Thermodynamics analysis of two-step thermochemical CO ₂ splitting with LaCo _0.7 Zr _0.3 O ₃ with gas–gas, gas–solid phase heat recuperation is performed based on experiment.

The lithium-ion battery is a complicated non-linear system with multi electrochemical processes including mass and charge conservations as well as electrochemical kinetics. The calculation process of the electrochemical model depends on an in-depth understanding of the physicochemical characteristics and parameters, which can be costly and time-consuming. We investigated the electrochemical modeling, reduction, and identification methods of the lithium-ion battery from the electrode-level to the system-level. A reduced 9th order linear model was proposed using electrode-level physicochemical modeling and the cell-level mathematical reduction method. The data-driven predictor-based subspace identification algorithm was presented for the estimation of lithium-ion battery model in the system-level. The effectiveness of the proposed modeling and identification methods was validated in an experimental study based on LiFePO₄ cells. The accuracy and dynamic characteristics of the identified model were found to be much more likely related to the operating State of Charge (SOC) range. Experimental results showed that the proposed methods perform well with high precision and good robustness in the SOC range of 90% to 10%, and the tracking error increases significantly within higher (100–90%) or lower (10–0%) SOC ranges. Moreover, to achieve an optimal balance between high-precision and low complexity, statistical analysis revealed that the 6th, 3rd, and 5th order battery model is the optimal choice in the SOC range of 90% to 100%, 90% to 10%, and 10% to 0%, respectively.