An Adaptive Reduced-Order-Modeling Approach for Simulating Real-Time Performances of Li-Ion Battery Systems

Abstract

In this work, a reduced-order-modeling(ROM) approach is introduced to simulate a battery system with multiple cells. The ROM is described by only two state variable equations and several explicit expressions. While running a stand-alone pseudo-2D (P2D) model by the nonlinear state variable modeling (NSVM) algorithm at a specified current, several parameters can be estimated through the NSVM procedure; and with these parameters, the cell voltage under additional current perturbations can be computed approximately by the ROM. This modeling scheme was tested for a 24P battery module in a co-simulation process: the stand-alone P2D model is solved at the battery-average current to estimate certain parameters to share with its ROM, then the ROM is implemented to evaluate the voltage response of each cell at its respective cell current. The ROM shows excellent accuracy and a much higher speed than the full-order-model with P2D models used for each cell. The battery management system (BMS) plays a crucial role in electrical vehicles (EV). During a standard vehicle development cycle, in-loop simulation is a useful technique to test and verify complex real-time embedded systems.1-3 To conduct in-loop simulation, the embedded system to be tested is connected to a mathematical representation of all related dynamic systems, because this arrangement lowers cost and improves safety as compared with using the real system. The mathematical representation interacting with embedded system is referred as "plant simulation". For the BMS software development, the plant simulation is performed by system-level battery models while the corresponding embedded system includes certain battery control and management algorithms. Therefore an accurate plant model for the battery system is vital for a successful BMS design. Besides accuracy, the plant battery model is also expected to work under high frequency inputs with noise and generate real-time output signals at low computational costs.The pseudo-2D (P2D) model developed by Fueler et al. 4 is a physical model that can be used to provide reliable predictions for the transport and electrochemical phenomena in Li-ion cells. However, it is still difficult to use the P2D model in plant simulation. The first challenge is the numerical issues in solving the nonlinear partialdifferential-equations (PDEs) contained in the P2D model at highfrequency inputs. During practical driving modes, the power requests from the powertrain to the EV battery change very quickly with time, and the currents and voltages are processed as discrete-time electrical signals. Most multi-physics PDE solvers (e.g., COMSOL) are designed to model continuous-time processes (e.g., constant current) and are slow for high-frequency simulation cases. Another challenge is the high computational costs to scale-up the P2D model from celllevel to pack-level. A single-cell P2D model normally includes more than 100 discretized state variables even using a very coarse mesh. To meet the high power and energy demands, typical EV battery...

Slow Current or Potential Scanning of Battery Porous Electrodes: Generalized Perturbation Solution and the Merits of Sinusoidal Current Cycling

“…The perturbation formulas we provide complement previous work on reduced order models (ROMs), the importance of which is captured in several recent papers. [5][6][7][8][9][10][11][12][13][14] Of these references, the work by Marquis et al 10 is most related to the methods used in this work; in Ref. 10, the authors examine constant current operation and derive a perturbation solution valid in the limit 0, e C  where e C is the ratio of the timescale for lithium-ion migration to that for full discharge.…”

Mathematical Model for a Lithium-Ion Battery with a SiO/Graphite Blended Electrode Based on a Reduced Order Model Derived Using Perturbation Theory

“…Finally, the ROMs are efficient tools in parametric studies and solution of inverse problems, i.e., the estimation of the kinetic and other parameters from a limited set of experimental data. The usage of various ROMs has been addressed in recent works, [10][11][12][13][14][15][16][17][18][19][20] all of which provide some level of review of past ROMs.…”

Reduced Order Models Derived from Perturbation Solutions and Applied to a Lithium Ion Intercalation Electrode

“…Perturbation solutions are computationally fast surrogates, in many cases, to full-model simulations. The utility of such reduced-order models (ROMs) has been addressed in several recent publications, [4][5][6][7][8][9][10][11][12][13][14][15] all of which provide some level of review of past ROMs. Of these references, the work by Marquis et al 9 is most related to the methods used in this work; in Ref.…”