LFP Battery Flat Voltage Curve SOC Estimation: An Expansion Force Method That Works Where Voltage Cannot

1. Introduction

Accurate state-of-charge (SOC) estimation is critical for the performance and safety of lithium-ion batteries, but LiFePO4 cells present a fundamental challenge for traditional voltage-based methods: their flat voltage curve. As this paper demonstrates, LFP cells exhibit a voltage plateau spanning 27%–94% SOC, during which the total voltage change is only 0.07 V — far too small a signal for reliable voltage-based SOC estimation across most of the cell’s usable capacity range. This is precisely the problem that motivated Dr. Peipei Xu and colleagues at Beijing University of Science and Technology to develop an alternative approach in their 2022 study: using cell expansion force, measured in-situ during cycling, as the SOC indicator instead of voltage. Their method combines a Least-Squares Support Vector Machine (LSSVM) to model the non-monotonic relationship between expansion force and SOC with an Adaptive Unscented Kalman Filter (AUKF) for real-time online correction, achieving SOC prediction errors of roughly 0.54%–1% across varied temperatures, dynamic current profiles, and mechanical preload conditions — providing a robust alternative or complement to voltage-based SOC estimation specifically in the operating window where LFP’s flat voltage curve makes voltage-based methods unreliable. This article summarizes their methodology and its implications for battery management system (BMS) design.

2. The Core Problem: LiFePO4’s Flat Voltage Plateau

LiFePO4’s olivine crystal structure produces a two-phase lithiation/delithiation reaction with a famously flat open-circuit voltage plateau — a property that underlies LFP’s excellent thermal stability and cycle life, but creates a specific practical problem: across the majority of the usable SOC range, the voltage signal that traditional BMS algorithms rely on for SOC estimation simply does not change enough to be measured reliably, especially under noisy real-world current and temperature conditions.

The novel method evaluated here estimates LiFePO4 SOC from in-situ expansion force measurements instead. Using LSSVM to model the non-monotonic relationship between expansion force and SOC, combined with AUKF for online correction, the method attains prediction errors of roughly 0.54%–1% across varied temperatures, current dynamics, and preload conditions. This technique provides a robust alternative or supplement to voltage-based SOC estimation methods for LFP cells — especially in the flat-voltage operating window where voltage-based approaches struggle most.

3. Experimental Setup and Test Scheme

3.1 LiFePO4 Battery Specifications

Table 1. LiFePO4 batteries Information

3.2 Test Equipment

The researchers used a LiFePO4 battery and specialized equipment including:

• In-situ swelling analyzer (IEST-SWE2100)

• Battery cycler (CT-8002-5V100A-NTFA)

The IEST-SWE2100 accurately measured thickness and force changes during cycling under controlled temperature and mechanical constraints — the foundational measurement enabling this expansion-force-based SOC estimation approach.

3.3 Test conditions

• Quasi-static low-rate (1/25C) charging to reveal fine expansion/voltage trends free of dynamic current artifacts.

• Two dynamic drive cycles (NEDC, DST) at different preloads (15 kg, 30 kg) and ambient temperatures (25 °C, 45 °C).

• Synchronized acquisition of force, current, voltage, and temperature throughout all tests.

Figure 1. Expansion force test instrument: IEST SWE2100

Figure 2. Battery Test Process

4. Result Analysis: Expansion Force Tracks SOC Where Voltage Cannot

Figure 3 shows the voltage curve and expansion force change curve obtained at 1/25C charge rate. It can be clearly seen from the figure that there is a voltage plateau from 27% to 94% SOC. Across this 67-percentage-point range — covering most of the cell’s usable capacity — the voltage change is only 0.07 V, far below the resolution needed for reliable voltage-based SOC estimation in real-world noisy conditions.

By contrast, expansion force changes substantially across this same range. The expansion force change in this stage is primarily caused by the phase transition of intercalated graphite from LiC₁₂ to LiC₆ at the anode — a mechanical signature of the lithiation process that remains strong even when the electrochemical voltage signal goes flat. This makes expansion force a highly promising SOC indicator precisely in the operating window where voltage fails. However, the expansion force change in this range is also non-monotonic — it does not increase or decrease smoothly with SOC — which introduces its own estimation challenge, addressed later by the LSSVM model.

