Journal of Green Energy Research and Innovation
Quarterly

Dynamic Modeling, Stability Analysis and State Estimation of the Hall-Héroult Aluminum Electrolysis Cell

Articles in Press

Document Type : Research article

Authors

Ali Farahani 1
Mohammad Sami 2
Meysam Ismailiyon 3
Masoud Sajjadi 4

1 Department of Electrical Engineering Faculty of Engineering, Tafresh University, Tafresh, Iran.

2 Department of Electrical Engineering Faculty of Engineering, Arak University, Arak, Iran.

3 Department of Industrial Management, Faculty of Management and Accounting, Islamic Azad University, Arak Branch, Iran

4 Department of Executive Management, Faculty of Management and Accounting, Islamic Azad University, Khomein Branch, Iran

10.61882/jgeri.2026.2069220.1071
Abstract
This study develops and analyzes dynamic models of an industrial Hall-Héroult aluminum electrolysis cell with a focus on Lyapunov-based stability assessment and control-oriented representation. Two modeling approaches are presented: a simplified formulation capturing the essential dynamics of alumina concentration and bath temperature, and an extended formulation that additionally accounts for the accumulation of produced aluminum mass and the evolution of bath height over time. For both models, Lyapunov candidate functions are systematically proposed and their time derivatives are derived to rigorously establish local asymptotic stability. Furthermore, the nonlinear models are linearized around practical steady-state operating points, and the resulting state-space matrices are computed numerically based on representative process parameters, including a line current of 200 kA and a nominal cell voltage of 4.3 V. A comparative analysis of the two formulations highlights the trade-offs between model simplicity and predictive fidelity, providing valuable insights to support advanced control design and state estimation in modern aluminum smelting operations. The validated nonlinear models and stability guarantees provide a critical foundation for designing advanced controllers that can enhance operational stability and pave the way for significant energy efficiency improvements in industrial smelting operations.

Keywords

Aluminum electrolysis cell dynamics
Lyapunov stability of aluminum electrolysis cell
State-space equations of aluminum electrolysis cell
Linearization of state-space model
State Estimation of the Hall-Héroult Aluminum Electrolysis Cell
Journal of Green Energy Research and Innovation

Articles in Press, Accepted Manuscript
Available Online from 24 February 2026

  • Receive Date 17 August 2025
  • Revise Date 11 February 2026
  • Accept Date 24 February 2026
  • Publish Date 24 February 2026

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