A Control-Oriented Simplified Single Particle Model with Grouped Parameter and Sensitivity Analysis for Lithium-Ion Batteries

TL;DR

The paper tackles parameter estimation bottlenecks in the Single Particle Model by formulating a control-oriented SPM using parabolic discretization and parameter grouping, reducing the parameter set from $P_{ ext{all}}$ to $P_{ ext{grouping}}$ and then to $P_{ ext{high-sensitivity}}$. It employs Sobol global sensitivity analysis across constant and dynamic current profiles to identify a six-parameter subset that dominates model output error, and validates that estimating only these parameters via PSO achieves comparable accuracy with a substantial speedup. The approach yields a practically useful, reduced-parameter model for BMS state estimation and control, with explicit guidance on which parameters require calibration under different operating conditions. The results highlight the importance of condition-aware sensitivity in designing efficient and robust battery management strategies.

Abstract

Lithium-ion batteries are widely used in transportation, energy storage, and consumer electronics, driving the need for reliable battery management systems (BMS) for state estimation and control. The Single Particle Model (SPM) balances computational efficiency and accuracy but faces challenges in parameter estimation due to numerous parameters. Current SPM models using parabolic approximation introduce intermediate variables and hard to do parameter grouping. This study presents a control-oriented SPM reformulation that employs parameter grouping and parabolic approximation to simplify model parameters while using average and surface lithium-ion concentrations as model output. By parameter grouping, the original 17 parameters were reduced to 9 grouped parameters. The reformulated model achieves a reduced-order ordinary differential equation form while maintaining mathematical accuracy equivalent to the pre-grouped discretized SPM. Through Sobol sensitivity analysis under various current profiles, the grouped parameters were reduced from 9 to 6 highly sensitive parameters. Results demonstrate that estimating these 6 parameters achieves comparable practical accuracy to estimating all 9 parameters, with faster convergence. This control-oriented SPM enhances BMS applications by facilitating state estimation and control while reducing parameter estimation requirements.

Figures (4)

• Figure 1: Sensitivity analysis using the Sobol method.
• Figure 2: Sensitivity analysis results for constant current.
• Figure 3: Sensitivity analysis results for dynamic current.
• Figure 4: PSO convergence comparison.