Physics-informed simulation links quantum models to LFP battery state estimation

Lithium iron phosphate (LFP) batteries are prized in electric vehicles for their high charging and discharging rates, but estimating their state of charge (SOC) remains notoriously difficult. The reason lies in the chemistry itself: LFP cells have an exceptionally flat open-circuit voltage (OCV) curve, meaning the voltage barely changes across much of the charge range. A new open-access study published in Discover Electronics on 5 October 2026 tackles this problem by fusing quantum-mechanical calculations with real-time state estimation in a single simulation pipeline.

The work, carried out by A. K. Wabeto, K. N. Nigussa and L. D. Deja, introduces a multi-scale, physics-informed framework that connects sub-atomic quantum metrics directly with macroscopic battery state estimation. Instead of relying on extensive empirical test data to parameterize equivalent circuit models — a dependence the authors identify as a significant development bottleneck — the team extracts nominal open-circuit voltage input vectors from first-principles Density Functional Theory (DFT) atomistic models. These models define the crystal structure and charge-transfer pathways of the LFP cathode material, and the resulting quantum-mechanical parameters are scaled and mapped onto a temperature-dependent second-order RC Thevenin circuit deployed in MATLAB Simulink/Simscape.

At the heart of the estimation scheme sits a modified Extended Kalman Filter (mEKF). Conventional EKF implementations are widely used for SOC estimation of simple nonlinear dynamical systems, but their performance can deteriorate when a battery exhibits strong nonlinear electrochemical behavior driven by temperature-dependent parameter variations. The modification here consists of integrating coupled electro-thermal state equations into the recursive estimation process, modeling the OCV as a nonlinear function of both SOC and temperature. The Jacobian matrices are evaluated using the electro-thermal model rather than a purely electrical one, allowing the estimator to incorporate the influence of thermal behavior on voltage prediction and SOC estimation.

The quantitative gains are substantial. Benchmarked against the conventional EKF under four increasingly demanding operating profiles, the mEKF reduces the reported estimation error by 26.5 percent during constant-current discharge, 35.2 percent during constant-current/constant-voltage (CC-CV) charging, 31.1 percent during pulse discharge, and 56.4 percent under the Dynamic Stress Test (DST). In raw terms, the conventional EKF produces errors of 1.89, 2.10, 2.70 and 6.59 percent for those four conditions respectively, while the mEKF brings them down to 1.39, 1.36, 1.86 and 2.87 percent. The largest improvement occurs under DST, the most dynamically varying load condition, which the authors interpret as direct evidence that incorporating temperature-dependent dynamics becomes increasingly valuable as operating conditions grow more demanding.

The logic behind that pattern is straightforward. Under constant-current operation the electrical dynamics are comparatively predictable, so the advantage of adding thermal information is limited. Under pulse and DST conditions, however, rapid changes in current modify both the ohmic and polarization voltage components and simultaneously alter irreversible heat generation. Because the proposed estimator embeds temperature-dependent battery dynamics into both the state-transition and measurement formulations, the predicted voltage and SOC are corrected using an electro-thermal representation rather than an electrical-only one. The framework simultaneously estimates terminal voltage, open-circuit voltage, SOC, polarization voltage, internal resistance, heat generation and cell temperature, treating thermal behavior as coupled to the electrical states rather than as an independent post-processing calculation.

Validation proceeded in two complementary stages. First, the electrical model and state-estimation results were evaluated against benchmark experimental battery data, including CALCE data, providing an external reference for predicted voltage and SOC behavior. The OCV-SOC relationship obtained from the model agrees closely with the benchmark observations, achieving a coefficient of determination of R² = 0.997. Second, after this benchmark validation, the electro-thermal framework underwent a systematic parametric robustness analysis across ambient temperatures from 10 °C to 50 °C and charging/discharging rates from 0.1 C to 10 C. The authors are explicit that the objective is to establish and assess the estimation framework rather than to claim comprehensive hardware-level experimental validation across the entire operating envelope.

The simulations themselves were run in MATLAB R2024a on a two-cell lithium-ion battery pack, with each simulation typically lasting two hours. Charge-discharge behavior was tested at six temperatures — 283 K, 293 K, 298 K, 303 K, 313 K and 323 K, corresponding to 10, 20, 25, 30, 40 and 50 °C — with default conditions of 298 K, a c-rate of one, and a convective heat transfer area of one square meter. The model incorporates temperature sensors, external temperature inputs, convective heat transfer, controlled OCV sources for charging and discharging, and thermal and electrical references, addressing each battery cell individually.

The electrical characterization yields several detailed relationships. Terminal voltage decreases as depth of discharge increases, and the decline steepens at higher discharge rates, suggesting cells operate for longer lifetimes at discharge rates around 1 A compared with higher rates. At a discharge rate of 1 A and 25 °C, the charge removed can reach as much as 9 × 10⁷ coulombs, with terminal voltage and OCV falling from about 2.9 V and 3.2 V respectively to 1.3 V and 1.5 V over the discharge process. During charging, the voltages range from 2.9 V and 3.2 V at the start to roughly 1.0 V and 1.2 V when fully charged, with charge storage of up to 7 × 10⁷ coulombs per two cells. The OCV-SOC curve was fitted with an eighth-order polynomial, and the discharge resistance varies linearly with SOC — decreasing as SOC increases — with a fit characterized by R² ≈ 1 and near-zero residual.

The thermal side of the analysis is equally detailed. The battery’s temperature evolution follows an energy balance that accounts for irreversible heat generation, reversible entropy heat, and dissipation through convection, with thermal radiation’s impact described as usually very small compared with thermal convection. The model predicts a maximum heat-power generation of about 500 mW, with total heat energy of up to 3 kJ, roughly half of which is generated in the first 1.5 hours and half in the following 1.5 hours. Heat-power generation increases with temperature across the tested range, and battery temperature rises with discharge time. Energy accounting suggests about 25 kJ can be stored per two cells during charging, while about 21 kJ is released to the load during discharging, with up to 3 kJ lost as heat.

Temperature emerges as a decisive performance factor. Charging at lower ambient temperatures around 10 °C appears to yield slightly higher energy storage capacity, while discharging at higher temperatures around 40–50 °C releases slightly more energy to the load, though over a longer discharge time. Room-temperature environments of roughly 20–30 °C achieve average performance in both directions and are identified as the preferred ideal conditions, with conditions above or below this range resulting in longer discharge times or lower energy yields respectively. The authors position the contribution not in the EKF or the second-order Thevenin model individually — both established techniques — but in their temperature-dependent integration within a single recursive estimation framework, and in demonstrating quantitatively how that coupling improves robustness under increasingly dynamic loads. Future work, they note, includes extending the framework to battery aging, establishing generality across different cells, and validating results through comprehensive experimental hardware platforms.

Subject of Research: A physics-informed electro-thermal simulation framework integrating DFT-derived parameters and a modified Extended Kalman Filter for state-of-charge and thermal estimation in LFP batteries

Article Title: Thermal and electrical behavior analysis of LFP-cathode battery

Article References: Wabeto, A. K., Nigussa, K. N., & Deja, L. D. (2026). Thermal and electrical behavior analysis of LFP-cathode battery. Discover Electronics, 3(1), Article 142. https://doi.org/10.1007/s44291-026-00296-7

Image Credits: AI Generated

DOI: 10.1007/s44291-026-00296-7

Keywords: lithium iron phosphate, state of charge, Extended Kalman Filter, Density Functional Theory, electro-thermal modeling, Thevenin equivalent circuit, battery management systems, MATLAB Simulink, Dynamic Stress Test, open-circuit voltage, electric vehicles, thermal behavior