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Energy xxx (2014) 1e10 Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy High thermal performance l...

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Energy xxx (2014) 1e10

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

High thermal performance lithium-ion battery pack including hybrid activeepassive thermal management system for using in hybrid/ electric vehicles Hassan Fathabadi* Engineering Department, Kharazmi University, Tehran, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 November 2013 Received in revised form 15 March 2014 Accepted 10 April 2014 Available online xxx

In this study, a novel Li-ion battery pack design including hybrid activeepassive thermal management system is presented. The battery pack is suitable for using in hybrid/electric vehicles. Active part of the hybrid thermal management system uses distributed thin ducts, air flow and natural convection as cooling media while the passive part utilizes phase change material/expanded graphite composite (PCM/ EG) as cooling/heating component to optimize the thermal performance of the proposed battery pack. High melting enthalpy of PCM/EG composite together with melting of PCM/EG composite at the temperature of 58.9  C remains the temperature distribution of the battery units in the desired temperature range (below 60  C). The temperature and voltage distributions in the proposed battery pack design consisting of battery units, distributed thin ducts and PCM/EG composite are calculated by numerical solving of the related partial differential equations. Simulation results obtained by writing M-files code in Matlab environment and plotting the numerical data are presented to validate the theoretical results. A comparison between the thermal and physical characteristics of the proposed battery pack and other latest works is presented that explicitly proves the battery pack performance. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Lithium-ion battery Phase change material Expanded graphite Temperature distribution Cooling duct Hybrid/electric vehicle

1. Introduction Thermal management of electrochemical products such as rechargeable batteries is very important because it results in high thermal/electrical performance of the product in ever-smaller packages. Design and implementation of rechargeable Li-ion batteries for using in hybrid/electric vehicles is subject of some recent researches [1]. As we know, a Li-ion unit cell has a low voltage and power which is not suitable to use in electric/hybrid vehicles. So, to provide an appropriate rechargeable Li-ion battery pack for using in hybrid/electric vehicles, a large number of unit cells should be connected in series and parallel to provide the necessary power and voltage. Long life cycle, keeping charge in longer time, appropriate power and reasonable cost are some benefits of Li-ion batteries [2]. A Li-ion battery generates heat during the discharge cycle, and thus the temperature of the unit cells increases. The operating temperature higher than the recommended operating range results in shortening the battery life cycle and damaging the unit cells [3]. The temperature below the recommended operating range

* Tel./fax: þ98 21 88884321. E-mail addresses: [email protected], [email protected]

increases the internal resistance, and consequently, decreases the unit cell voltage. To obtain the best performance of a Li-ion battery pack, providing an appropriate operating temperature and uniform temperature distribution among the unit cells of the battery pack are two important factors. Thus, to design a suitable battery pack, the temperature distribution should be calculated. A cooling process modeling in Li-polymer batteries was reported in Ref. [4] which showed that better temperature distribution can be obtained by using cooling system. Heat generation of a cylindrical Liion unit cell during the discharge and heat consumption during the charge process under different state of charge (SOC) was studied in Ref. [5]. Design of passive cooling media by using phase change material (PCM) was carried out and reported in Ref. [6]. Comparing between forced air cooling and natural air cooling showed that natural air cooling often is not a good solution to keep the battery temperature in the appropriate temperature range [7,8]. The calculation of temperature distribution in a prismatic Li-ion battery during a discharge cycle proved that the battery pack with the laminated cross section has lower temperature than the battery with square cross section [9]. A new electrochemicalethermalcoupled model for a Li-ion cell consisting of the individual electrode and three-electrode cell was reported in Ref. [10]. Thermal cooling using PCMs under various ambient temperatures and SOC

http://dx.doi.org/10.1016/j.energy.2014.04.046 0360-5442/Ó 2014 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Fathabadi H, High thermal performance lithium-ion battery pack including hybrid activeepassive thermal management system for using in hybrid/electric vehicles, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.04.046

