1

Updates to BatPaC to Support US EPA/DOT Proposed Rules

Paul Nelson and Kevin Gallagher

Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, IL USA

March 1

st

, 2012

1. Summary

The United States Environmental Protection Agency (EPA) requested the inclusion of two 

expanded features into the publically available Battery Performance and Cost model, BatPaC 

v1.0, created by Argonne National Laboratory. The first request was to add additional battery 

pack thermal management options to the model. The thermal management of the pack with 

forced cabin air and conditioned cabin air was desired. The EPA also requested an increasing 

number of options for parallel arrangements at the module and pack level. These additions have 

now been implemented into BatPaC v2.0 Beta. The remainder of this document details the 

approach and demonstrates the results of the modifications on the calculated battery volume, 

weight, and cost to the original equipment manufacturer (OEM).

The addition of forced air thermal management required a redesign of the battery modules to 

increase the surface area available for heat transfer. This design change will always result in air 

thermally managed battery packs that are greater in volume than those using the liquid thermal 

management option. The use of forced cabin air will sometimes result in a slightly less expensive 

pack, particularly for hybrid electric vehicle (HEV) batteries. For example, a 140V, 5 Ah, 35 kW 

LMO-G HEV battery pack has a total cost to the OEM of $1,150 using forced cabin air thermal 

management as compared to $1,210 for liquid thermal management, thus only a modest savings 

of $60. If conditioned cabin air is used, then this cost savings becomes even less. The HEV 

battery pack demonstrated here with air thermal management has 2.7 times greater volume than 

the pack with liquid thermal management. Selection of the thermal management mode may be 

made in cell F53 on the Battery Design worksheet.

The model was amended to include the use of parallel modules and battery packs. BatPaC v1.0 

was already capable of using parallel cells. The designed batteries will increase in price in the 

following order: all connections made in series, cells in parallel, modules in parallel, and packs 

in parallel. The selection of parallel modules or packs can be made on rows F61-F63 on the 

Battery Design worksheet. Care must be used when entering the number of modules and cells or 

specifying pack energy and power if a parallel arrangement is selected. For example, a 50 kWh, 

100 kW pack with 96 series connected cells over 6 modules would be simulated as two parallel 

packs by entering 25 kWh for energy, 50 kW for power, 96 cells, but with 2 parallel packs (row 

F62) and entering a “P” for parallel in row F63. Designing the above pack with two sets of 

parallel modules would require entering in 50 kWh, 100 kW, but 12 modules with 2 in parallel 

(row F61).

The updated version of BatPaC also includes the automatic calculation of error bars based on the 

previous variation study communicated in the Argonne report that accompanied BatPaC v1.0. 

The calculations for the uncertainty occur on a separate worksheet and do not affect the 

previously communicated design methodology.
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2. Provision for Parallel Modules and Parallel Packs

The provision for specifying multiple modules and multiple packs was added to the worksheet 

“Battery Design” and the equations throughout the spreadsheet were altered as necessary. A 

sample set of calculations is shown in Table 1 for an EV100 battery. The first column is for a 

battery designed with 128 series connected cells (calculated to be 75-Ah in capacity). This 

configuration results in the least volume, weight and cost, if it can be done safely. The second 

column is for two small cells connected in parallel. To implement this design choice, the user 

must designate the number of cells in parallel and increase the number of cells in a module

accordingly. The model program will automatically select a cell thickness of 6 mm, which is half 

the thickness selected by the model for EV cells if all are connected in series. For the selections 

made here, the cells for the battery of column two are approximately the same length and width 

as for the cells of column one. Because of the larger number of cells, the price of the battery with 

parallel connected cells is higher than that for the battery of column one.

Table 1. Various Lithium-Ion (NMC-441/G) Battery Configurations for Electric Vehicles with 

100-Mile Range, 120-kW Power and Glycol-Water Battery Cooling

Two small Small cells Small cells Small cells

Single string cells in with modules with packs with packs

 of large cells parallel in parallel in parallel in series

Battery pack power, kW 120 120 120 60 60

Battery system energy, kWh 35.3 35.3 35.3 35.3 35.3

Battery nominal voltage, V 480 480 480 480 960

Cell capacity, Ah 75.0 38.3 38.3 37.5 37.5

Cell thickness, mm 12.0 6.0 12.0 12.0 12.0

Length-to-width for positive electrode 3.0 3.0 1.5 1.5 1.5

Number of cells per module 16 32 16 16 16

Number of cells in parallel 1 2 1 1 1

Number of modules in row 4 4 4 4 4

Number of rows of modules per pack 2 2 4 2 2

Number of modules per battery pack 8 8 16 8 8

Number of modules in parallel 1 1 2 1 1

Number of packs per vehicle 1 1 1 2 2

 Parallel packs (P) or series (S) P S

Cells per battery pack 128 256 256 128 128

Total cells per battery system 128 256 256 256 256

Total weight of battery pack(s), kg 207.6 225.4 223.6 222.6 222.6

Total volume of battery pack(s), L 121.3 125.7 133.3 139.0 139.0

Battery pack length, mm 884 886 884 884 884

Battery pack width), mm 805 822 886 454 454

Battery pack height, mm 161 163 161 161 161

Heat generation at 80 mph, kW 4.13 4.01 3.89 2.13 2.13

Cooling system power, kW 1.65 1.61 1.56 1.71 1.71

Price to OEM for battery pack, $ 6,824 7,546 7,942 3,963 3,963 

Pack integration, $ 475 475 735 750 750 

Additional for thermal management, $ 340 340 340 460 460 

Total cost to OEM for system, $ 7,639 8,361 9,017 9,135 9,135 

Error bars on price to OEM for battery pack, %

 Potential positive error, % 22 17 17 17 17

 Potential negative error, % 15 15 15 15 15
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The battery of column three has small cells with modules connected in parallel. To select this 

choice, the user of the model must increase the number of modules and select the desired number 

of modules in parallel. Because there are more modules than in the first two batteries, the lengthto-width ratio of the electrodes was reduced from 3.0 to 1.5 to make the overall dimensions of 

the battery more like those of the first two batteries. The cost of the third battery is more than 

that of the second battery because of costs for extra module hardware especially for the extra 

circuits for state-of-charge regulation.

