Pack-level Electro-Thermal Modelling of Parallel-Connected LFP Cells

Abstract

Lithium iron phosphate (LFP) is widely used as a cathode material in batteries because of its long service life, good thermal stability and relatively low cost. However, an inherent behavior of this material makes the modeling and estimation of its internal state particularly challenging. Due to the flat voltage response of LFP over a wide range of state of charge (SOC), noticeably different internal states can produce only small differences in terminal voltage. The problem becomes more important in battery packs containing cells connected in parallel, where cells with similar voltages may carry different currents and gradually develop an imbalance that may remain unaccounted for by pack-level measurements and control systems. This behaviour of LFP is associated with phase separation during the intercalation and de-intercalation of lithium in the active-material particles. This thesis examines how phase-separation-related behaviour, represented through different open-circuit-potential and hysteresis formulations, affects current sharing, SOC distribution and thermal response in a parallel-connected battery pack. The investigation was first carried out at the cell scale by comparing three Doyle-Fuller-Newman models under the same operating conditions. Although the models produced broadly similar terminal-voltage curves, clear differences were observed in their internal reaction distributions, local positive-electrode concentrations and retention of spatial heterogeneity following changes in current direction. The physically motivated models showed stronger reaction localisation at low rates, while these distinctions became less apparent at higher rates because of the increasing influence of transport polarisation. The thermal behaviour of the models was subsequently compared over a range of C-rates, with particular attention given to the calculation of reversible heat. Entropic coefficients for the physical models were generated using the same simulated potentiometric procedure, allowing a consistent comparison with the empirical formulation. Differences in reaction localisation and entropic response resulted in different irreversible and reversible heat contributions, even when the predicted terminal voltages remained similar. For the pack-scale study, independent DFN and lumped thermal models were assigned to each cell and coupled through a sequential electrical-thermal solver that accounted for busbar resistance, terminal arrangement, self-heating and heat transfer between neighbouring cells. After numerical verification and comparison with previously reported pack behaviour, the framework was used to study the effect of cell formulation, discharge rate, interruption depth, terminal topology and dynamic loading. The results showed that electrical-path asymmetry initiates unequal current sharing, whereas the flat and state-dependent LFP voltage response controls how the resulting SOC imbalance develops and relaxes. During discharge interruptions, cell voltages equalised much faster than their SOCs, leaving a persistent internal imbalance, particularly when the interruption occurred within the voltage plateau. Higher C-rates and self-heating generally increased the imbalance, while an opposite-end terminal arrangement produced considerably Slimmer current and SOC differences than the same-end arrangement. Finally, varying the regular-solution interaction parameter showed that a stronger phase-separation-related thermodynamic response amplified and prolonged an imbalance created by the electrical topology, but was not itself the original source of that imbalance. Overall, the work shows that pack-level voltage can appear normal while important differences continue to exist between parallel cells, and that the effect of LFP phase-separation behaviour must be considered together with electrical topology, operating conditions and thermal coupling when assessing pack performance.