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
Ma rch 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 add itional battery pack thermal management options to the model. T he thermal management of the pack with
forced cabin air and conditioned cabin air wa s 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 v 2.0 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, p articularly for hybrid electric vehicle (HEV) batteries. For example, a 14 0V, 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 incre ase 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 module s or packs can be made on rows F61

- F6 3 on the Battery Design worksheet. Care must be used wh en 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 paralle l (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 separat e worksheet and do not affect the previously communicated design methodology

.2

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 equati ons 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
batter y 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 increa se 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 Cooling3

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 length

to

- width ratio of the electrodes was reduced f rom 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 us er 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, BatPa C 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 req u irements 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 e mploy 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 fr action 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 et hylene 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 ultrasonica lly welded to the current collector tabs. The cell stack is then4

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 t he 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 l iquid 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

c ells 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 a n 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 module5

Figure 2

. Pr ovision for cooling cells with air

For liquid cooling t he 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 comm on 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 t o 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 state

of

- charge (SOC) control. The SOC control is activated whenever the battery is at re st 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 batt ery, the module must be open to allow air to flow between the cells (Fig. 4 ).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 bottom7

The model designs the battery pack s (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, t he 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 ca sings 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. T he 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 m aking the final closure. The bolts depicted in the diagram s for making this closure are only illustrative.

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

- mm thick layer of ridged, light

- weight high

- effici ency 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 c ools 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 th e 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 ef

ficiency. 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 air

cooling is sufficient for HEV battery packs and for some larger battery packs, but it may limit the driving profiles that are feasible.8

Figure 5

. Insulated battery jacket with enclosed modules that are cooled on their upper and lower surfaces by et hylene glycol

- water solution9

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 an d 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 d riven. The heat capacity of the battery pack smooths out fluctuations in the heat generation rate. The rate that the cooling system10

must handle is the average rate for the most difficult sustained driving conditions to which the battery pack will be subjec ted.

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 drivin g 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 accessibl e , 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 BatPa C 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 ente red on line 3 5 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 40 o C 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 p ower calculated from the energy requirement per mile, ( default value 300 Wh/mile entered on the Battery Design worksheet, line 1 77 , and also transferred to the Thermal worksheet, line 7) and the constant vehicle speed, S
o (default val ue 50 mph entered on line 1 79 and 8 of the respective worksheets)11

that will require this rate of energy. The battery power, P
o (kW) will sustain a vehicle speed of S
o for the designated value of : ⁄ (3.1)

The total battery power ( P
o ) for maintaining the designated speed for the energy requirement provides power to the vehicle for accessory power ( P
a ), rolling friction power ( P f ), and aerodynamic drag power ( P d ). In this approximate calculation, w e 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: ⁄ (3.2)

The rolling friction is assumed to be directly proportional to the speed ( S
o , 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 because heavy vehicles with high energy usage tend to require a larger
fraction of the total en ergy and power to overcome rolling friction than light vehicles. Thus, the power factor for rolling friction ( f Pf , kW/mph) is: ( ⁄ ) (3.3)

And, (3.4)

By subtraction, (3.5)

The drag factor (

f P d ), which includes both the drag coefficient and the vehicle frontal area is: ⁄ (3.6)

The value of P d at any vehicle speed ( S
o ) may be calculated with the expression:

(3.7)

I n Fig. 7 the distribution of the po wer 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 all at a vehicle speed ( S
o ) of 50 mph.12

Figure 7

. Distribution of power from the battery versus the energy requirement ( ) defined at a sustained vehicle speed ( S
o ) of 50 mph

At any sustained vehicle speed, S , higher than S
o at which 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
S
o , and noting that the total battery power, P s , can be calculated from:

(3.8)

For battery packs o ther than microHEV battery packs, the BatPaC model calculates the heat generation rate ( q b , kW) from the battery current ( I b , A) and the battery resistance for a sustained constant discharge ( R bs , ohms ):

= (3.9)

For HEV

- HP batteries, the battery is operated for an estimated 30 to 60 seconds and the value of
R bs 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 g eneration rate is about 60% of

q b 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 ge nerator and motor. For PHEV and EV batteries, the heat generated in the battery pack is calculated directly from Eq. (3.9). Battery current ( I b ) and voltage ( V b ) are
calculated as follows where P s (kW ) is the maximum sustained power and U is the open

- circuit voltage at 50% SOC: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 3 6 , 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 line s 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 6 8 or the cabin

- air cooling section beginning on line 11 3 , as d etermined by the type of
cool ant ( line 6 7) . 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 agreemen t 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 11 2 and
1 73 , 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 o C or less Excellent
Over 35 o C to 40 o C Good
Over 40 o C to 45 o C Fair
Over 45 o C Poor14

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 po wer. 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 wate r

- 50% glycol solution (lines 8 6

- 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. T his 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 surfac es 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 effective ly 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 P HEVs 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 coolin g 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 modul e 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 transfer red 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 m odule 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 w ith 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 ca n 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 l ong 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 v 1.0

.

The temperature drop from the center of the cell to the cell wall, ∆T cell , was calculated as follow s:

The length of the cooled section of the cell is taken to be the same as the length of the positive
electrode. The n umber 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 pro vide 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. T he 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 th e cells, the air must be allowed to rise in temperature by about 5 o C, whereas for liquid

cooled packs, 1 o C 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 pac ks. The pressure drop for air16

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 dis tribution 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
discu ssed 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 fro m the cell sleeve wall to the bu lk a ir 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 t o 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 rang es from 80 to 1 2 0 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 7 5 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 highe st 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 45 o C (see table on page 13). The batteries with higher power generate less heat and

, the refore , are able to maintain moderate temperatur es 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 Pack s of 80 to 120

- kW Power providing 15

- mile Range for PHEVs requiring 300

- Wh/mile Energy18

Table 3. Thermal Worksheet from BatPaC v2.0 for LMO

- G Battery Packs of 80 to 120

- kW
Power providing 15

- mile Ra nge for PHEVs requiring 300

- Wh/ mile Energ y, EG

- W Cooling19

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 Ra nge for PHEVs requiring 300

- Wh/ mile Energy , EG

- W Cooling20

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 batter y cells cooled with EG

- W would permit driving at 75 mph, the Cabin

air 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 th at 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 (30 o C) , which is the entrance temperature (25 o C) plus the21

temperature rise (5 o C) 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 th e 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 r equiring 300

- Wh/mile Energy, (Same as Table 4, but with Cabin

- Air Cooling)

The battery pack volume s are 47 to 57% higher for the c abin

- air coo led 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 a ir 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.