A national laboratory of the U.S. Department of Energy 

Office of Energy Efficiency & Renewable Energy 

National Renewable Energy Laboratory 

Innovation for Our Energy Future 

Conference Paper Improving Battery Design NREL/CP-540-37652 with Electro-Thermal April 2005 

Modeling 

Preprint 

A. Pesaran, D. Bharathan, and G. Kim 

National Renewable Energy Laboratory 

A. Vlahinos 

Advanced Engineering Solutions 

T. Duong 

U.S. Department of Energy

To be presented at the 21st Electric Vehicle Symposium 

Monte Carlo, Monaco 

April 2-6, 2005

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 
NOTICE 

The submitted manuscript has been offered by an employee of the Midwest Research Institute (MRI), a 

contractor of the US Government under Contract No. DE-AC36-99GO10337. Accordingly, the US 

Government and MRI retain a nonexclusive royalty-free license to publish or reproduce the published form of 

this contribution, or allow others to do so, for US Government purposes. 

This report was prepared as an account of work sponsored by an agency of the United States government. 

Neither the United States government nor any agency thereof, nor any of their employees, makes any 

warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or 

usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not 

infringe privately owned rights. Reference herein to any specific commercial product, process, or service by 

trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, 

recommendation, or favoring by the United States government or any agency thereof. The views and 

opinions of authors expressed herein do not necessarily state or reflect those of the United States 

government or any agency thereof. 

Available electronically at http://www.osti.gov/bridge 

Available for a processing fee to U.S. Department of Energy 

and its contractors, in paper, from: 

U.S. Department of Energy 

Office of Scientific and Technical Information 

P.O. Box 62

Oak Ridge, TN 37831-0062 

phone: 865.576.8401 

fax: 865.576.5728 

email: mailto:reports@adonis.osti.gov 

Available for sale to the public, in paper, from: 

U.S. Department of Commerce 

National Technical Information Service 

5285 Port Royal Road 

Springfield, VA 22161 

phone: 800.553.6847 

fax: 703.605.6900 

email: orders@ntis.fedworld.gov 

online ordering: http://www.ntis.gov/ordering.htm 

Printed on paper containing at least 50% wastepaper, including 20% postconsumer waste 
1 

Improving Battery Design with Electro-Thermal Modeling 

Ahmad Pesaran, Andreas Vlahinos, Desikan Bharathan, Gi-Heon Kim, Tien Duong 

Abstract 

Temperature greatly affects the performance and life of batteries in electric and hybrid vehicles under real 

driving conditions, so increased attention is being paid to battery thermal management. Sophisticated 

electrochemical models and finite element analysis tools are available for predicting the thermal 

performance of batteries, but each has limitations. In this study we describe an electro-thermal finite 

element approach that predicts the thermal performance of a cell or module with realistic geometry, 

material properties, loads, and boundary conditions. To show the process, we simulated the thermal 

performance of two generations of Panasonic prismatic nickel-metal-hydride modules used in the Toyota 

Prius. The model showed why the new generation of Panasonic modules had better thermal performance. 

Thermal images from two battery modules under constant current discharge indicated that the model 

predicts the experimental trend reasonably well. These tools will greatly enhance the opportunity for 

lithium and other advanced batteries to perform better and become cost-effective alternatives in the 

future. The model has been used to improve the thermal performance of cylindrical lithium-ion batteries. 

Keywords: HEV (hybrid electric vehicle), thermal management, nickel metal hydride, battery model, 

simulation 

Introduction 

Temperature greatly affects the performance and life of batteries, so battery thermal control must be used 

in a hybrid electric vehicle under real driving conditions. In recent years, automakers and their battery 

suppliers have paid increased attention to battery thermal management, especially with regard to life cycle 

and related warranty costs. A thermal management system could be designed ranging from “simple 

energy balance equations” to more “sophisticated thermal and computational fluid dynamic models.” 

However, the basic performance of the management system is dictated by the thermal design of each cell 

or module. So it is critical to design cells and modules that have inherently good thermal performance. 

