NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

P.I.: Gi-Heon Kim, ES Modeling Task Lead

National Renewable Energy Laboratory

Lab Lead, Ahmad Pesaran

Project ID #: ES197

This presentation does not contain any proprietary, confidential, or otherwise restricted information.

Significant Enhancement of Computational Efficiency 

in Nonlinear Multiscale Battery Model 

for Computer Aided Engineering

Kandler Smith, Peter Graf, Myungsoo Jun, Chuanbo Yang: NREL

Genong Li, Shaoping Li, Amit Hochman, Dimitrios Tselepidakis: ANSYS

Jacob White: ANSYS/MIT

Annual Merit Review and Peer Evaluation Meeting

June 17, 2014

Washington, D.C.

PR-5400-61865
2

Overview

• Start Date: October 2013

• End Date: September 2015

• Percent Complete: 25% • Limited Multiphysics Integrity

• Wide-varied Time & Length Scales

• Instability Caused by Nonlinearity

• Total Project Funding: $1,218K

o DOE Share : $718K

o TARDEC Share: $500K

• Funding Received in FY13: $718K

• Funding for FY14: 

Awaiting funds from TARDEC

Timeline

Budget

Barriers in Battery CAE

Partners

• ANSYS

o Physics Business Unit

o Electronics Business Unit

• Project Lead: National Renewable 

Energy Laboratory (NREL) 

This PROJECT was awarded based on a proposal in response to 

FY13 DOE Vehicle Technologies Office Funding Opportunity Announcement

CAE accelerates product development cycle, 

reduce cost and improve performance 

CAE = computer aided engineering TARDEC = The US Army Tank Automotive Research, Development and Engineering Center
3

Relevance – Previous CAEBAT Accomplishment

Modular Nonlinear Multiscale Framework “MSMD”

Kim et al., “Multi-Domain Modeling of Lithium-Ion Batteries Encompassing Multi-Physics in Varied Length Scales,” J. Electrochem. Soc., 2011, Vol. 158, No. 8, pp. A955–A969

• Developed the Multi-Scale Multi-Domain (MSMD) model, recognized as the most 

comprehensive model of its kind for modular architecture, linking interdisciplinary 

battery physics across varied length and time scales

• Resolves the battery geometry into three coupled computational domains

• Achieves high computational efficiency

• Provides flexible & expandable modularized framework

Particle Domain

Electrode Domain

Cell Domain

Orthotropic Continuum Model 

Uneven Kinetics over Unwound View of Jelly-roll

Model for All Major Form-factor Cells
4

Model Quantifies Non-uniform Cell Usage

Kim et al., JES, 2011

Lee et al., JPS, 2013

Stacked Pouch Cell Model Analysis

Wound Cylindrical Cell Model Analysis

• NREL’s orthotropic cell-composite model greatly reduces the computational load and 

resolves the complex transports and kinetics in the micron-scale strata cell geometries 

from various form-factor cells.

• The model captures unmeasurable internal cell quantities, revealing the impact of 

macroscopic design and the usage of the cells on local electrochemical processes.

Relevance – Previous CAEBAT Accomplishment

Kim et al., J. Electrochem. Soc., 2011, Vol. 158, No. 8, pp. A955–A969; Lee et al, Journal of Power Sources. Vol. 241, 1 November 2013; pp. 20-32.
5

Relevance – Motivation

• Material Engineering: Significant efforts continue being invested to improve energy-power 

capability and reliability of batteries through engineering at the material level by controlling 

particulate morphology and size, modifying the particle surface, or redesigning thermodynamics.

• However, due to the complex nonlinear interactions across a wide range and scale of physics, 

computational cost becomes excessively high to quantify such improvements for the benefits in 

device level response even with the state-of-the-art models.

• Pack Engineering: The CAEBAT program has resulted in software 

packages providing 3-D battery pack simulation modeling 

capability. 

• Because of the system’s extreme complexity, the computational 

cost of simulating a battery pack response is still high: results 

take weeks, unless low-fidelity submodels are used to represent 

the battery’s current/voltage response. 

