A control-oriented electrochemical model for lithium-ion battery, Part I: Lumped-parameter reduced-order model with constant phase element

Abstract

• The P2D model is reformulated using lumped parameters to reduce the number of parameters. • A series of lumped-parameter transfer functions are derived for the reduced-order model. • CPEs are added to the model firstly for better prediction of dynamic behavior of real cells. • An overall improvement in estimation of cell voltage and internal state variables are made. The most commonly used type of lithium-ion battery model in current battery management systems is the equivalent circuit model (ECM), but ECMs can predict only the input/output dynamics of cells but not internal electrochemical states. Since knowledge of these internal electrochemical states is needed to devise controls that can directly mitigate premature aging, researchers increasingly demand advanced control-oriented electrochemical models. Historically, electrochemical models have been computationally complex; in order to reduce this computational complexity many efforts have been made to simplify the original electrochemical model. However, in order to facilitate the application of the electrochemical model, there are still two issues to address: (1) electrochemical parameter identification and (2) taking into account the electric double layer and constant-phase-element (CPE) dynamics. In this paper, we first reformulate the original electrochemical model using lumped parameters to produce a full-order model (FOM) with the number of parameters reduced from 36 down to 24. All redundant/unobservable parameters are eliminated, and thus a minimum set of parameters are obtained, making system identification possible. Then, a series of lumped-parameter transfer functions are derived using only the required assumption of linearity. CPEs are added to the transfer functions to capture more accurately dynamic behavior of real cells. The derived lumped-parameter transfer functions are used to generate a lumped-parameter discrete-time state-space model. Time-domain data are generated by a virtual battery cell created via COMSOL using the FOM as a benchmark for comparison. Testing results under different conditions shows an overall improvement in estimation of cell voltage and state variables for a cell having realistic double-layer capacitance by using the lumped-parameter reduced-order model with CPE.