The batteries for columns four and five each have two battery packs, one with the packs in 

parallel and one with them in series. To select these configurations, the user must first configure 

the battery packs, remembering that each pack provided only a part of the energy, and then select 

the number of packs and designate whether they are in parallel or series connection. The user 

must also determine the capacity of the pack at the bottom of the “Battery Design” worksheet. 

The user makes this determination by selecting one of the following: (1) the pack capacity (note: 

not the cell or total battery system capacity), (2) the pack energy, or (3) the range of the vehicle. 

For Table 1, we selected a 100 mile range for all five sample battery systems. With the above 

mentioned adjustments to the length-to-width ratio of the positive electrodes, all of the battery 

systems have about the same length and height. The total volume is slightly higher for the last 

two battery systems because of the extra volume in the pack walls. The battery system with 

series-connected packs has twice the voltage and half the system capacity of the other four 

battery systems.

3. Changes in Thermal Management Modeling

As in the earlier version, BatPaC v2.0 has a separate worksheet for estimating the thermal 

parameters and requirements for lithium batteries and for designing the thermal management 

system. The results are transferred to the Battery Design worksheet to calculate the mass, volume 

and materials requirements for the battery pack.

3.1 Cell and Battery Designs

To allow a quick comparison, the cell and battery designs for both the liquid-cooled batteries 

discussed previously and the new air-cooled system added herein are presented below. Both 

designs employ a prismatic cell in a stiff-pouch container. The terminals are almost as wide as 

the full width of the cell with the positive terminal at one end of the cell and the negative 

terminal at the opposite end. The electrical performance of a cell with this construction is near 

optimum, with a very low fraction of the resistance in the current collection structure. This cell 

design is amenable to either liquid cooling or air cooling. For liquid cooling, the cells are 

enclosed in hermetically sealed modules, which are cooled on their exterior surfaces by ethylene 

glycol-water solution. The module enclosure protects the cell terminals from the coolant, which 

is an electrolyte. As an additional safety precaution, the cells could be cooled by a dielectric 

liquid, such as a transformer coolant, but that approach has not been studied here.

The stiff-pouch containment for the cell and the terminal seal is illustrated in Fig. 1. The cell 

terminals are formed from flat stock to be almost as wide as the entire cell. They are bent to the 

required shape and ultrasonically welded to the current collector tabs. The cell stack is then 
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sealed between the two halves of the cell container. The cell housing material is a tri-layer 

consisting of an outer layer of polyethylene terephthalate (PEP) for strength, a middle layer of

0.1-mm aluminum for stiffness and impermeability to moisture and electrolyte solvent vapors 

and an inner layer of polypropylene (PP) for sealing by heating. The two halves of the cell 

container are pre-shaped to facilitate assembly. The aluminum foil in the cell container material 

provides stiffness and it may be increased in thickness to assist in conducting heat to the module 

container. After sealing the edges of the cell, the edges are flattened along the sides of the cell to 

form a compact shape. For liquid cooling, an aluminum conduction channel is added to assist in 

heat rejection at the sides of the cells (Fig. 1). For batteries cooled by air, the cell design format 

is the same as for liquid-cooled batteries. To provide space for air flow between the cells, the

cells are enclosed in an aluminum sleeve that provides the flow passages, as illustrated in Fig. 2. 

The ridges between the cooling passages are 2-mm wide. The cooling passages are about 20-mm

wide, the exact width being calculated to provide an integer number of passages across the length 

of the positive electrode.

Figure 1. Prismatic cell in stiff pouch container with aluminum conduction channel added for 

heat rejection from a liquid cooled module

Cell with Stiff, MultiLayer Container

Terminal Seal

Polymer Seal of 

Cell Container 

to Terminal 

Ultrasonic Welds

of Terminal to 

Collector Foils

Cell Cross-Sections

After Edge Sealing

After Edge Shaping and 

Addition of Aluminum 

Conduction Channel

Aluminum 

Conduction 

Channel
5

Figure 2. Provision for cooling cells with air

For liquid cooling the module format is based on a casing of 0.5-mm thick aluminum that is 

sealed by double seaming, a process that is well established and inexpensive because it is 

automated, rapid, and uses low-cost equipment that is common in the container industry. The 

sealing of the module provides an additional barrier to the loss of electrolyte solvent from the 

cells and the entrance of water vapor. These deleterious transfers through the seals of pouch cells 

may shorten their lives to less than the desired fifteen years. 

The cells are placed on their sides in the module and the terminals of adjacent cells are connected 

either mechanically with rivets and flat springs to maintain contact or by laser welding. Space is 

provided within the module casing on the left side, as sketched in Fig. 3, for an electronics 

package that includes cell monitoring for malfunctions (temperature and voltage) and for stateof-charge (SOC) control. The SOC control is activated whenever the battery is at rest and it 

diverts charge from the cells at highest voltage to those at lowest voltage.

For air cooling, the cells must be individually cooled and are, therefore, enclosed in an aluminum 

sleeve which provides air flow channels as discussed above; the module enclosure is open at the 

bottom and top to accommodate upward flow of air through these channels. Both the liquid and 

the air cooled designs are configured to be compact, light-weight and amenable to low-cost 

manufacture. For air cooling of the battery, the module must be open to allow air to flow 

between the cells (Fig. 4).