Sophisticated electrochemical models are available for predicting the performance of electrochemical 

cells [1 and 2], but they can’t capture the heat transfer aspects of the actual geometry with cell or module 

hardware (case, terminal posts, connectors, interconnects, relief valves, current collectors, seals, etc). 

Some finite element models can capture geometry [3 and 4], but can’t capture heat generation aspects 

because of currents in the hardware components. In the past, we have used ANSYS commercial finite 

element analysis software, which captured the thermal aspects only [3]. The heat generation terms were 

added by estimating the Ohmic heating and enthalpy of electrochemical reactions. 

For this study, we focused on integrating the electrical aspects of the cells and modules (including the cell 

hardware) into a finite element thermal analysis model. Our goals were to (1) develop the electro-thermal 

process or model for predicting thermal performance of cells and modules; (2) apply the model to predict 

the thermal performance of a baseline design (such as the 2001 Panasonic nickel-metal-hydride [NiMH] 

module) and compare it to the performance of a next-generation design (2004 Panasonic NiMH module); 

and (3) compare the predictions with infrared thermal imaging of modules under discharge. 

1 �
2 Approach 

It is particularly challenging to capture and model all the physical elements and details of a cell and drive 

the design parametrically for simultaneous electrical and thermal (electro-thermal) modeling, while 

considering performance limits and specifications for optimum efficiency and cost considerations. The 

process of engineering optimization via highly connected computer-aided engineering approaches is 

considered to be the best method, but it is not standard industry practice. During this project, we worked 

closely with a battery developer to develop such a tool. If the cell design is complicated, we use 

ProEngineer (ProE) software, a computer-aided design (CAD) tool, to build detailed virtual model of a 

cell or module. The CAD model consists of the cell core (positive electrode, negative electrode, separator, 

and electrolyte), the case of the cell or module, internal connectors from the core to the terminals, 

connectors to posts of terminals and (in the case of a module) cell-to-cell interconnects. 

We generally assume that the core (the electrochemically active part of the cell) is orthotropic—a 

homogenous combination of all its elements, but with different thermal and electrical properties in 

different directions. The CAD model is transferred to ANSYS to create a finite element model that can 

perform both electrical and thermal analysis. If the design of the cell is simple, we use ANSYS to capture 

the geometry and details of the cell or module. Once the geometry and material properties are selected 

and specified, ANSYS can calculate the electrical resistance of each component. The direct current (DC) 

resistance of the total cell or module could be also used to adjust for any unknown components to come 

up with the proper resistance. A current flows through the cell when a voltage drop is applied across the 

two terminals. This causes resistive heat generation that increases the temperature of all components 

proportional to the internal DC resistance. We also add the heat caused by the electrochemical reactions 

to the core. ANSYS uses the heat generated in each element to estimate the temperature distribution in the 

cell. Hot spots could be identified during steady-state or transient loads. 

To our knowledge, this is the first time that this type of electro-thermal analysis process has been applied 

to batteries. The designer can use this approach to improve the thermal design by reducing resistances, 

improving the power capability of batteries, and avoiding extreme hot spots in cells that lead to premature 

failure of cells. 

3 Modeling and Results 

To illustrate how this process works, we first applied the electro-thermal process to the prismatic 

Panasonic NiMH module used in the 2001 Toyota Prius and then compared it with the new Panasonic 

module used in the 2004 Prius. Figure 1 shows a picture of the 2001 Panasonic module, which has 6 cells, 

with total capacity of 6.5 Ah, module voltage of 7.2 V, and power capability of 1000 W/kg [5]. Figures 2 

and 3 show the associated finite element model that we captured with ProE and ANSYS based on a good 

geometrical understanding of how the modules are built. We captured six cores, cell-to-cell interconnects, 

weld junction, current collectors, and terminals. We ignored the capturing dimples on the surface of the 

case, but captured their impact with an adjusted heat transfer coefficient on the case. We made 

assumptions for properties of each material based on our understanding of the construction of NiMH 

batteries. The major cell features that we captured are six homogenous cores connected to current 

collectors on the each side, the current collectors are connected in series on top using a circular weld, cells 

on each side are connected to the external terminals. All the components are encapsulated in a 

polypropylene case. 

