[Paper Review] One-Shot Parameter Identification of the Thevenin's Model for Batteries: Methods and Validation

Ning Tian, Yebin Wang+2 more|arXiv (Cornell University)|Mar 13, 2020

Advanced Battery Technologies Research76 references72 citations

TL;DR

This paper proposes a one-shot offline method for identifying all parameters of the Thevenin’s equivalent circuit model for batteries, including resistance, capacitance, and state-of-charge (SoC)-open-circuit voltage (OCV) mapping parameters. Using constrained optimization and Tikhonov regularization within a nonlinear least squares framework, the method achieves high-accuracy parameter estimation in a single run, validated through simulations and experiments with sub-20 mV prediction errors and near-perfect SoC-OCV matching.

ABSTRACT

Parameter estimation is of foundational importance for various model-based battery management tasks, including charging control, state-of-charge estimation and aging assessment. However, it remains a challenging issue as the existing methods generally depend on cumbersome and time-consuming procedures to extract battery parameters from data. Departing from the literature, this paper sets the unique aim of identifying all the parameters offline in a one-shot procedure, including the resistance and capacitance parameters and the parameters in the parameterized function mapping from the state-of-charge to the open-circuit voltage. Considering the well-known Thevenin's battery model, the study begins with the parameter identifiability analysis, showing that all the parameters are locally identifiable. Then, it formulates the parameter identification problem in a prediction-error-minimization framework. As the non-convexity intrinsic to the problem may lead to physically meaningless estimates, two methods are developed to overcome this issue. The first one is to constrain the parameter search within a reasonable space by setting parameter bounds, and the other adopts regularization of the cost function using prior parameter guess. The proposed identifiability analysis and identification methods are extensively validated through simulations and experiments.

Motivation & Objective

• Address the challenge of inefficient, multi-step battery parameter identification requiring lengthy calibration procedures.
• Enable full one-shot offline identification of all Thevenin model parameters—resistance, capacitance, and SoC-OCV relationship—without prior knowledge.
• Overcome the non-convexity and local minima issues in nonlinear system identification through constrained and regularized optimization.
• Provide a robust, accurate, and computationally feasible method for battery management systems requiring high-fidelity models.

Proposed method

• Formulate the parameter identification problem within a prediction-error-minimization framework using nonlinear least squares (NLS).
• Introduce parameter bounds to constrain the search space and prevent physically meaningless solutions.
• Apply generalized Tikhonov regularization to the cost function using prior parameter estimates to guide optimization toward meaningful minima.
• Use a Bayesian interpretation to justify the regularization term as a maximum a posteriori (MAP) estimation framework.
• Implement numerical optimization to solve the non-convex problem, ensuring convergence to a stable and accurate solution.
• Validate the method using both synthetic simulations and real-world experiments with constant and variable current profiles (e.g., UDDS).

Experimental results

Research questions

• RQ1 Can all parameters of the Thevenin’s battery model—including RC elements and the nonlinear SoC-OCV function—be uniquely identified in a single offline procedure?
• RQ2 How can non-convexity in the parameter identification problem be mitigated to avoid unphysical or inaccurate estimates?
• RQ3 To what extent does incorporating parameter bounds and regularization improve estimation accuracy and convergence reliability?
• RQ4 How well do the proposed methods (C-NLS and R-NLS) perform compared to standard NLS in real-world voltage tracking and SoC-OCV recovery tasks?
• RQ5 Can the one-shot method achieve high accuracy without requiring prior calibration of the SoC-OCV relationship?

Key findings

• All parameters of the Thevenin’s model are locally identifiable, confirming the theoretical feasibility of one-shot identification.
• The C-NLS and R-NLS methods achieved sub-20 mV prediction errors on average when tracking voltage under UDDS current profiles, significantly outperforming the benchmark NLS method.
• The estimated SoC-OCV relationships from C-NLS and R-NLS closely matched the measured ground truth, with minimal deviation observed in the intermittent discharging experiment.
• The R0 + R resistance values estimated by C-NLS and R-NLS showed strong agreement with the measured recovery voltages after discharge pauses, confirming accurate RC parameter estimation.
• The proposed methods reduced estimation errors by a large margin compared to standard NLS, especially in nonlinear and non-convex regions of the parameter space.
• The regularization and constrained optimization approaches effectively mitigated local minima issues, leading to stable and physically plausible parameter estimates.