6 mm

2 mm

̴10-20 mm

Aluminum Cell Sleeve 

Providing Channels 

for Air Flow 

̴10-20 mm
6

Figure 3. Module with hermetically sealed aluminum container for liquid cooled batteries

Figure 4. Module designed for air cooling with polymer container open at top and bottom

Heat Transfer Surfaces

on Top and Bottom of 

Container in Contact with Cell Conductors

Module 

Terminal 

Cell Terminal 

Connections

Double-Seamed Module Closure

Cell State-ofCharge Controller

Polymer Strip 

Blocking Air Flow 

at Cell Terminals 

Module 

Terminal 

Cell Sleeves

Air Flow 

Channels
7

The model designs the battery packs (Fig. 5 for liquid cooling and Fig. 6 for air cooling) in 

sufficient detail to provide a good estimate of the total weight and volume of the pack and the 

dimensions of the battery jacket so that its cost can be estimated. For liquid-cooled packs, the 

modules are arranged within the battery jacket either in a single row, with the terminals facing 

the same side of the pack, or in an even number of rows with the terminals in one row facing the 

terminal of an adjacent row. For a pack with a single row of modules, a busbar must be provided 

to carry the current to the front of the battery pack. This feature results in an additional cost for 

the busbar. For batteries with more than one row of modules (Fig. 5), the terminals are laid out in 

the module so as not to interfere with those on the opposite row of modules, thus conserving 

space in the battery pack. The modules in a row are interconnected, negative to positive 

terminals, by copper connectors. The modules casings are compressed together between steel 

sheets at each end of the battery pack. The compression force is applied by steel bands wrapped 

around the top and bottom of the row of modules. The compression is necessary to ensure 

intimate contact between the active layers that make up the pouch cells that are tightly fit into the 

modules. The compressive force also serves to add structural support to the module casings.

The modules are supported by a tray that positions the modules mid-way between the inside top 

and bottom of the pack jacket and provides space for heat transfer fluid (liquid or air) to flow so 

that it cools or heats each module. The rows of modules are assembled, compressed between end 

plates, interconnected and attached to the module tray. The module tray is attached to the pack 

closure at the front of the pack so that all connections to the pack terminals that lead to the 

exterior of the pack and signal wire feedthroughs can be made before inserting the attached 

modules into the jacket and making the final closure. The bolts depicted in the diagrams for 

making this closure are only illustrative.

For both cooling options, the battery jacket consists of a sheet of aluminum on each side of a 10-

mm thick layer of ridged, light-weight high-efficiency insulation. The thickness of each of the 

aluminum layers is selected by the modeling program to be 1- to 2-mm thick, depending on the 

total volume of the modules. The insulation slows the interaction of the battery with the external 

environment that cools the battery in the winter and heats it in the hot summer weather.

The air-cooled battery format is similar to the liquid-cooled format in that the cells are the same 

and the modules casings are held together by steel sheets at the ends of the row of modules and 

compressed by steel straps. The battery pack for air cooling differs, however, in that much more 

space must be allotted for air flow than for liquid flow (Fig. 6). Air is admitted along the entire 

length of the bottom of the pack to minimize the thickness of the flow passages above and 

beneath the modules. The air leaving the module is ducked to the inlet side of the fan, which can 

be located nearby to suit the vehicle design. The pack-long entrance and exit passages are 

insulated for thermal efficiency. These additions and the air passages between the cells and the 

wide passages required above and below the modules add considerable volume to air-cooled

packs over that required by liquid cooled packs. The thermal calculations indicate that cabin aircooling is sufficient for HEV battery packs and for some larger battery packs, but it may limit the 

driving profiles that are feasible.
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Figure 5. Insulated battery jacket with enclosed modules that are cooled on their upper and 

lower surfaces by ethylene glycol-water solution 

 
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Figure 6. Battery pack cooled by cabin air

3.2 Heat Generation Rates in the Battery Pack during Driving

Because air cooling is strictly limited in the rate at which it can remove heat from the battery, 

more attention was needed to the conditions that cause heat generation in the battery in providing 

for air cooling than was done for the previous version of the model. It was also realized that for 

some vehicle driving conditions and battery combinations, heat generation should be addressed 

even for the liquid-cooling option.

During driving, the heat generation rate depends on the driving cycle and the power of the 

battery relative to the demands of the cycle for the vehicle being driven. The heat capacity of the 

battery pack smooths out fluctuations in the heat generation rate. The rate that the cooling system 

A

A

Section A-A

Air Flow 

Passages 

between Cells

Duct to 

Fan Inlet
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must handle is the average rate for the most difficult sustained driving conditions to which the 

battery pack will be subjected.

There are two types of driving profiles that will generate high heating rates in the battery pack. 

One is a demanding diving profile with fluctuating speeds, rapid accelerations to high speeds and 

minimum speeds of at least 40 mph. The average heat generation rate for such driving profiles is 

difficult to evaluate and is best done by vehicle simulation studies. These studies require a 

battery impedance algorithm that makes possible accurate estimates of internal battery heating 

during vigorous driving patterns. The results of vehicle simulation studies of battery heating can 

be entered on line 36 in the “Thermal” worksheet to override the estimated default values. 

However, since pertinent results for demanding driving cycles are not always accessible, we 

have provided some estimations for a second type of driving pattern for which heat generation is 

easier to calculate, that of driving at a high constant speed. Such driving may cause battery heat 

generation that is at least as high as for a vigorous driving profile. The high heating rate results 

because constant rate discharge of the battery pack causes high battery impedance, which reaches 

more than twice the impedance of the battery when operated with fluctuating charge and 

discharge operation. The heat generation rate within the battery pack during constant-speed 

driving is estimated by BatPaC v2.0 as outlined below with sufficient accuracy for battery cost 

estimation, but perhaps not sufficient for final design of the thermal management system for the 

battery.

