Modeling of Non-linear Dynamics of Lithium-ion Batteries via Delay-Embedded Dynamic Mode Decomposition

Abstract

The complex electrochemical behavior of lithium-ion batteries results in non-linear dynamics and appropriate modeling of this non-linear dynamical system is of interest for better management and control. In this work, we proposed a family of dynamic mode decomposition (DMD)-based data-driven models that do not require detailed knowledge of the composition of the battery materials but can essentially capture the non-linear dynamics with higher computational efficiency. Only voltage and current data obtained from hybrid pulse power characterization (HPPC) tests were utilized to form the state space matrices and subsequently used for predicting the future terminal voltage at different state of charge (SoC) and aging levels. To construct the system model, 60\% of the data from a single HPPC test was utilized to generate time-delay embedded snapshots, with embedding dimension ranging from 40 to 2000. Among these, an embedding dimension of 1810 resulted in the least residual sum of squares (RSS) error of 3.86 for the dynamic mode decomposition with control (DMDc) model and 30 for the standard DMD model. For DMDc model, delay embeddings (ranging from 1 to 12) were also incorporated into the input current signals. For the input matrix, an embedding dimension of 6 resulted in a minimum RSS error of 1.74. Furthermore, the system matrices A and B, identified from the HPPC test when the cell is in its healthy state, were held fixed and used to simulate the system dynamics for aged batteries by updating only the control input. Despite the presence of nonlinear degradation effects in later cycles, the DMDc model effectively captured key inner dynamics such as voltage dips and transient responses for subsequent charge and discharge cycles.