Capacity Estimation of Lithium-ion Batteries Using Invariance Property in Open Circuit Voltage Relationship

TL;DR

This work introduces an invariance-based method for Li-ion battery capacity estimation that exploits a calibrated SOC–OCV relationship, enabling accurate capacity estimation from only one OCV cycle or from partial discharge data. By aligning the aged battery's OCV data with the nominal OCV–SOC curve through an optimization over the aged capacity $C_a$ and initial SOC, the method computes calibrated SOC trajectories and yields invariant OCV curves across aging. Validation on the Stanford Accelerated Aging dataset shows sub-0.5% absolute relative error (ARE) using OCV test data and about 0.85% ARE across 12 aging cycles when using OCVs identified from dynamic discharge data, demonstrating strong practicality for online capacity monitoring in EVs. The approach eliminates the need for full-cycle tests, reduces data collection costs, and supports online capacity estimation from operational data, with limitations tied to the invariance assumption and temperature effects.

Abstract

Lithium-ion (Li-ion) batteries are ubiquitous in electric vehicles (EVs) as efficient energy storage devices. The reliable operation of Li-ion batteries depends critically on the accurate estimation of battery capacity. However, conventional estimation methods require extensive training datasets from costly battery tests for modeling, and a full cycle of charge and discharge is often needed to estimate the capacity. To overcome these limitations, we propose a novel capacity estimation method that leverages only one cycle of the open-circuit voltage (OCV) test in modeling and allows for estimating the capacity from partial charge or discharge data. Moreover, by applying it with OCV identification algorithms, we can estimate the capacity from dynamic discharge data without requiring dedicated data collection tests. We observed an invariance property in the OCV versus state of charge relationship across aging cycles. Leveraging this invariance, the proposed method estimates the capacity by solving an OCV alignment problem using only the OCV and the discharge capacity data from the battery. Simulation results demonstrate the method's efficacy, achieving a mean absolute relative error of 0.85\% in capacity estimation across 12 samples from 344 aging cycles.

Figures (6)

• Figure 1: Relationships of OCV versus discharge capacity and OCV-SOC for the NMC pozzato2022lithium and the LMO batteries mcturk2015minimally.
• Figure 2: Scaling and translation of the uncalibrated OCV-SOC relationship for capacity estimation.
• Figure 3: OCV-SOC transformations of capacity estimation of validation cycles using OCV test data.
• Figure 4: OCV-SOC transformations of capacity estimation using partial data of the OCV tests. (a)(c)(e): Transformation for the 159th cycle. (b)(d)(f): Transformation for the 194th cycle.
• Figure 5: Transformations of the identified OCV-SOC relationships of capacity estimation from cycles 159 and 344.

Theorems & Definitions (1)

• Corollary 1