Application of Karhunen–Loéve decomposition and piecewise linearization to a physics-based battery model

Abstract

Order reduction of an electrochemistry-based Lithium-ion battery model using the Proper Orthogonal Decomposition and Trajectory PieceWise Linearization is studied in this paper. Physics-based equations of the high-fidelity battery model, derived based on the chemical and electrical phenomena, are presented in state-space form. The obtained equations are in differential-algebraic form and highly nonlinear, which makes it computationally expensive for optimization and control-oriented problems. Therefore, reducing the order of the model would be essential and beneficial from different perspectives. The Proper Orthogonal Decomposition, a reduction scheme designed for large-scale nonlinear systems, is used to explore its efficacy in reducing the small-scale nonlinear battery model, which is crucial for design, control, and optimization tasks in automotive systems applications. Trajectory PieceWise Linearization is applied to linearize the battery equations for two reasons: (i) constructing a linearized model suitable for further investigations in model order reduction and (ii) reducing the battery equations using the nested approach. Satisfying algebraic constraints in the battery dynamic equations is quite a challenging task, especially in estimating the linearization points for which the Jacobians are ill-conditioned. The proposed reduction schemes demonstrate excellent performance in terms of computation cost and time, suitable for control-oriented problems and real-time application.