2 �
Figure 1: Panasonic NiMH module used in 2001 Toyota Prius 

Figure 2: Simulated model of the 2001 Panasonic module. The polypropylene case with terminal 

connectors is shown on the left. The case is removed to show the core and current collectors on the right. 

Figure 3: 2001 NiMH module. Left: Schematic of cell-to-cell connections by Panasonic [5]. Right: Our 

model of the weld junction. 

The DC resistance of the cell that we used to find the effective resistivity of the core was assumed to be 

15.0 mOhm [5]. We applied a voltage drop of 1.5 volts across the terminal to have a current of about 100 

A through the cell. Figure 4 shows the voltage distribution and current density in the cores and the weld. 

The weld junction has the highest current density and one would expect more heat to be generated in the 

weld junction because of higher current density and thus the weld junction would be the hottest spot. In 

fact, Figure 5 shows the transient temperature distribution obtained for a module, with an initial 

temperature of about 28°C, being cooled with natural convection while discharged with constant current 

of 100 A. This simulates a similar case that we tested while obtaining infrared thermal images for 

comparison. In Figure 5, the voltage drop across the terminals is 1.5 V, the bottom of the module is 

3 �
insulated, and the heat transfer coefficient on all other sides is 5 W/m2

/°C. As seen in Figure 5, the hottest 

spot is at the weld junction of the cell-to-cell connectors. 

Figure 4: 2001 module. Left: Voltage distribution in each cell. Right: Current density in the module; 

insert shows the highest current density through the weld junction. 

After 2 minutes of discharge After 2.5 minutes of discharge 

Color scale (°C) 

Increasing 

After 3 minutes of discharge 

Figure 5: Model predictions for 2001 module. Temperature distribution in the polypropylene case after 

the start of 100 A discharge. 

To validate the predictions of the model, or at least its trends, we obtained the infrared thermal image of 

the 2001 Panasonic module under constant current discharge of the 100 A while the module sat on a table 

with no cooling except natural convection in a room that was 25°C–28°C. Infrared thermal images show 

the external temperature. Figure 6 shows the thermal images of the 2001 module after start of the 100 A 

discharge. The hot spots are at the weld junctions similar to the electro-thermal model predictions. 

Comparing the model predictions in Figure 5 with the experimental images in Figure 6, we conclude that 

the electro-thermal model predicted the trend of temperature distribution reasonably well. 

4 �
After 2 minutes of discharge After 2.5 minutes of discharge 

Color scale (°C) 

Increasing 

After 3 minutes of discharge 

Figure 6: Thermal images of the 2001 NiMH module after the start of 100 A discharge 

One of the objectives of developing the electro-thermal model was the ability to find hot spots with a 

particular design, and proposing solutions to eliminate it or reduce its impact. By looking at the thermal 

images of the 2001 Panasonic NiMH module, we can suggest reducing the current density at the weld by 

adding an additional weld junction between current collectors of two adjacent cells. Although this could 

be difficult or expensive to do, it could improve both thermal and electrical performance of the module. 

In fact, the engineers at Panasonic have found a way to add additional weld junctions between the current 

collectors of each adjacent cell [5 and 6] for the 2004 generation, as shown in Figure 7. The five new 

weld junctions are about 2/3 of the way down the module below the top weld. Panasonic indicates that 

the DC resistance of its 2004 prismatic NiMH modules has decreased to 11.4 mOhm, and thus its power 

capability has increased by a factor of 30% to 1300 W/kg while its capacity remains the same [5 and 6]. 

