Current and temperature imbalances in parallel-connected grid storage battery modules

A key challenge with large battery systems is heterogeneous currents and temperatures in modules with parallel-connected cells. Although extreme currents and temperatures are detrimental to the performance and lifetime of battery cells, there is not a consensus on the scale of typical imbalances within grid storage modules. Here, we quantify these imbalances through simulations and experiments on an industrially representative grid storage battery module consisting of prismatic lithium iron phosphate cells, elucidating the evolution of current and temperature imbalances and their dependence on individual cell and module parameter variations. Using a sensitivity analysis, we find that varying contact resistances and cell resistances contribute strongly to temperature differences between cells, from which we define safety thresholds on cell-to-cell variability. Finally, we investigate how these thresholds change for different applications, to outline a set of robustness metrics that show how cycling at lower C-rates and narrower SOC ranges can mitigate failures.

💡 Research Summary

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The paper addresses a critical issue in large‑scale grid‑storage battery systems: the emergence of heterogeneous currents and temperatures among cells that are connected in parallel. While such imbalances are known to accelerate degradation, reduce usable energy, and pose safety risks, quantitative data on the typical magnitude of these effects in industrial‑scale modules has been lacking.

To fill this gap, the authors focus on a representative module built from four large‑format prismatic lithium‑iron‑phosphate (LFP) cells, a chemistry that is rapidly becoming dominant in stationary storage due to its low cost, high capacity (≥ 100 Ah), and low internal resistance (≤ 500 µΩ). The flat open‑circuit‑voltage (OCV) versus state‑of‑charge (SOC) curve of LFP cells makes voltage‑based self‑balancing ineffective, so even modest variations in cell resistance or contact resistance can lead to significant current sharing disparities.

Model Development
A physics‑based electro‑thermal model is constructed in a nonlinear state‑space framework. Each cell is represented by an equivalent circuit model (ECM) comprising an OCV source, a series ohmic resistance (RΩ), a contact resistance (Rc), and an RC pair that captures charge‑transfer dynamics (Rct, Rw, C). Temperature dependence is introduced through an Arrhenius relationship for Rct, and a lumped thermal network models heat flow from the cell core to the surface and then to ambient. By formulating the parallel connection as a set of differential‑algebraic equations (DAEs) and analytically eliminating the Kirchhoff constraints, the authors derive explicit expressions for the branch currents (eqs. 5‑6). This approach enables the model to compute individual cell currents from the total module current and a set of cell‑specific parameters, without needing to solve a full DAE system at each step.

The model is implemented in MATLAB using ode45, with initial conditions set to 99.8 % SOC, zero RC voltage, and an ambient temperature of 22.2 °C. At each integration step, the OCV lookup table (based on 520 measured points) provides f(z), the temperature‑dependent Rct is updated, and branch currents are calculated via a compact matrix formulation (eq. 14). Heat generation is modeled as Qgen = i²RΩ + VRC²/(Rct + Rw), and the core temperature dynamics follow a first‑order thermal balance (eq. 11).

Experimental Validation
Two test cases are designed to provoke imbalance: (1) a single‑cell failure simulated by inserting a high‑resistance fault between one cell and the DC terminals, and (2) a multi‑cell failure where two cells are simultaneously faulted. The module is cycled with current profiles ranging from 0.2 C to 1 C while surface temperatures of each cell are logged at 1 Hz. In the single‑fault scenario, the defective cell’s resistance roughly doubles, leading to a 15–30 % increase in its current share and a temperature rise of 5–7 °C relative to the healthy cells. The healthy cells experience a corresponding current reduction and modest cooling. The multi‑fault case amplifies these effects, confirming the positive feedback loop: higher current → higher temperature → lower resistance → even higher current.

Simulation results, using parameters extracted from the measured cells (RΩ, Rc, thermal resistances, heat capacities), reproduce the experimental current and temperature trajectories within a 95 % confidence interval. A global sensitivity analysis identifies the ratio Rc/RΩ as the dominant factor governing temperature differentials. Maintaining Rc/RΩ < 0.02 (i.e., contact resistance less than 2 % of the cell’s internal resistance) keeps temperature differences below 3 °C under the tested operating conditions.

Safety Thresholds and Design Metrics
From the statistical distribution of ΔR (cell‑to‑cell resistance variation) and ΔT (temperature difference) observed across multiple runs, the authors propose safety thresholds of ΔR ≤ 10 % and ΔT ≤ 5 °C. These limits translate into concrete manufacturing specifications: (i) control contact resistance to ≤ 2 % of the nominal cell resistance, and (ii) limit cell‑to‑cell resistance spread to ≤ 5 % during cell sorting and module assembly.

Application‑Specific Recommendations
The paper further explores how operating strategies affect the thresholds. For high‑power (peak‑shaving) applications that demand C‑rates ≥ 1 C and wide SOC swings (0 %–100 %), the model predicts ΔT values exceeding 5 °C, indicating a heightened risk of thermal runaway unless additional cooling or active balancing is employed. Conversely, for long‑duration energy‑storage or frequency‑regulation services that operate at ≤ 0.5 C and restrict SOC to 20 %–80 %, ΔT remains under 2 °C, and the module’s lifetime is substantially extended. The authors suggest that BMS algorithms incorporate current‑limiting and SOC‑window enforcement as low‑cost mitigation measures, especially when individual cell sensing is unavailable.

Conclusions
The study demonstrates that in parallel‑connected large‑format LFP modules, current and temperature imbalances are primarily driven by variations in cell internal resistance and, more critically, contact resistance. By quantifying the feedback loop between temperature‑induced resistance change and current redistribution, the authors provide a rigorous framework for predicting worst‑case thermal gradients. The derived safety thresholds and operational guidelines give system designers actionable criteria for both hardware (tight contact resistance control, cell matching) and software (C‑rate limits, SOC window constraints). Importantly, the presented electro‑thermal model can be integrated into existing BMS simulation tools to evaluate module‑level safety without the need for per‑cell current or temperature sensors, thereby supporting cost‑effective, reliable deployment of grid‑scale battery storage.