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Nomenclature A c cPCM C0 Eoc F h h1 h2 i I IB Lf m mPCM q q_ Q QPCM Qf r Ri S SOC t Tair Tair-input Ti

cross-sectional area [m2] specific heat capacity [J kg1  C1] specific heat capacity of the PCM/EG composite used in the battery pack [J kg1  C1] electric capacity of battery [A h] open voltage of the unit cell [V] Faraday number (96,485 [C mol1]) heat transfer coefficient [W m2  C1] local heat transfer coefficient at x ¼ 0 cm [W m2  C1] local heat transfer coefficient at x ¼ 16 cm [W m2  C1] discharge current of a Li-ion unit cell per unit volume [A m3] discharge current of one unit cell [A] discharge current of the battery pack [A] latent heat [J kg1] mass of the air flowing through the duct during Dt [kg] mass of the PCM/EG composite used in the battery pack [kg] heat transfer/generation rate [W] rate of internal heat generation per unit volume [W m3] heat transfer/generation rate [W] absorbed heat by the PCM/EG composite used in the battery pack [J] latent heat of the PCM/EG composite used in the battery pack [J] internal equivalent resistance of the unit cell [U] internal equivalent resistance per unit volume of the unit cell [U m3] entropy [J mol1 K1] state of charge discharge duration [min] temperature of the air flowing through the cooling duct [ C] air temperature in the entrance of the cooling duct (y ¼ 0) [ C] ambient temperature [ C]

was studied in Ref. [11]. Based on a proposed thermal model, all thermal parameters such as heat transfer coefficients and heat capacity were experimentally measured and reported in Ref. [12]. As another modeling, an electricalethermal model including equivalent electrical and thermal circuits which is used to predict the thermal and electrical responses was presented in Ref. [13]. A numerical comparison between forced and natural cooling media was carried out in Ref. [14]. Physical behavior and modeling of heat generation/consumption in Li-ion batteries were studied in Refs. [15e18]. Thermal stability during the chemical process in a Li-ion unit cell was reported in Refs. [19,20]. An electrochemicalethermal analysis of 18,650 Lithium Iron Phosphate cell showing variation in cell temperature during electrochemical process was studied in Ref. [21]. A new experimental work including potentiometric and calorimetric measurement of entropy changes in a highpower lithium-ion battery was reported in Ref. [22]. The aim of thermal management in a Li-ion battery pack is to keep the temperature of all battery units at a desirable average temperature together with providing uniform temperature and voltage distributions. Recent researches show a basic relation between energy management and thermal management of batteries in electric vehicles [23e26]. It has been proved that the life cycle of

unit cell temperature [ C] surface temperature on the left PCM/EG composite wall [ C] TR.Wall surface temperature on the right PCM/EG composite wall [ C] Tm average melting point of PCM/EG composite [ C] VL voltage of the unit cell [V] V unit cell volume [m3] Vmiddle volume of a middle unit cell of each battery unit [m3] VSide volume of a unit cell located on the left or right side of each battery unit [m3] VAir velocity of the air flowing through the cooling duct [m s1] Vave average voltage observed between all battery units of the proposed battery pack [V] VMax maximum voltage observed between all battery units of the proposed battery pack [V] VMin minimum voltage observed between all battery units of the proposed battery pack [V] Vvolume battery pack volume before adding the cooling media [m3] W depth of the cooling ducts [m] x spatial direction on x coordinate axis [m] y spatial direction on y coordinate axis [m] a thermal diffusivity [m2 s1] k thermal conductivity [W m1  C1] r bulk density [kg m3] rair bulk density of air [kg m3] DS entropy change [J mol1 K1] DSduct surface of the duct wall (right or left wall) passed by air flow during Dt [m2] DT temperature variation of the PCM/EG composite used in the battery pack [ C] DTMax maximum temperature dispersion [ C] DV volume of the air flowing through the duct during Dt [m3] DV% percent of voltage regulation DVvolume increase in the battery pack volume after adding the cooling media [m3] DVvolume% percent of the increase in the battery pack volume T(x,y,t) TL.Wall

a Li-ion battery strictly depends on the operation temperature of the battery [27]. A thermal management system can operate as an active cooling system or passive cooling system. When thermal management system uses air or liquid for heat transferring, it is in active mode while in passive type, PCM is only used [28e31]. As third case, a hybrid activeepassive thermal management system including both active and passive components such as air and PCMs can be also designed and implemented. In this study, a hybrid activeepassive thermal management system is considered for the proposed battery pack. Air and phase change material/expanded graphite (PCM/EG) composite are applied as active and passive cooling/heating components, respectively. Simulation results will show that the proposed Li-ion battery pack has higher thermal performance compared to other Liion battery packs reported in the literature. The rest of this paper is organized as follows. PCMs and expanded graphite (EG) are introduced in Section 2. The concepts of heat generation in a thin-film flat Li-ion cell are presented in Section 3. Section 4 concerns with the numerical solutions of the partial differential equations which express the temperature distribution in the proposed battery pack. Simulation results obtained from numerical solutions are presented in Section 5. Internal resistances, the temperature and voltage

Please cite this article in press as: Fathabadi H, High thermal performance lithium-ion battery pack including hybrid activeepassive thermal management system for using in hybrid/electric vehicles, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.04.046

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distributions among the battery units are calculated and plotted. Finally, Section 6 concludes the study.