Figure 7 shows the finite element model of the 2004 Panasonic NiMH module. The weld junctions were 

simulated as small cylindrical rods. Figure 8 shows the model prediction for current density in the 2004 

NiMH module under 100 A discharge. As could be seen, the current density is less in the top welds 

compared to the 2001 module under the same 100A discharge (Figure 4) since now almost half of the 

current is going through the second set of welds below the middle of the module. With lower current 

density in the weld, less heat is being generated and thus its temperature increase is expected to be less. 

5 �
Figure 7: New Panasonic NiMH Module used in 2004 Toyota Prius (top picture and schematic; schematic 

of cell-to-cell connections by Panasonic [5] (bottom left); our simulated model of the module and weld 

junction (colored images on the right) 

Figure 8: Current density for 100 A discharge for 2004 NiMH module 

Figure 9 shows the temperature distribution in the 2004 module at the end of 3 minutes of discharge. In 

the left side image, the polypropylene case temperature is shown, the right image shows the core, current 

collector, and cell-to-cell interconnects. By comparing these results with similar case in Figure 5, we can 

see that the overall temperature of the 2004 module is lower than that of the 2001 module (maximum of 

48°C vs maximum of 55°C), and also 2004 module has a much better temperature uniformity; both of 

which would help the battery to perform better and last longer. 

6 �
Color scale (°C) 

Increasing 

Figure 9: Model predictions for 2004 module. Temperature distribution in the case (left) and in the core 

(right) after 3 minutes from the start of 100 A discharge. 

Figure 10 shows the thermal images of a 2004 NiMH module under 100 A discharge. Unlike the 2001 

module (shown in Figure 6), it does not have any hot spots at the top cell-to-cell interconnects, it has 

lower overall temperature, and has better uniform temperature distribution. Our electrochemical model 

prediction compares reasonably well with these observations and these experimental thermal images. 

Figure 10: Thermal image of the 2004 NiMH module 3 minutes after the start of 100 A discharge. 

Concluding Remarks 

Thermal control is critical to ensure batteries provide the desired electrical performance and long life. 

Good thermal performance starts with designing good cells and modules. Using a commercial finite 

element analysis software, we developed a process to capture both electrical and thermal behavior of cells 

and modules with all of the geometrical details. To show how the electro-thermal modeling works, we 

7 �

4 
applied it to the 2001 prismatic Panasonic NIMH module and found hot spots near cell-to-cell 

interconnects. The analysis showed the benefit of decreasing the contact resistance between the two 

adjacent cells by using additional welds to decrease the overall DC resistance, reduce hot spots, improve 

temperature uniformity, and reduce the overall temperature of the module. This is in fact what Panasonic 

has done in their 2004 module. We performed constant current discharges of 2001 and 2004 modules and 

obtained thermal images. Comparing the thermal images with model predictions indicated that the model 

predicts the thermal performance reasonably well. We have applied the electro-thermal process described 

here to two other batteries from FreedomCAR battery developers to help them improve thermal designs. 

The current version of the electro-thermal model does not capture the transient nature of the internal 

resistance of the battery due to electrochemical changes in the battery as it charges or discharges. It also 

does not capture the chemical behavior of the various materials in the cells. We plan to update and 

upgrade the model to include these features. Including the chemical behavior of the materials in the cells 

may allow us to predict the thermal performance of a cell and its propagation to other cells in module 

under abuse conditions (overcharge, overheating, and short-circuit). 

Acknowledgments 

The U.S. Department of Energy (DOE), Office of the FreedomCAR and Vehicle Technology supported 

this effort. We appreciate the support of the members of the United States Advanced Battery Consortium 

and FreedomCAR Energy Storage Tech Team. We appreciate Mark Mihalic and Matt Keyser for thermal 

imaging and calorimetery of the battery modules for this work. 

References 

[1] V. Srinivasan and C.Y. Wang, “Analysis of Electrochemical and Thermal Behavior of Li-Ion Cells”, Journal of 

Electrochemical Society, Vol. 150, ppA98-A106, 2003. 

