Development of a Mathematical Model of the Electromagnetic Field Formation Process Based on System Analysis Methods

This paper uses a systematic approach to constructing a mathematical description of the technological process of aluminum production, aimed at addressing control challenges and improving energy sustainability through a comprehensive analysis of technological parameters. Using expert assessment and correlation–regression analysis methods, the most significant technological parameters were identified, and quantitative relationships among them were established. Based on available statistical data from the current supply subsystem, a regression model was constructed that describes the influence of subsystem parameters on the voltage drop across the straight section of the bus and confirms the key role of transition resistances in welded joints in energy loss formation. Using the obtained dependencies, a conceptual model of the electrolysis process and its mathematical representation describing interactions among the electrical, thermal, and physicochemical subsystems of the electrolyzer was developed. The developed model is applicable to the analysis and prediction of technological modes, the construction of digital twins, and the development of automated control systems. In future work, the model is planned to be experimentally verified using a laboratory aluminum electrolysis setup in order to refine model parameters and assess applicability under industrial electrolyzer conditions.