-dependent RDE definition for LiBs. The shaded areas represent the RDE at different discharging C-rate levels. The present time is $t$ and the remaining discharge time is $\Delta t_{\mathrm{RDT}}$.
• Figure 2: Variation of the RDE of an NCA cell across different C-rates under a modified US06 discharging profile, with $V_\mathrm{min} = 3\ \mathrm{V}$, $T_\mathrm{max} = 50 ^\circ\mathrm{C}$, and $T_\mathrm{amb} = 25 ^\circ\mathrm{C}$. (a) $E_\mathrm{RDE}$ subject to the limits of $V_{\mathrm{min}}$ and $T_{\mathrm{max}}$; (b) $E_\mathrm{RDE}$ subject to only the limit of $V_{\mathrm{min}}$; (c) difference of $E_\mathrm{RDE}$ between (a) and (b). The results show the C-rate dependence of a cell's RDE and demonstrate the effect of $T_{\mathrm{max}}$ limit for RDE prediction at high discharging C-rates. When only considering $V_\mathrm{min}$ limit, the cell's temperature reaches a maximum of $67.5 ^\circ\mathrm{C}$ during the prediction of $E_\mathrm{RDE}$ at $z = 8\ \mathrm{C}$ and $t=0\ \mathrm{s}$.
• Figure 3: Diagrams of (a) the NDC model and (b) the lumped thermal model.
• Figure 4: (a) The NDCTNet model, which integrates physics with ML to predict the terminal voltage and temperature of a LiB cell, see Section \ref{['Sec: LiB modeling']}; (b) the pipeline chart of the proposed RDE prediction approach, see Section \ref{['Sec: RDE prediction']}.
• Figure 5: Bisection search for $\Delta t_\mathrm{RDT}^{T_\mathrm{max}}$.

Theorems & Definitions (2)

• Remark 1
• Remark 2