[2] J. N. Harb , V. H. Johnson and D. Rausen, “Use Of A Fundamentally Based Lead-Acid Battery Model In Hybrid 

Vehicle Simulations”, Proceedings of Annual Electrochemical Society Conference Seattle, Washington, Spring 

1999. 

[3] Ahmad Pesaran, “Battery Thermal Management in EVs and HEVs: Issues and Solutions”, Proceedings of 

Advanced Automotive Battery Conference, Las Vegas, Nevada, February 6-8, 2001 

[4] Said Al-Hallaj, et. al, “Novel PCM Thermal Management Makes Li-Ion Batteries A viable Option for High 

Power Applications”, Battery Power Products and Technology Magazine, November 2004. 

20

[5] Kojiro Ito, et al, “Development of Prismatic Type Nickel / Metal-Hydride Battery for HEVs”, Proceedings of the 

th Electric Vehicle Symposium, Long Beach, CA, November 2003. 

[6] Shuichi Nagata, et. al, “Development of a New Battery System for Hybrid Vehicles” Proceedings of the 20th 

Electric Vehicle Symposium, Long Beach, CA, November 2003. 

Authors 

Ahmad Pesaran, Principal Engineer, National Renewable Energy Laboratory, 1617 Cole Blvd, MS 

1633, Golden, CO, 80401, 303-275-4441, 303-275-4415, ahmad_pesaran@nrel.gov 

Dr. Pesaran joined NREL in 1983 and has been working on various energy systems such as solar 

cooling, ocean thermal energy conversion, air conditioning, desiccant dehumidification/cooling for 

buildings and buses, and most recently hybrid electric vehicles. Since 1995, he has been working on 

hybrid electric vehicle projects. He is currently the project manager for various activities related to 

8 �
battery thermal characterization, battery thermal analysis, and battery modeling and management. Dr. Pesaran holds 

a B.S. in chemical engineering from Shiraz University, as well as an M.S. in engineering and a Ph.D. in mechanical 

engineering from UCLA. He is a member of the FreedomCAR Electrochemical Energy Storage Technical Team. 

Andreas Vlahinos, Principal Advanced Engineering Solutions, 4547 North Lariat Drive 

Castle Rock, CO 80104, (303) 814-0455, (303) 814-0147, andreas@aes.nu 

Dr. Vlahinos is the founder of Advanced Engineering Solutions. He received his Ph.D. in 

Engineering Science and Mechanics from Georgia Institute of Technology. He has been a 

professor of structural engineering at the University of Colorado, teaching courses in structural 

mechanics and computer-aided structural engineering and receiving the Professor of the Year 

Award several times. Dr. Vlahinos has written over 90 publications related to structural stability and dynamics, and 

design optimization. He has received a R&D 100 award and holds several patents. He has been instrumental in rapid 

product development through the implementation of Six Sigma and Computer Aided Concurrent Engineering for 

several government agencies and industry partners. 

Desikan Bharathan, Principal Engineer, National Renewable Energy Laboratory, 1617 Cole Blvd, 

MS 1633, Golden, CO, 80401, 303-275-4613, 303-275-4415, desikan_bharathan@nrel.gov 

Dr. Bharathan joined NREL in 1980. His experience includes developing solar-assisted gas turbine 

power systems, modeling and analyzing hybrid vehicles, and researching advanced power cycles 

using mixed working fluids. Dr. Bharathan holds a PhD and MS in Aerospace Engineering from the 

University of Virginia in Charlottesville, VA. He also holds a B. Tech. in Aeronautical Engineering 

from the Indian Institute of Technology in Madras, India. He has been awarded six patents and has received 

numerous awards including a Federal Laboratory Consortium for Technology Transfer award, a Colorado 

Technology Transfer award, and two R&D 100 awards. 