For microHEV battery packs, heat generation is intermittent and substantial periods of little or no 

heat generation exist in the load profile. The model estimates the heat generation rate for 25-kW 

micro-HEV batteries at 100 W, which is entered on line 35 in the Thermal worksheet

For the larger battery packs (HEV-HP, PHEV and EV), the BatPaC model calculates the vehicle 

constant speed at which the centerline of the hottest cells in the battery will reach the maximum 

allowed temperature with steady state cooling, which is set at 40oC in the sample calculation on 

line 17. That speed is deemed to be the maximum speed that the vehicle can be driven without 

damaging the battery. Presumably, the battery control system will limit the battery output as this 

condition is approached. This maximum speed will depend on vehicle design parameters, the 

type of electric drive (HEV-HP, PHEV or EV), the battery maximum power, the type of cooling 

system, (cabin air or liquid) and the battery design as it affects the efficiency of cooling. Under 

some conditions, it might be desirable to set a lower speed than that limited by battery heating to 

reduce the required capability and cost of the cooling system. This can be done by entering the 

maximum constant speed at which the vehicle will be operated on line 19 and BatPaC will 

calculate the maximum steady-state temperature of the battery pack on line 18.

To estimate the power needed to drive the vehicle at any desired speed, approximate equations 

are needed for vehicle parameters including accessory power, rolling friction and aerodynamic 

drag. A starting point for deriving these equations is the battery power calculated from the 

energy requirement per mile, 

E



(default value 300 Wh/mile entered on the Battery Design 

worksheet, line 177, and also transferred to the Thermal worksheet, line 7) and the constant 

vehicle speed, So (default value 50 mph entered on line 179 and 8 of the respective worksheets) 
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that will require this rate of energy. The battery power, Po (kW) will sustain a vehicle speed of So

for the designated value of

E



:

 

 

E



 

 

⁄ (3.1)

The total battery power (Po) for maintaining the designated speed for the energy requirement 

provides power to the vehicle for accessory power (Pa), rolling friction power (Pf), and 

aerodynamic drag power (Pd). In this approximate calculation, we define these distributed power 

values to include the appropriate inefficiencies of the electrical and mechanical systems needed 

to operate the vehicle. The accessory power is estimated to be 1.5 kW at the default energy 

requirement of 300 Wh/mile and to be proportional to the energy requirement, thus:

 

E



 

⁄ (3.2)

The rolling friction is assumed to be directly proportional to the speed (So, mph) and to be 0.09 

kW/mile for the default energy requirement of 300 Wh/mile. It is assumed to increase more than 

proportionately with 

E



because heavy vehicles with high energy usage tend to require a larger 

fraction of the total energy and power to overcome rolling friction than light vehicles. Thus, the 

power factor for rolling friction (fPf, kW/mph) is:

 (

E



 

⁄ )

 

(3.3)

And, (3.4)

By subtraction, (3.5)

The drag factor (fPd), which includes both the drag coefficient and the vehicle frontal area is:

 

 

 

⁄ (3.6)

The value of Pd at any vehicle speed (So) may be calculated with the expression:

 

 

(3.7)

In Fig. 7 the distribution of the power drawn from the battery for the three uses of power for the 

vehicle that we have defined is illustrated for a range of values of 

E



all at a vehicle speed (So) of 

50 mph.
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Figure 7. Distribution of power from the battery versus the energy requirement (

E



) defined at a 

sustained vehicle speed (So) of 50 mph

At any sustained vehicle speed, S, higher than So at which 

E



is defined, the power increases and 

can be calculated by means of the equations (3.2), (3.4), and (3.7), with the substitution of S for 

So, and noting that the total battery power, Ps, can be calculated from:

 (3.8)

For battery packs other than microHEV battery packs, the BatPaC model calculates the heat 

generation rate (qb, kW) from the battery current (Ib, A) and the battery resistance for a sustained 

constant discharge (Rbs, ohms):

 = 

 

 (3.9)

For HEV-HP batteries, the battery is operated for an estimated 30 to 60 seconds and the value of 

Rbs is estimated to be 20% more than for the battery resistance at maximum power, which is for 

10 seconds at 80% of OCV (0.8U). Also the average battery heat generation rate is about 60% of 

qb as defined by Eq. (3.9) because only about 60% of the power for the vehicle is delivered from 

the battery; the balance of the power for the vehicle comes from the engine by direct coupling to 

the drivetrain or through a generator and motor. For PHEV and EV batteries, the heat generated 

in the battery pack is calculated directly from Eq. (3.9). Battery current (Ib) and voltage (Vb) are 

calculated as follows where Ps (kW) is the maximum sustained power and U is the open-circuit 

voltage at 50% SOC:

0

5

10

15

20

25

150 200 250 300 350 400 450 500 550 Battery Power, kW

Energy Requirement at Battery, Wh/mile

Aerodynamic Drag

Rolling Friction
13

 

 

 

⁄ (3.10)

 

 √ 

 

(3.11)

The heat generation rate in the battery is selected on line 37 in the Thermal worksheet from three 

possible values: (1) for microHEV batteries it is 100 W (line 35), (2) for batteries that have been 

modeled in a vehicle simulation program to determine maximum sustained heat generation and 

the result entered on line 36, and (3) for all other battery packs, the heat generation rate 

calculated on line 33 (based upon Eq. 3.9) is selected.

The vehicle speed and the associated maximum battery temperature are determined in an 

iterative process and the results are entered on lines 18 and 20, respectively. The desired 

maximum battery temperature at steady-state is entered by the user on line 17 and the model 

calculates the maximum sustained battery power, line 29, the internal battery heat generation 

rate, line 33, and the maximum sustained vehicle speed associated with those values, line 20. In 

this process, the heat generation value is calculated either in the liquid cooling section beginning 

on line 68 or the cabin-air cooling section beginning on line 113, as determined by the type of 

coolant ( line 67). In carrying out this calculation, if the temperature calculated is different from 

the temperature target on line 17, the program automatically adjusts the vehicle speed and the 

process is repeated until agreement is reached between the calculated temperature on line 18 and 

the target on line 17. The maximum battery temperature is calculated at the end of the heat 

transfer calculations for the liquid-cooled and the cabin-air cooled battery packs (lines 112 and 

173, respectfully).

As noted above, an alternative to selecting the maximum battery temperature is to select the 

maximum continuous vehicle speed under electric power as determined by the vehicle power 

control system and to enter that value on line 19. Then the model program will calculate the 

maximum battery temperature associated with that continuous vehicle speed.