Figure 3. Voltage and expansion force vs LiFePO4 SOC under quasi-static conditions — the flat voltage plateau (27–94% SOC, only 0.07 V change) versus the substantial, SOC-sensitive expansion force change over the same range

To verify the SOC prediction model under realistic conditions, expansion force experiments were carried out under two dynamic drive cycles (NEDC and DST) with different preloads (15 kg and 30 kg) and different test temperatures (25 °C and 45 °C). As shown in Figure 4, results show that the same obvious voltage plateau persists at 20%–90% SOC under dynamic conditions, and the trend of expansion force change closely resembles that observed under constant-current (quasi-static) charging. This indicates that expansion force is not sensitive to dynamic current changes, but is strongly sensitive to SOC change — exactly the robustness property needed for a practical BMS estimation signal.

This behavioral difference has a clear physical explanation: voltage depends on the lithium-ion concentration at the electrode surface, which responds quickly (and noisily) to instantaneous current, while expansion force reflects the lithium-ion concentration throughout the electrode bulk phase, which integrates more slowly and tracks the true state of lithiation — i.e., SOC — more robustly. Additionally, the expansion force of the battery increases significantly with increasing preload, meaning that preload magnitude must be a deliberate design consideration in battery module mechanical design, not an afterthought, if expansion-force-based SOC estimation is to be deployed.

Figure 4. Swelling force and current-voltage curves under NEDC and DST dynamic drive cycle conditions — confirms expansion force remains SOC-sensitive and current-insensitive across temperature and preload variations

5. The SOC Estimation Algorithm: LSSVM + AUKF

The research team developed a machine-learning-based model using a Least-Squares Support Vector Machine (LSSVM) to capture the non-linear, non-monotonic relationship between expansion force and SOC identified in Figure 3. This was combined with an Adaptive Unscented Kalman Filter (AUKF) to improve accuracy and adaptability for real-time, online SOC estimation applications. The algorithm flow is shown in Figure 5.

This combined approach achieved estimation errors between 0.54% and 1% across temperatures, dynamic loads, and mechanical preconditions — a significant improvement over voltage-based methods specifically in the flat-voltage operating window where this study’s data shows voltage-based estimation is least reliable.

Figure 5. Flow chart of SOC estimation based on LSSVM (modeling the force-SOC relationship) and AUKF (real-time online correction)

6. Future Directions

• Extend the method to other chemistries where mechanical strain correlates with SOC — e.g., silicon-augmented anodes, which exhibit even larger volume change signals than graphite.

• Incorporate SOH (state-of-health) estimation jointly with SOC by augmenting the state vector in the AUKF to track aging parameters that modulate the force-SOC mapping over the cell’s lifetime.

• Evaluate long-term drift and model transferability between cell manufacturers, formats, and pack geometries — important for practical BMS deployment beyond the specific cell tested in this study.

7. Summary

This paper introduces a method to estimate LiFePO4 SOC using expansion force instead of relying on the cell’s notoriously flat voltage curve. The LFP voltage plateau spans 27%–94% SOC with only 0.07 V of change — too small a signal for reliable voltage-based estimation across most of the usable capacity range. Expansion force, by contrast, changes substantially and predictably with SOC over this same range, reflecting the bulk-phase lithium intercalation state rather than the noisier surface-concentration signal that drives voltage. Using LSSVM (to model the non-monotonic force-SOC relationship) and AUKF (for real-time online correction), the estimation error is reduced to below 1%, and the method is applicable across different temperatures, dynamic current profiles, and mechanical preload conditions. Future work is expected to extend this approach to other battery chemistries and to jointly estimate SOC alongside SOH and under low-temperature conditions.

8. Original Paper

Peipei Xu, Junqiu Li, Qiao Xue, Fengchun Sun. A syncretic state-of-charge estimator for LiFePO4 batteries leveraging expansion force. Journal of Energy Storage, 50 (2022) 104559.

9. Recommended Test Equipment of IEST

The SWE series in-situ expansion analysis system (IEST) uses a highly stable, automated platform equipped with high-precision thickness measurement sensors. It measures the thickness change and rate of change throughout the entire charge-discharge process — the exact measurement foundation needed for expansion-force-based SOC estimation research like the study analyzed above. Key functions:

• Battery swelling thickness curve testing under constant pressure
• Battery swelling force curve testing under constant gap conditions
• Battery compression performance testing: stress-strain curve, compression modulus
• Stepwise battery expansion force testing
• Temperature control range: −20 °C to 80 °C

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