Gi-Heon Kim, Post-Doctoral Researcher, National Renewable Energy Laboratory, 1617 Cole Blvd, 

MS 1633, Golden, CO, 80401, 303-275-4437, 303-275-4415, gi-heon_kim@nrel.gov 

Gi-Heon Kim has worked as a post-doctoral researcher with the Advanced Vehicle Systems group 

since 2004. Before coming to NREL, Dr. Kim completed a Ph.D. in Mechanical Engineering from 

Colorado State University. His professional experience includes a position as a Research Assistant 

with the Engines and Energy Conversion Laboratory at Colorado State University and a position as 

a Research Assistant with the Institute of Advanced Machinery and Design, Seoul National University. His 

background includes work in heat and mass transfer, fluid mechanics, turbulence, combustion, and fluid dynamics. 

In addition to his Ph.D., Dr. Kim holds an M.S. and B.S. in Mechanical Engineering from Seoul National University 

in Seoul, Korea. 

Tien Q. Duong, Office of FreedomCAR and Vehicle Technologies, U.S. Department of Energy, 1000 

Independence Avenue, SW, Washington, DC 20585, USA 202-586-2210, 202-586-1600 (fax), 

Tien.Duong@ee.doe.gov 

Mr. Duong is Vehicles Technologies Team Lead at the Department of Energy’s FreedomCAR and 

Vehicle Technologies Program Office. Mr. Duong received his M.S. degree in Civil Environmental 

Engineering, and his B.S. degree in Electrical Engineering from Virginia Polytechnic Institute and 

State University in Blacksburg, Virginia. He is a member of USABC Managing Committee. 

9 
REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, 

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this 

collection of information, including suggestions for reducing the burden, to Department of Defense, Executive Services and Communications Directorate (0704-0188). Respondents 

should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a 

currently valid OMB control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION. 

1. REPORT DATE (DD-MM-YYYY) 

April 2005 

2. REPORT TYPE 

Conference Paper 

3. DATES COVERED (From - To) 

4. TITLE AND SUBTITLE 

Improving Battery Design with Electro-Thermal Modeling: Preprint 

5a. CONTRACT NUMBER 

DE-AC36-99-GO10337 

5b. GRANT NUMBER 

5c. PROGRAM ELEMENT NUMBER 

6. AUTHOR(S) 

A. Pesaran, A. Vlahinos, D. Bharathan, G. Kim, and T. Duong 

5d. PROJECT NUMBER 

NREL/CP-540-37652 

5e. TASK NUMBER 

FC056000 

5f. WORK UNIT NUMBER 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 

National Renewable Energy Laboratory 

1617 Cole Blvd. 

Golden, CO 80401-3393 

8. PERFORMING ORGANIZATION 

REPORT NUMBER 

NREL/CP-540-37652 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) 

NREL 

11. SPONSORING/MONITORING 

AGENCY REPORT NUMBER 

12. DISTRIBUTION AVAILABILITY STATEMENT 

National Technical Information Service 

U.S. Department of Commerce 

5285 Port Royal Road 

Springfield, VA 22161 

13. SUPPLEMENTARY NOTES 

14. ABSTRACT (Maximum 200 Words) 

Temperature greatly affects the performance and life of batteries in electric and hybrid vehicles under real driving 

conditions, so increased attention is being paid to battery thermal management. Sophisticated electrochemical 

models and finite element analysis tools are available for predicting the thermal performance of batteries, but each 

has limitations. In this study we describe an electro-thermal finite element approach that predicts the thermal 

performance of a cell or module with realistic geometry, material properties, loads, and boundary conditions. 

15. SUBJECT TERMS 

HEV; thermal management; nickel metal hydride; battery model; simulation 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION 

OF ABSTRACT 

UL 

18. NUMBER 

OF PAGES 

19a. NAME OF RESPONSIBLE PERSON 

a. REPORT 

Unclassified 

b. ABSTRACT 

Unclassified 

c. THIS PAGE 

Unclassified 19b. TELEPHONE NUMBER (Include area code) 

Standard Form 298 (Rev. 8/98) 

Prescribed by ANSI Std. Z39.18 

F1147-E(12/2004)