The overall adequacy of the cooling is estimated on line 40 as a function of the maximum 

temperature of the battery at steady-state cooling as follows:

Maximum Cell Temperature Cooling Adequacy

35 oC or less Excellent

Over 35 oC to 40 oC Good

Over 40 oC to 45 oC Fair

Over 45 oC Poor
14

3.3 Active Cooling Systems

There are several choices of coolant that have been considered for cooling battery packs 

including air from the cabin, which may be heated or cooled, water-ethylene glycol solutions and 

dielectric liquids such as transformer fluids. Also, cooling plates in contact with surfaces on the 

cells or the modules may be cooled directly with refrigerant. Air is the least expensive, but it is 

less effective than the liquid coolants because of its poor conductivity, the need for large flow 

passages and high pumping power. Dielectric liquids are expensive, but have the advantage of 

being compatible with terminals and other parts at electrical potential. Water-50% glycol 

solution is inexpensive and has better properties as a coolant (thermal conductivity, heat 

capacity, and viscosity) than typical transformer fluids. Cooling directly with a refrigerant would 

eliminate the need for an intermediate heat transfer fluid and may be the most efficiency of the 

systems, but it is more technically complex to access, which was not attempted here. In this 

study we consider both cooling with cabin air and cooling with water-50% glycol solution. To 

evaluate cooling with a dielectric fluid, it would only be necessary to substitute the properties of 

the dielectric fluid for those of water-50% glycol solution (lines 86-89) and to increase the cost 

of the thermal management system to allow for the higher cost of the coolant.

For both the liquid-cooled and the cabin-air cooled batteries, we selected a general cell design 

that can be adapted to all of the electric-drive batteries from micro-HEVs packs to EV packs 

(section 2). For all types of batteries, the liquid-cooled design incorporates a hermetically sealed 

module closure. This design can be effectively cooled by liquids and requires that only the 

module terminals and connectors be protected from contact with a conducting coolant, thus 

accommodating water-glycol coolant. Heat is transferred from the cells to the cooled surfaces of 

the modules by aluminum conductors in contact with the broad surfaces of the cells and the 

module closure surfaces from which the heat is conducted (Fig. 2.5).

Unfortunately, the enclosure does not have sufficient surface area to be cooled effectively by air. 

For cooling with cabin air, it is necessary to cool the individual cells by means of flow passages 

between the cells, which add considerably to the pack volume. That design feature permits air 

cooling for microHEV and HEV-HP batteries. Also, for some combinations of vehicle 

parameters and PHEV and EV battery configurations that result in low heat generation rates, air 

cooling might be used. However, air cooling is much less effective than liquid cooling and 

cannot be considered for instance for PHEVs that are powered electrically at highway speeds. 

3.3.1 Cooling with Ethylene Glycol-Water Solution

For the battery designs in BatPaC v2.0 for liquid cooling (and air cooling also), the battery pack 

coolant is contained by the battery jacket, which severely limits the practical pressure drop in the 

coolant circuit. The pack is on the suction side of the pump so the module structure assists in 

supporting the walls of the battery jacket. This approach is simple to calculate and appears to 

result in a workable design of low cost. Alternatively, cooling plates with built-in flow channels 

and capable of withstanding high pressure may be used with ethylene glycol-water heat-transfer 

fluid reducing the likelihood of this electrolyte contacting cell or module terminals, but the cost 

would be higher than for the design we have adopted.
15

As described above, the cells transfer heat to the cooled walls of a hermetically sealed module 

with the aid of an aluminum heat conduction channel. Some of the heat is transferred through the 

sides of the cell to the channel and from there to the module wall and some is transferred directly 

through the seal edge of the cell to the conduction channel flange which is in contact with the 

module wall. The heat is transfer from the module wall by the flowing coolant. 

The method for calculating the heat transfer rates is detailed in the manual accompanying 

BatPaC 1.0 and no change has been made to that method of calculation. However, the cooling of 

the battery pack has been linked with the new section on heat generation in the pack during 

driving and is illustrated below in section 4.

3.3.2 Cooling with Cabin Air

For cooling with air, it is necessary to provide much more cooling surface area than that of the 

module surfaces cooled by liquid coolants as discussed in section. In this study the extra cooling 

area was gained by cooling the individual cells as shown in Fig. 2 and 4. This approach greatly 

simplifies the calculation of heat transfer from the interior of the cells, which can be solved as a 

one-dimensional calculation as contrasted with the more complex two-dimensional calculation 

done for liquid cooling of the outside of the module. The coolant flow is complex for air, 

however, in that the air flows in at the bottom of the long side of the battery pack, splits into 

many flow steams as it flows up the passages between the cells and then recombines and flows 

out the top of the battery pack.

The composite conductivity across the cell layers was calculated by dividing the total cell 

thickness by the sum for all layers of the conductivity of each layer divided by its thickness as 

illustrated in the manual accompanying BatPaC v1.0. 

The temperature drop from the center of the cell to the cell wall, ∆Tcell, was calculated as 

follows:

 

 

 

 

 

 

 

The length of the cooled section of the cell is taken to be the same as the length of the positive 

electrode. The number of air flow channels is calculated by dividing this length by the target 

width of an air flow channel plus one rib and rounding down to an integral number. The target

channel width was taken to be 1.0 cm for good structural strength, but any width between 1.0 and 

2.0 cm will provide similar results for cooling. The exact width of the channels is calculated 

from the electrode length and the number of channels. The thickness of the channel is calculated 

in an iterative process to meet the pressure drop for the required flow rate. The required flow for 

a single channel is that which will carry off the heat generated by the cell divided by the number 

of cooling channels per cell.

