Joint parameter identification in lithium-ion battery models: Real-time single-step approach

In battery management systems (BMS), achieving a balance between accuracy and computational simplicity is crucial. In this regard, equivalent-circuit models (ECMs) are widely used for the monitoring and control of lithium-ion batteries (LIBs). This study therefore proposes an integrated parameter-estimation method based on a first-order Thevenin ECM (1-RC), where the OCV is represented as a function of SOC, R0 is parameterized as a function of SOC and load current, and R1 and C1 are modeled as SOC-dependent functions through empirically identified coefficients. A nonlinear least-squares trust-region reflective (TRR) algorithm implemented in MATLAB is employed to minimize the residual error between measured and simulated terminal voltages for each trial set of parameter coefficients. All model parameters (R0[jls-end-space/], R1[jls-end-space/], C1[jls-end-space/], and OCV) are estimated simultaneously within a single optimization framework, avoiding separate multi-stage fitting and the need for a separately characterized full OCV–SOC curve as an input to the optimization. For validation, the proposed formulation was evaluated on one laboratory dataset and two external datasets under both constant and dynamic discharge conditions to assess its accuracy and adaptability. A two-point validation procedure was further introduced to independently assess the estimated OCV–SOC relationship using low-current discharge and zero-current extrapolation. Results show close agreement between simulated and measured terminal voltages, with RMSE values between 1.25 and 15.9 mV for the laboratory and NASA datasets while the CALCE DST profile resulted in an RMSE of 38.4 mV. The computational performance of TRR was evaluated in comparison to particle swarm optimization (PSO). Additionally, the trade-off between accuracy and complexity for the 1-RC and 2-RC models, as well as sensitivity to initialization, was assessed. The findings indicate that TRR produced lower fitting errors, required fewer function evaluations, and achieved shorter execution times than PSO under the specified conditions. The 2-RC model demonstrated enhanced fitting accuracy for the CALCE DST dataset, although this improvement required additional parameters and increased execution time. Sensitivity analysis showed that moderate initialization perturbations produced similar fitting errors, while larger perturbations occasionally led to higher fitting errors. Overall, the proposed approach provides a practical framework for BMS-oriented parameter identification and battery-state monitoring.