Remaining Challenges

• Awareness and Control: Physics-based models are desired for use in advanced battery 

management to improve the performance of the battery management system and to 

implement sophisticated control strategies.

• However, significant reduction of model computation time and the number of states that are 

carried is required. 
6

Relevance – Objectives

To develop a computational methodology for a significant enhancement in 

computation speed of nonlinear multiscale battery modeling while maintaining or 

improving the solution accuracy from the most advanced state-of-the-art models

Speed-Up! 

Integrity

or

Accuracy

Convenience or Speed

High 

Accuracy

&

High 

Speed

objectives

Retain or Improve Fidelity of Physics, but Run 100 times Faster
7

FY14 Milestones

Month/Year Description Status

10/2013 Project Kick-off Meeting/Report met

02/2014 Progress Update Report: Efficient Nonlinear Multiscale Framework

• Standardize the input-output protocol and the data structure for particle domain (PD) 

and electrode domain (ED) models

• Prototype the restructured PD MATLABT codes

• Demonstrate new framework linkage between PD and ED models

met

05/2014 Progress Update Report: Adaptive Reduced Order Model (ROM)

• Complete evaluation of possible candidate approaches

• Begin prototype code development for electrode-level submodels

on

track

06/2014 Annual Merit Review Presentation on 

track

09/2014 Annual Milestone Report on 

track
8

Approach – Complementary Parallel Tasks

“The project will achieve the suggested objectives through complementary parallel 

efforts in the areas of framework and component efficiency and functionality 

improvement.”

Task 1: Project Management

Task 2: Framework Efficiency Improvement and Verification

To significantly improve the computational efficiency of a modular multiphysics battery model 

framework

Task 2.1 Efficient Nonlinear Multiscale Framework

Task 3: Component Model Efficiency Improvement and Verification

To provide advanced constituent submodels to enhance overall model performance in terms of 

computational speed and accuracy

Task 3.1 Adaptive Reduced Order Model

Task 3.2 Nonlinear Reduced Order Model 

Task 3.3 Module Inventory Enhancement

Task 4: Implementation on ANSYS Battery Simulation Platform

To bring immediate benefits to industries, the outcome model should be numerically robust and 

usable in an engineering environment. 
9

Approach – Task 2.1 

a. The inevitable nested iteration, ensuring self-consistency in the state-of-the-art MSMD, becomes a 

factor limiting further improvement of computation speed. 

b. The traditional multiphysics approach, collapsing scales into a single, large, differential algebraic 

equation system, renders the system impractically large and stiff, sacrificing modularity.

T2.1 Efficient Nonlinear Multiscale Model Framework 

Barrier to address: 

inevitable nested iteration

impractically large and stiff, 

sacrificing modularity

› Develop an innovative multiscale coupling method using time-scale separation and 

variable decomposition to eliminate several layers of nested iteration, while still keeping 

the modular framework architecture that is critical to battery behavior simulations. 

Strategy to address barriers:
10

Approach – Task 2.1 

Integrity

Convenience

objectives

Seeking for Convenience

Seeking for Integrity

• The explicitly given 

“states” (U , Ri

) are 

induced by processing 

often a large amount of 

test data; treated as 

“black boxes” 

“Relations between input and output (Io , Vo , Po , Rload) 

are given as explicit functions.”

Empirical Polarization Model

• The “states” are 

solved for with a 

nonlinear 

implicit system 

of equations.

“Battery behaviors are determined through 

nonlinear relations among physicochemical 

processes coupled across the scales.”

Integrated Multiscale Model

Pursuit of “Model of Dream” – Beyond MSMD

Quasi-Explicit Physics-Based Nonlinear Multiscale Model

I

Gξ Hξ

Gx Hx

• Remove nested 

iteration

• Explicit math 

expressions of 

“states”

• Retain modularity 

of framework

New Framework: GH-MSMD
11

Approach – Task 3.1 

• As soon as the ROM basis is acquired in a reduced dimension space, physical interpretations 

are easily lost. 

• The ROM basis is restricted to reuse in the system where its characteristics are evolving, such as 

the battery aging process.