Because of the difficulty in moving sufficient air through the pack to carry out the heat generated 

in the cells, the air must be allowed to rise in temperature by about 5oC, whereas for liquidcooled packs, 1oC temperature rise is sufficient. We also used a higher pressure drop to force the 

air through the pack, 0.02 bar versus 0.01 bar for liquid-cooled packs. The pressure drop for air 
16

cooling is divided between that through the channels between the cells (90%) and that in the 

large passages across the bottom of the pack where the air enters and across the top of the pack 

where the air leaves (10%). This distribution of the available pressure drop, which is achieved by 

sizing the thickness of the channels between the cells and those at the top and bottom of the 

pack, provides an even supply of air to all channels between the cells. All of the parameters 

discussed for managing the air flow are adjustable by the model user, but large deviations from 

the suggested values may adversely affect the feasibility of the design.

The heat transfer to establish the temperature drop from the cell sleeve wall to the bulk air stream 

is calculated in much the same way as described for the liquid-cooled battery packs. However, 

for the air-cooled packs, heat is transferred from both sides of the channel rather than from only 

one side as for the liquid-cooled modules, which have insulated jacket walls on the opposite side 

of the cooling channel, and the Nusselt number is adjusted accordingly.

4. Illustration of Model Results for Cooling while Driving

The calculations for cooling of HEV batteries are straightforward and the use of the default 

parameters and warnings provided by the spreadsheet appear to be adequate for most cases. A 

more difficult application, that of cooling PHEV battery packs, was selected to illustrate some of 

the features of BatPaC v2.0. 

Table 2 is a replica of part of the “Battery Design” worksheet where most of the battery design 

variables are entered. The input parameters are identical for the five batteries including cooling 

with ethylene glycol-water (EG-W), except for the power, which ranges from 80 to 120 kW. To 

complete the parameter selection, the electric range of the vehicles associated with these battery 

packs was set at 15 miles. 

In the “Thermal” worksheet for these batteries (Table 3) we have limited the speed of the 

vehicles to 75 mph. Under these conditions, the heat generated in the batteries ranges from 7.21

kW for the 80-kW battery to 4.14 kW for the 120-kW battery. The 80-kW battery has the highest 

heat generation and is the most difficult to cool and thus is deemed “poor” in this regard (red 

letter warning at bottom of table) because the maximum temperature at the center of the cells is 

over 45oC (see table on page 13). The batteries with higher power generate less heat and,

therefore, are able to maintain moderate temperatures at the center of the cells.

The higher the battery power, the more costly is the battery pack (Table 4). However, the 

increase in cost of the battery pack is almost offset by the lower cost to the OEM for providing 

the means of cooling the more powerful batteries. Also, the more powerful batteries need less 

energy for cooling and would, therefore, provide slightly longer electric ranges.

The results for cooling these same batteries with cabin air are as illustrated in Tables 5 and 6 and 

comments are provided below these tables.
17

Table 2. Battery Design Worksheet from BatPaC v2.0 for LMO-G Battery Packs of 80 to 120-

kW Power providing 15-mile Range for PHEVs requiring 300-Wh/mile Energy

Battery 1 Battery 2 Battery 3 Battery 4 Battery 5

Length-to-width ratio for positive electrode 3.00 3.00 3.00 3.00 3.00

Cell thickness, mm 8.0 8.0 8.0 8.0 8.0

Thickness of cell edge from positive electrode to outside of fold, mm 1.0 1.0 1.0 1.0 1.0

Thickness of terminal material, mm 1.00 1.00 1.00 1.00 1.00

Top of positive electrode to top of terminal, mm 15 15 15 15 15

Cell Capacity Parameters

Positive active material capacity, mAh/g: 100 100 100 100 100

Positive electrode capacity, Ah/cm3 0.223 0.223 0.223 0.223 0.223

Negative active material capacity, mAh/g: 330 330 330 330 330

Negative electrode capacity, Ah/cm3 0.441 0.441 0.441 0.441 0.441

Negative-to-positive capacity ratio after formation 1.20 1.20 1.20 1.20 1.20

Cell Voltage and Resistance Parameters

OCV at full power, V 3.819 3.819 3.819 3.819 3.819

Open circuit voltage average for discharge, V 3.954 3.954 3.954 3.954 3.954

Electrode system ASI for energy, ohm-cm2 44.0 44.0 44.0 44.0 44.0

Excess negative area, % 3.61 3.56 3.52 3.47 3.43

Default maximum allowable electrode coating thickness, mm 100 100 100 100 100

Cell terminal contact voltage loss, % of cell OCV 0.01 0.01 0.01 0.01 0.01

Rate of terminal temperature rise at full power, oC/sec 0.05 0.05 0.05 0.05 0.05

Target % OCV at full power 80 80 80 80 80

% OCV at full power adjusted for thickness limit 80.0 80.0 80.0 80.0 80.0

Battery Input Parameters

Vehicle type (microHEV, HEV-HP, PHEV, EV) PHEV PHEV PHEV PHEV PHEV

Pack heat transfer fluid (EG-W, CA, CoolA ) EG-W EG-W EG-W EG-W EG-W

Duration of power burst (10 or 2), s 10 10 10 10 10

Battery pack power, kW 80 90 100 110 120

Number of cells per module 20 20 20 20 20

Number of cells in parallel 1 1 1 1 1

Number of modules in row 3 3 3 3 3

Number of rows of modules per pack 2 2 2 2 2

Number of modules per battery pack 6 6 6 6 6

Number of modules in parallel 1 1 1 1 1

Number of packs per vehicle (parallel or series) 1 1 1 1 1

 Parallel packs (P) or series (S)

Cells per battery pack 120 120 120 120 120

Total cells per battery system 120 120 120 120 120

Voltage drop for bus bar for packs with one row of modules, V 0.03 0.03 0.03 0.03 0.03

Battery pack insulation thickness, mm 10 10 10 10 10

Battery jacket total thickness, mm 13 13 13 13 13

Number of batteries manufactured per year 100,000 100,000 100,000 100,000 100,000

Cell Chemistry Input

Battery Performance and Design Input

Program for Calculating Performance and Materials Requirements

Manganese-Spinel/Graphite
18

Table 3. Thermal Worksheet from BatPaC v2.0 for LMO-G Battery Packs of 80 to 120-kW 

Power providing 15-mile Range for PHEVs requiring 300-Wh/mile Energy, EG-W Cooling

Thermal Data Input

Battery 1 Battery 2 Battery 3 Battery 4 Battery 5

Maximum Sustained Heat Generation Rates in Battery Pack

Vehicle requirements (Note: Not for design ,but for estimating cooling requirements.)

