Residue grouping order reduction method in solid-phase lithium-ion battery models

Abstract

Obtaining precise reducer order battery models is a key component in designing lithium-ion battery management systems. In general, with conventional order reduction techniques, low order is followed by low accuracy. To overcome such limitation, this paper presents a frequency-based constructive method to obtain broad-band low-order approximations of the solid-phase lithium-ion diffusion submodel, the core of the reference pseudo-two-dimensional electrochemical model of lithium-ion cells. The proposed method is a combination of an improvement on the residue grouping technique and of standard balancing and truncation/residualization methods borrowed from control systems theory. As main result, dramatic order reductions from 3000th to 5th-order with minimum accuracy losses are obtained. Taking a well-known case-study of a lithium-ion battery model, it is shown that 5th-order models offer approximations with maximum absolute errors of 0.5%, for characteristic times up to 9.54 × 10 4 s . The proposed method will help to obtain accurate real-time estimations of surface concentration and state of charge of lithium-ion batteries.

Electrochemical models: methods and applications for safer lithium-ion battery operation

“…Advanced reduced order models.-Various researchers have studied to reduce the order and dimensionality of equations in the full order P2D, retaining the significant part of battery dynamics. 26,71 We will systematically categorize them into three basic segments for better understanding -spatially semi-discretized, frequency-domain method, and polynomial approximation method. • Couples multiple PDEs to show the internal mechanisms.…”

“…86 Residue grouping (RG).-Residue Grouping calculates the residues of the transfer function to form an accurate low order of equation matrices, grouping the similar eigenvalues, and their residues in a frequency band. 71,93 To apply the RG method, first transcendental transfer function (TFF) containing infinite poles needs to be obtained. These poles are grouped and approximated by new ones by minimizing a frequency response cost function using the optimization method.…”

A Robust Model Order Reduction Scheme for Lithium-Ion Batteries in Control-Oriented Vehicle Models

“…Ortiz-Ricardez et al 7 presented a frequency-based model reduction strategy for pseudo-two-dimensional electrochemical model of lithiumion cells by broad-band low-order approximations of the solid-phase lithium-ion diffusion submodel. The authors presented a numerically efficient family of residue grouping-based techniques to describe the one-dimensional radial diffusion problem of electrochemical battery models in a broad frequency band.…”