Reduced-order multi-particle model of lithium-ion batteries capturing electrochemical heterogeneity at subzero temperatures

Under low-temperature conditions, lithium-ion batteries exhibit aggravated diffusion limitations, intensified polarization, and highly non-uniform electrochemical reactions, posing critical challenges to accurate state estimation and control. Two key features of lithium-ion batteries at subzero temperatures, temperature-dependent diffusion and spatially varying reaction rates, cannot be simultaneously captured by existing simplified control-oriented battery models, whereas high-fidelity physics-based models lack the real-time computational efficiency required for practical implementation. To address these challenges, this study develops a Krylov-subspace interpolated parameterized multi-particle reduced-order (KIpmor) model, which achieves real-time execution while preserving key electrochemical heterogeneity. By leveraging orthogonal basis alignment and low-order matrix interpolation, the proposed KIpmor method uniquely enables real-time adaptation to varying diffusion coefficients without costly solving large-scale systems. Furthermore, a multi-particle representation with piecewise-linear flux distributions accurately resolves spatial reaction variations through coupled Butler-Volmer equations, capturing significant electrochemical heterogeneity across electrodes. Extensive simulations and experimental validations at subzero temperatures demonstrate that the proposed model maintains voltage prediction errors below 50 mV, accurately tracks internal lithium concentrations within 3%, and achieves over 350 times computational speedup relative to the full-order electrochemical models. These outcomes provide a robust foundation for accurate, real-time battery management systems under challenging cold-weather conditions.