Energy requirement for pack, Wh/mile 300 300 300 300 300

Designated constant speed at energy requirement, mph 50 50 50 50 50

Power Requirement from Each Pack for Sedan Including Inefficiencies

 Power for accessories, kW 1.5 1.5 1.5 1.5 1.5

 Power factor for rolling friction, kW/mph 0.090 0.090 0.090 0.090 0.090

 Power for aerodynamic drag, kW 9.00 9.00 9.00 9.00 9.00

 Power factor for aerodynamic drag, kW/(mph)3 0.000072 0.000072 0.000072 0.000072 0.000072

 Total Power at designated speed, kW 15.0 15.0 15.0 15.0 15.0

 Designed battery pack power for short bursts, kW 80 90 100 110 120

Maximum Sustained Vehicle Speed with Electric Power

 Target temperature at center of hottest cell, oC 40 40 40 40 40

 Maximum temperature at center of hottest cells, oC 45.6 40.8 37.4 34.7 32.6

 Override maximum sustainable vehicle speed, mph 75 75 75 75 75

 Calculated maximum sustained vehicle speed, mph 75.00 75.00 75.00 75.00 75.00

 Calculated maximum (holding) 75.0 75.0 75.0 75.0 75.0

 Selected maximum, mph 75.0 75.0 75.0 75.0 75.0

HEV-HP Battery Packs NA NA NA NA NA

 Fraction of energy delivered through battery, % 60 60 60 60 60

 Battery resistance for sustained power, ohms 0.504 0.448 0.403 0.367 0.336

PHEV and EV Battery Packs

 Battery resistance for sustained power, ohms 0.773 0.685 0.615 0.558 0.510

Heat Generation in Pack at Maximum Sustained Speed

Sustained battery power, kW 38.6 38.6 38.6 38.6 38.6

Applicable battery resistance, ohms 0.773 0.685 0.615 0.558 0.510

Voltage on discharge, V 400 410 418 424 429

Current on discharge, I 96.6 94.2 92.5 91.2 90.1

Heat generation, W or joules/sec 7212 6083 5261 4635 4142

Efficiency for discharge, % 84.3 86.4 88.0 89.3 90.3

microHEV battery packs, default heat generation 100 100 100 100 100

Override heat generation, W

Selected heat generation rate for pack, W 7212 6083 5261 4635 4142

Cooling system power requirement for entire battery system, W 2889 2437 2108 1857 1659

Excessive battery volume, reduce sustainable speed (if X)

Adequacy of Cooling Poor Fair Good Excellent Excellent

Thermal Modeling
19

Table 4. Summary of Results of Calculations from BatPaC v2.0 for LMO-G Battery Packs of 80 

to 120-kW Power providing 15-mile Range for PHEVs requiring 300-Wh/mile Energy, EG-W 

Cooling

Battery 1 Battery 2 Battery 3 Battery 4 Battery 5

Battery pack power, kW 80 90 100 110 120

Battery system energy, kWh 6.4 6.4 6.4 6.4 6.4

Battery nominal voltage, V 474 474 474 474 474

Cell capacity, Ah 13.6 13.6 13.6 13.6 13.6

Cell thickness, mm 8.0 8.0 8.0 8.0 8.0

Positive electrode thickness, mm 86 76 68 62 56

Length-to-width for positive electrode 3.0 3.0 3.0 3.0 3.0

Number of cells per module 20 20 20 20 20

Number of cells in parallel 1 1 1 1 1

Number of modules in row 3 3 3 3 3

Number of rows of modules per pack 2 2 2 2 2

Number of modules per battery pack 6 6 6 6 6

Number of modules in parallel 1 1 1 1 1

Number of packs per vehicle 1 1 1 1 1

Cells per battery pack 120 120 120 120 120

Total cells per battery system 120 120 120 120 120

Total weight of battery pack(s), kg 62.0 63.3 64.7 66.1 67.5

Total volume of battery pack(s), L 43.4 43.9 44.3 44.8 45.4

Battery pack length, mm 568 568 567 567 567

Battery pack width), mm 546 552 558 564 569

Battery pack height, mm 118 118 119 119 119

Heat generation at 75 mph, kW 7.21 6.08 5.26 4.64 4.14

Cooling system power, kW 2.89 2.44 2.11 1.86 1.66

Price to OEM for battery pack, $ 2,466 2,531 2,596 2,664 2,729 

Pack integration, $ 435 435 435 435 435 

Additional for thermal management, $ 440 400 360 360 320 

Total cost to OEM for system, $ 3,341 3,366 3,391 3,459 3,484 

Error bars on price to OEM for battery pack, %

 Potential positive error, % 23 20 18 15 13

 Potential negative error, % 10 10 10 10 10
20

Table 5. Thermal Worksheet from BatPaC v2.0 for LMO-G Battery Packs of 80 to 120-kW 

Power providing 15-mile Range for PHEVs requiring 300-Wh/mile Energy (Same as Table 3, 

but with Cabin-Air Cooling)

Whereas these same battery cells cooled with EG-W would permit driving at 75 mph, the Cabinair cooled cells would permit driving up to only 40 mph. At speeds higher than that, the volume 

of the batteries becomes excessive, as indicated by the warning note near the bottom of Table 5. 