• The ROM build process becomes computationally costly, especially with an increased number of 

parameters.

› Establish a new technique to identify low order 

State Variable Model (SVM) that is adaptive to 

system evolution, such as during aging. 

T3.1 Adaptive Reduced Order Model

Barrier to address: 

Reduced order models (ROMs) are used in various practical applications where fast 

computation is needed to repeatedly solve discretized systems of differential equations. 

Strategy to address barriers:

3rd Dimension of Model Speed-up :

Enhancement of Model Applicability

• Previous SVM: Basis functions determined in the 

preprocessing step. Only valid for one cell design 

at one state of health

• Adaptive SVM (this project): Analytical/numerical 

mapping of basis functions applicable to entire 

parameter space
12

Approach – Task 3.2 & Task 3.3 

• The model applicability can be limited for varied design, environment, and operation conditions.

› Construct multiple options of modular component models for various subsystems.

T3.2 Nonlinear Reduced Order Model

Barrier to address: 

Strategy to address barriers

T3.3 Module Inventory Enhancement

• Most state-of-the-art efficient battery models addressed coupling battery physics only within limited 

scales.

• The state-of-the-art ROMs suggested for battery models lose validity when severe nonlinearities 

arise.

› Design a new ROM that does not fail under severe nonlinear condition and achieves 

speeds that are compatible with state-of-the-art ROMs for battery models.

Barrier to address: 

Strategy to address barriers
13

Technical Accomplishments and Progress

Successfully implemented a newly developed “GH-MSMD” framework in linking the 

particle domain (PD) model into the electrode domain (ED) model

GH-MSMD Protocol

I

Gξ Hξ

Gx Hx

• Established a new model 

framework that removes 

nested iteration and still 

retains modular architecture

• Reformulated the model 

using; 

o Time-scale separation 

o Variable decomposition

o Partial linearization

• Evaluated several options for 

model implementation 

structures 

• Standardized the input-output protocol, and the data structure for PD and ED models

• Prototyped the restructured PD MATLAB codes

• Developed the further simplified edLPD model 

CD

ED

PD
14

Technical Accomplishments and Progress

GH-MSMD enables a ED model integrated with a 

more sophisticated PD model to run fast enough to 

investigate complex dynamic response of battery 

systems.

Pseudo 2D r

DDPM

Discrete Diffusion Particle Model (DDPM)

• The model solves solid-phase lithium diffusion 

dynamics and transfer kinetics in a discrete diffusion 

particle system.

• The particles are considered electronically continuous, 

but ionically discrete. 

• An arbitrary number of quantized discrete particles 

can be given as a user input.

• Kinetic, transport, and thermodynamic model 

parameters of each discrete particle can be 

independently determined.

NREL has developed the DDPM as an advanced option for 

MSMD particle-domain model, addressing particulate 

morphology, size distribution, surface modification, contact 

resistances, mixture composition of active particles.
15

Technical Accomplishments and Progress

HEV

PHEV

Driving Profile – US06

Physical & Chemical Material Characteristics

Application & Usage Characteristics

Speed [mph]

0 2 4 6 8 10 12 14 16 18 20 0.55

0.6

0.65

0.7

0.75

0.8

time [min]

x

i

0 2 4 6 8 10 12 14 16 18 20

0.4

0.5

0.6

0.7

0.8

0.9

1

time [min]

x

i

smallest particle

largest particle

system average

HEV

PHEV

• HEV:

o State of charge (SOC) swing is wider in small particles than in large 

particles. 

o Small particles respond more sensitively to load variation. 

o Both amplitude and frequency of concentration change are larger in small 

particles.

• PHEV10: 

o Lithium concentration difference between the particles grows initially and 

decreases back during charge sustaining mode. 

o Change of lithium concentration is nearly monotonous in large particles, 

while small particle concentrations fluctuate. 

o Large particles respond mostly to energy demand and small particles to 

both power and energy demands.

Model Application: Complex DDPM runs faster (x10~50) with the new 

framework to evaluate the impact of environmental factors on 

inhomogeneous use of materials with distributed particulate attributes. 

