Towards a BMS2 Design Framework: Adaptive Data-driven State-of-health Estimation for Second-Life Batteries with BIBO Stability Guarantees

TL;DR

This work tackles accurate SOH estimation for second-life LIBs with unknown histories by proposing BMS2, an online adaptive health estimator that guarantees BIBO stability. The method fuses clustering-based adaptation with an Elastic-Net Regression (ENR) baseline to operate on real-time SL battery data, ensuring bounded error growth as new measurements arrive. Validation on a lab-aged dataset of eight Nissan Leaf SL cells shows that the online approach reduces estimation errors (e.g., RMSE dropping from ENR baselines to 0.8610% for some cases) and maintains stability, with aleave-one-out RMSPE around 3.27%. The framework enables robust, in-field SL BMS2 operation, improving SOH tracking under variable histories and operational conditions and highlighting the value of online adaptation for practical SL battery management.

Abstract

A key challenge that is currently hindering the widespread use of retired electric vehicle (EV) batteries for second-life (SL) applications is the ability to accurately estimate and monitor their state of health (SOH). Second-life battery systems can be sourced from different battery packs with lack of knowledge of their historical usage. To tackle the in-the-field use of SL batteries, this paper introduces an online adaptive health estimation approach with guaranteed bounded-input-bounded-output (BIBO) stability. This method relies exclusively on operational data that can be accessed in real time from SL batteries. The effectiveness of the proposed approach is shown on a laboratory aged experimental data set of retired EV batteries. The estimator gains are dynamically adapted to accommodate the distinct characteristics of each individual cell, making it a promising candidate for future SL battery management systems (BMS2).

Figures (12)

• Figure 1: Initial distribution of C/20 capacity for all SL cells with a small difference between initial charge capacity $Q_{init,ch,C/20}$ and initial discharge capacity $Q_{init,dis,C/20}$. Cell 2.1 has the highest initial capacity while Cell 2.4 has the lowest initial capacity among all cells.
• Figure 2: Capacity and temperature for the SL cells used in this work. (a) C/20 charge capacity as a function of Ah-throughput. (b) Temperature as a function of Ah-throughput (below) and months (above) with a parabolic shape reaching a maximum value during the months of August/September 2022 indicating the effect of seasonal variation of temperature on all the cells. Gaps in temperature lines represent missing data for those cells e.g., Cell 2.3.
• Figure 3: ENR model with input features $X^{test}$ from the test set and an estimated scalar output $\hat{Q}^{test}_{ch,C/20}$ as a function of Ah-throughput.
• Figure 4: Design of experiments showing Reference performance tests (RPTs) and aging cycles. RPTs contain C/20 capacity test, HPPC test, and OCV test, which makes one set. For the complete campaign, $N$ sets of aging cycles are performed while $M+1$ sets of RPTs are performed. $N >> M$ for the dataset. $Q_{ch,C/20}$, the battery health indicator, is obtained once from the C/20 capacity test of each RPT set, as highlighted in brown. $Q_{age}$, the aging cycle charge, is obtained from each cycle, as highlighted in red. The limits of $Q_{ch,C/20}(i)$ are given by $t_{ch}^{C/20}(i)$ and $t_{dis}^{C/20}(i)$ where $i=1,2,...,M+1$, and the limits of $Q_{age}(j)$ are given by $t_{ch}^{age}(j)$ and $t_{dis}^{age}(j)$ where $j=1,2,...,n,...,N$. Positive current indicates charge and negative current indicates discharge.
• Figure 5: Example of cell classification defined in Definition \ref{['eqn:class_ind_seq']} with Cell 1.4 as the test cell compared against Cell 1.2 ($S_n^z=2$) and Cell 2.4 ($S_n^z=8$). Red arrows points to the aging cycle charge trajectory with the minimum distance from $Q_{age}^z$ -- where $z=1.4$ -- at different Ah-throughputs. Zoomed plot shows that these are highly dense discrete points since $Q_{age}^z$ is extracted from every cycle.

Theorems & Definitions (12)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Definition 6
• Definition 7
• Definition 8
• Theorem 1
• proof