The warning note is actuated for battery packs with densities less than 1.0 kg/L and it is evident 

that the first three battery packs do not meet that criterion even at a sustained speed of only 40 

mph. Cooling with air cooled with the vehicle air conditioning system would not remove more 

heat because the maximum temperature at the center of the cells is already approaching the 

temperature of the air exiting the pack (30oC), which is the entrance temperature (25oC) plus the 

Thermal Data Input

Battery 1 Battery 2 Battery 3 Battery 4 Battery 5

Maximum Sustained Heat Generation Rates in Battery Pack

Vehicle requirements (Note: Not for design ,but for estimating cooling requirements.)

Energy requirement for pack, Wh/mile 300 300 300 300 300

Designated constant speed at energy requirement, mph 50 50 50 50 50

Power Requirement from Each Pack for Sedan Including Inefficiencies

 Power for accessories, kW 1.5 1.5 1.5 1.5 1.5

 Power factor for rolling friction, kW/mph 0.090 0.090 0.090 0.090 0.090

 Power for aerodynamic drag, kW 9.00 9.00 9.00 9.00 9.00

 Power factor for aerodynamic drag, kW/(mph)3 0.000072 0.000072 0.000072 0.000072 0.000072

 Total Power at designated speed, kW 15.0 15.0 15.0 15.0 15.0

 Designed battery pack power for short bursts, kW 80 90 100 110 120

Maximum Sustained Vehicle Speed with Electric Power

 Target temperature at center of hottest cell, oC 40 40 40 40 40

 Maximum temperature at center of hottest cells, oC 31.7 31.4 31.2 31.1 30.9

 Override maximum sustainable vehicle speed, mph 40 40 40 40 40

 Calculated maximum sustained vehicle speed, mph 40.00 40.00 40.00 40.00 40.00

 Calculated maximum (holding) 40.0 40.0 40.0 40.0 40.0

 Selected maximum, mph 40.0 40.0 40.0 40.0 40.0

HEV-HP Battery Packs NA NA NA NA NA

 Fraction of energy delivered through battery, % 60 60 60 60 60

 Battery resistance for sustained power, ohms 0.504 0.448 0.403 0.367 0.336

PHEV and EV Battery Packs

 Battery resistance for sustained power, ohms 0.773 0.685 0.615 0.558 0.510

Heat Generation in Pack at Maximum Sustained Speed

Sustained battery power, kW 9.7 9.7 9.7 9.7 9.7

Applicable battery resistance, ohms 0.773 0.685 0.615 0.558 0.510

Voltage on discharge, V 458 460 462 463 464

Current on discharge, I 21.2 21.1 21.0 21.0 20.9

Heat generation, W or joules/sec 347 305 272 245 223

Efficiency for discharge, % 96.5 97.0 97.3 97.5 97.8

microHEV battery packs, default heat generation 100 100 100 100 100

Override heat generation, W 0.0 0.0 0.0 0.0 0.0

Selected heat generation rate for pack, W 347 305 272 245 223

Cooling system power requirement for entire battery system, W 354 311 278 250 228

Excessive battery volume, reduce sustainable speed (if X) X X X

Adequacy of Cooling ExcellentExcellentExcellentExcellent Excellent

Thermal Modeling
21

temperature rise (5oC) of the air. The limit on cooling is the increase in heat content of the air 

passing through the battery, which is dependent on the air flow (constrained by the allowable 

pressure drop and allowable volume of air passages) and the temperature rise. Both of these 

factors are already at what we consider to be the maximum values.

Table 6. Summary of Results of Calculations from BatPaC v2.0 for LMO-G Battery Packs of 80 

to 120-kW Power providing 15-mile Range for PHEVs requiring 300-Wh/mile Energy, (Same as 

Table 4, but with Cabin-Air Cooling)

The battery pack volumes are 47 to 57% higher for the cabin-air cooled battery packs than for 

EG-W cooled packs. The air-cooled packs are slightly more expensive because of the additional 

cost of the larger pack jacket. This is more than offset by the lower cost of the thermal 

management system to the OEM for air cooled packs. However, the ineffectiveness of air 

cooling, which limits the allowable vehicle speed, and the large volume of the air-cooled battery 

packs is seen as a serious drawback for short-range PHEVs. 

Battery 1 Battery 2 Battery 3 Battery 4 Battery 5

Battery pack power, kW 80 90 100 110 120

Battery system energy, kWh 6.4 6.4 6.4 6.4 6.4

Battery nominal voltage, V 474 474 474 474 474

Cell capacity, Ah 13.6 13.6 13.6 13.6 13.6

Cell thickness, mm 8.0 8.0 8.0 8.0 8.0

Positive electrode thickness, mm 86 76 68 62 56

Length-to-width for positive electrode 3.0 3.0 3.0 3.0 3.0

Number of cells per module 20 20 20 20 20

Number of cells in parallel 1 1 1 1 1

Number of modules in row 3 3 3 3 3

Number of rows of modules per pack 2 2 2 2 2

Number of modules per battery pack 6 6 6 6 6

Number of modules in parallel 1 1 1 1 1

Number of packs per vehicle 1 1 1 1 1

Cells per battery pack 120 120 120 120 120

Total cells per battery system 120 120 120 120 120

Total weight of battery pack(s), kg 63.3 64.7 66.2 67.7 69.2

Total volume of battery pack(s), L 68.5 67.8 67.4 67.1 67.0

Battery pack length, mm 662 657 654 650 647

Battery pack width), mm 546 552 558 564 569

Battery pack height, mm 173 171 169 167 166

Heat generation at 75 mph, kW 0.35 0.31 0.27 0.25 0.22

Cooling system power, kW 0.35 0.31 0.28 0.25 0.23

Price to OEM for battery pack, $ 2,503 2,568 2,632 2,700 2,765 

Pack integration, $ 435 435 435 435 435 

Additional for thermal management, $ 160 160 160 160 160 

Total cost to OEM for system, $ 3,098 3,163 3,227 3,295 3,360 

Error bars on price to OEM for battery pack, %

 Potential positive error, % 23 20 18 15 13

 Potential negative error, % 10 10 10 10 10