A battery with NCA cathode, particles distributed in size between 0.5-5 μm (N=100)
16

0 1 2 3 4 5 6 7 8

LCO

NMC

throughput [Ah]

discharge

charge

 

 

200 400 600 800 1000 1200 0.5

0.6

0.7

0.8

0.9

stoich, x

t / sec

PTCL Stoichiometry Number

 

 

200 400 600 800 1000 1200

-5

0

5

i'' / Am⋅ -2

t / sec

PTCL Transfer Current Density (charge:+, discharge:-)

Technical Accomplishments and Progress

Model Application: The model 

captures the impact of application 

characteristics on inhomogeneous 

use of materials for a mixed 

chemistry battery. 

 

 

100 200 300 400 500 600 700 800 900 1000 1100 1200 0.4

0.6

0.8

1

stoich, x

t / sec

PTCL Stoichiometry Number

 

 

100 200 300 400 500 600 700 800 900 1000 1100 1200

-2

0

2

i'' / Am⋅ -2

t / sec

PTCL Transfer Current Density (charge:+, discharge:-)

0 1 2 3 4 5 6 7 8

LCO

NMC

throughput [Ah]

discharge

charge

20-minutes Drive of Midsize Sedan on US06 Driving Profile

PHEV10

Particle Current Density

Particle Stoichiometry

Ah-Throughput

Mixed Cathodes

0.4 0.5 0.6 0.7 0.8 0.9 1

3

3.5

4

4.5

5

x, stoichiometry

voltage [V]

LCO (Thomas-Alyer)

NMC (Awarke, 2013)

Computed LCO:NMC=1:1

Measured (LCO/NMC)

Cathode OCP

HEV

Particle Current Density

Particle Stoichiometry

Ah-Throughput

• PHEV10: Since the battery is operated over a wide range of SOC in charge depleting mode, thermodynamic 

balance between the mixture components substantially varies, so is the usage of the materials. Stoichiometry 

difference between LCO and NMC grows during the drive. In charge sustaining mode (after ~ 800 sec), the 

battery is cycled with LCO nearly saturated. Discharge throughput is much larger for LCO particles, but NMC 

takes more current in charging events. 

• HEV: While discharge and charge throughputs are balanced for the both components, LCO is used more .
17

Technical Accomplishments and Progress

GH-MSMD Protocol

I

Gξ Hξ

Gx Hx

 ANSYS/Fluent  Star-CCM+

 BDS

 AutoLion

Connectivity to Existing CAEBAT Platform: Prototyped ANSYS/Fluent API for NREL’s edLPD 

• Significant enhancement of computation speed (~102) was demonstrated with ANSYS’s “MSMD Battery 

Model,” when it runs integrated with NREL’s edLPD model for a physics-based submodel option.
18

Collaboration and Coordination with Other Institutions

• The project team will integrate the outcome models on ANSYS’s battery simulation platform. ANSYS 

developers will support NREL researchers with required software engineering. 

• With the ANSYS battery simulation software as a platform for the MSMD research, appropriate 

source code access, prototype versions of ANSYS tools, developer-level technical support, and 

advisory consultation on NREL’s use will be provided. 

• Professor Jacob White, the Associate Director of the Research Laboratory of Electronics at MIT and 

an ANSYS Director of Research, brings his leading expertise in numerical methods focusing on 

simulation and optimization algorithms and software.

• From the previous collaboration, ANSYS developers participating in the project have established a 

profound understanding of the MSMD architecture.

To bring immediate benefits to industries, the outcome model should be numerically 

robust and usable in an engineering environment 

To leverage what has been accomplished through the previous efforts in the program 

Partner: ANSYS
19

Proposed Future Work

• Extend GH-MSMD nonlinear multiscale 

framework to the linkage between CellDomain (CD) models and the subscale domain 

models.

• Look into opportunities to further reduce 

balanced reduction, while desiring explicit 

method to achieve reduction.

• Implement the Discrete Empirical Interpolation 

Method (DEIM) for a representation of the 

nonlinear functions needed to retain the ROM 

in the low-dimensional reduced space. 

