Real-time simulation of reversible solid oxide cells for digital twins: exploration based on mechanism models and data-driven methods

To address the conflict between physical fidelity and computational efficiency in vehicle-to-grid applications, this paper proposes a mechanism-data hybrid digital twin framework for reversible solid oxide cells. A quasi-two-dimensional dynamic model is developed using the control volume method to describe the axial multi-physics coupling. Crucially, to overcome the high computational burden of nonlinear node current solution in distributed models, which limits real-time execution, a PID-modulated current allocation algorithm is introduced into the node current allocation process. This method reformulates current allocation from a numerical solution problem into a closed-loop voltage-error regulation process. While maintaining stable convergence, it reduces the maximum average iteration order from approximately 10⁵ to within 10². Consequently, the model achieves a real-time ratio of 6.21% under a 5 ms time step with 15 nodes, while maintaining a real-time ratio of 47.2% even under a 1 ms time step with 20 nodes. These results indicate that the model satisfies the real-time execution criterion under the tested millisecond-level time steps and node configurations. Hardware-in-the-loop tests further show that the model can maintain stable real-time operation during dynamic electrical interaction and output continuous dynamic responses of multi-physics state variables. To ensure fidelity, Sobol global sensitivity analysis is employed to reduce the number of uncertain parameters from 15 to 8. Data calibration is then conducted under 12 experimental conditions, keeping the cell voltage prediction error within 5%. Finally, the non-uniform distributions of internal electric, fluid, and thermal fields captured by the model provide a reference for understanding the coupled multi-physics evolution inside the cell. The proposed framework balances physical explainability, computational efficiency, and predictive accuracy, thereby offering a feasible solution for digital twin applications and real-time control strategy optimization of solid oxide cells.