Indirect Battery Internal-Temperature Estimation: A Fractional-Order Thermal Modeling Approach
- 1Faculty of BERG, Technical University of Košice, 042 00 Košice, Slovakia
Abstract
The internal temperature of a lithium-ion cell governs aging and safety, but commercial cells cannot be measured without invasive sensors. We survey direct and indirect (thermoelectric-model, PDE-observer, impedance-based) estimation methods and find that fractional-order operators appear in battery electrical models but have not been used in thermal state equations for internal-temperature estimation. In this paper, we generalize the classical two-state lumped thermal model by Caputo derivatives of orders α1,α2∈(0,1] and give a Caputo-consistent Grünwald–Letnikov discretization, verified against Mittag-Leffler and L1 reference solutions. In a numerical study with drive-cycle-like excitation, we compare the fractional plant and two independent integer-order plants (one with unmodeled entropic heat) with integer chains of the same parameter count. Identification from surface temperature alone is ill-conditioned for all models; a better surface fit does not guarantee a better core estimate, and the fractional model is advantageous only when the plant dynamics are indeed fractional. When calibrated with an internal sensor, the core temperature is estimated from the surface within 0.01–1.1°C. The results are simulation-based; experimental validation is the next step.
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BibTeX
@article{petras2026indirect,
title = {{Indirect Battery Internal-Temperature Estimation: A Fractional-Order Thermal Modeling Approach}},
author = {Ivo Petráš},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203814},
url = {https://www.mdpi.com/2227-7390/14/20/3814},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Indirect Battery Internal-Temperature Estimation: A Fractional-Order Thermal Modeling Approach
AU - Ivo Petráš
PY - 2026
DA - 2026/10/20
JO - Mathematics
DO - 10.3390/math14203814
UR - https://www.mdpi.com/2227-7390/14/20/3814
AB - The internal temperature of a lithium-ion cell governs aging and safety, but commercial cells cannot be measured without invasive sensors. We survey direct and indirect (thermoelectric-model, PDE-observer, impedance-based) estimation methods and find that fractional-order operators appear in battery electrical models but have not been used in thermal state equations for internal-temperature estimation. In this paper, we generalize the classical two-state lumped thermal model by Caputo derivatives of orders α1,α2∈(0,1] and give a Caputo-consistent Grünwald–Letnikov discretization, verified against Mittag-Leffler and L1 reference solutions. In a numerical study with drive-cycle-like excitation, we compare the fractional plant and two independent integer-order plants (one with unmodeled entropic heat) with integer chains of the same parameter count. Identification from surface temperature alone is ill-conditioned for all models; a better surface fit does not guarantee a better core estimate, and the fractional model is advantageous only when the plant dynamics are indeed fractional. When calibrated with an internal sensor, the core temperature is estimated from the surface within 0.01–1.1°C. The results are simulation-based; experimental validation is the next step.
SN - 2227-7390
ER -