I

Gξ Hξ

Gx Hx

GH-MSMD Framework

• Link the outcomes from each task to the MSMD infrastructure, providing synergistically 

integrated battery simulation capability. 

• Develop and suggest an appropriate metric to evaluate the advancement of model 

computation speed.

• Incorporate into ANSYS CAEBAT framework and Oak Ridge National Laboratory’s Open 

Architecture Software

• Validate and verify the model codes against the baseline full-order models.
20

Summary

• Future Implication: The success of the project would shift the paradigm to using a model for battery 

system design and evaluation, with significant potential to change the standard development 

process while advancing battery system management and control. 

• This will be achieved through complementary parallel efforts in the 

areas of framework and component efficiency and functionality 

improvement.

• The objective of the project is to develop a computational 

methodology for a significant enhancement in computation speed 

of nonlinear multiscale battery modeling while maintaining or 

improving the solution accuracy from the most advanced state-ofthe-art models.

o To develop an innovative nonlinear multiscale model framework

o To provide advanced ROMs with enhanced model applicability

o To connect to previously developed CAEBAT development platforms 

• Newly developed “GH-MSMD” framework has been successfully implemented to link ParticleDomain (PD) models into a Electrode-Domain (ED) model.

• GH-MSMD enables a ED model integrated with a more sophisticated PD model to run fast enough 

to investigate complex dynamic responses of battery systems.

• Significant enhancement of computation speed (~102) was demonstrated with ANSYS’s “MSMD” 

battery simulation module, when it runs integrated with NREL’s edLPD model for a physics based 

electrochemistry submodel option.
Technical Back-Up Slides
22

Relevance – Background

Multiphysics Coupled across Scales

Physics of Li-Ion Battery Systems in 

Different Length Scales

Li diffusion in solid phase

Interface physics

Particle deformation & 

fatigue

Structural stability

Charge balance and 

transport

Electrical network in 

composite electrodes

Li transport in electrolyte 

phase

Electronic potential &

current distribution

Heat generation and 

transfer

Electrolyte wetting

Pressure distribution

Atomic Scale

Particle Scale

Electrode Scale Cell Scale

System Scale

System operating 

conditions

Environmental 

conditions

Control strategy

Module Scale

Thermal/electrical

inter-cell 

configuration

Thermal 

management

Safety control Thermodynamic properties

Lattice stability

Material-level kinetic barrier

Transport properties

• Physicochemical processes in lithium batteries occur in intricate geometries over a wide 

range of time and length scales. 

• Without better knowledge of the interplay among the multiphysics occurring across the 

varied scales, it is costly to design long-lasting, high-performing, safe, large battery systems. 

• The electric-drive vehicle (EDV) industry recognizes that the lack of a battery model that can 

predict thermal, electrical, electrochemical, and mechanical responses in various operating 

conditions is an urgent barrier to overcome.
23

Relevance – Background

Computer Aided Engineering of Batteries (CAEBAT) Program

DOE initiated the CAEBAT program to help industry shorten the time and cost to design and 

develop EDV battery systems through development of models and tools that can:

1. Integrate battery physics on a widely varied scale in a computationally efficient manner.

2. Provide a modularized multiphysics platform so the user can choose from multiple 

submodel options with various physical/computational complexities.

3. Provide an expandable framework to add new physics of interest or to drop physics of 

low significance or of indifference. 
24

Technical Accomplishments and Progress

Two different approaches are examined and 

pursued for an adaptive SVM to be flexible for 

design space searches, model parameter 

identification and coupling with aging models.

Analytical: 

• Developed interconnection-of-systems approach 

for assembling state-space matrices of ROM. 

• Analytical approach results in ~60th order statespace model. 

• This can be further reduced to ~15th order using 

numerical “balanced realization” technique from 

control theory.

Numerical: 

• Developed prototype code for fitting model 

transfer functions in low-order pole/residue form 

using vector fitting. 

• Method results in ~15th order models. 

• Drawback is large look-up tables necessary to 

represent parameter space.