Table 1 Physical properties of the PCM/EG composite used in this study [6,32].

2. Phase change material/expanded graphite (PCM/EG) composite The idea of using PCMs for passive thermal management of devices is to use of the latent heat of a phase change, usually between the solid and the liquid state. A phase change involves a large amount of latent energy at small temperature changes, so PCMs can be used for storing heat with large energy densities in combination with small temperature changes. Passive thermal management using PCMs is suitable for applications where heat dissipation is intermittent or transient. PCMs such as paraffin wax typically have low thermal conductivity, so the applications of PCMs are limited to environments with a low heat transfer rate. During last years, several researches have showed that thermal conductivity of paraffin wax can be improved by incorporating EG into the wax matrix. The results show that thermal conductivities of the composite PCM (paraffin wax) with mass fraction of 2%, 4%, 7%, and 10% EG increase the thermal conductivity of paraffin wax (0.22 W m1  C1) up to 81.2%, 136.3%, 209.1%, and 272.7%, respectively [6,32,33]. 2.1. Expanded graphite (EG) The expanded graphite is formed from flake graphite through a heat treatment process that breaks the weak van der Waals bonds between the sheets of carbon which construct the flake graphite. In a well-known heat treatment process, EG is prepared from graphite to maximize mass fraction of paraffin to be absorbed into its porous structure. First, the graphite sample is converted to expandable graphite through chemical oxidation in the presence of a mixture of sulfuric and nitric acid, and then is dried in a vacuum oven at 65  C for 24 h. Finally, EG is obtained by rapid expansion and exfoliation of expandable graphite in a furnace over 900  C for 60 s. So, this process greatly increases the porosity of the graphite and similarly decreases the bulk density. Large volumes of expanded graphite particles are then compacted to form a solid matrix of graphite. The degree of compaction determines the resulting porosity and the thermal conductivity of the matrix in the direction perpendicular to compaction. It can be summarized that more compaction decreases the porosity and increases the thermal conductivity in the perpendicular plane. The green compacts density is 0.04375 g cm3 [6,32]. 2.2. Manufacturing process of PCM/EG composite Paraffin wax with technical grade (melting point ¼ 58e60  C and thermal conductivity ¼ 0.2 W m1  C1) is generally used as PCM. The produced EG compact is then impregnated in the molten paraffin wax at 80  C for about 12 h. The density of the composite is about 0.83 g cm3 which is 17e18 times more than the density of the produced EG compact. Thermal conductivity of the PCM/EG composite produced by this method has enormous thermal conductivity up to 16.6 W m1  C1 [6,32]. Physical properties of the PCM/EG composite used in this study are summarized in Table 1. The compaction direction of the PCM/EG composite is vertical direction, so the thermal conductivity of the PCM/EG composite shown in Table 1 (16.6 W m1  C1) is in the direction perpendicular to compaction (horizontal plane). 3. Heat generation during the discharge cycle Comparing with other types of Li-ion unit cells, thin-film flat Liion unit cell has appropriate size and shape for constructing a battery pack that is suitable for electric vehicles. The structure of a

3

Property

Value

k [W m1  C1] Lf [J kg1] c [J kg1  C1] Bulk density (r) of composite [kg m3] Bulk density (r) of graphite [kg m3] Tm [ C]

16.6 127,000 1980 789 210 58.9

thin-film flat Li-ion unit cell consisting of a positive electrode, a negative electrode performed by using a thin layer of powdered graphite, and separator constructed by porous plastic film was reported in detail in Ref. [34]. Each battery unit is built by utilizing several Li-ion unit cells. During charge/discharge process, the heat produced by a Li-ion unit cell is expressed as [4,35]

q ¼ I$ðEOC  VL Þ  I$T

dEOC dT

(1)

where the term I$TðdEOC =dTÞ is the heat generated/consumed during the discharge/charge cycle, and the term I $ (EOC  VL) is heat generation resulting from the power loss caused by the internal resistance of the unit cell [4,14]. The term dEOC =dT is the temperature coefficient which can be obtained as

DS dEOC ¼ F dT

(2)

Substituting dEOC =dT from Eq. (2) into Eq. (1), results that

DS ðE  VL Þ  I$T q ¼ I 2 $ OC I F

(3)

or

q ¼ I 2 $r  I$T

DS

(4)

F

Heat generation per unit volume can be found by dividing both sides of Eq. (4) to the unit cell volume as following:

q_ ¼

DS q I2 I DS ¼ 2 $ðr$VÞ  $T ¼ Ri $i2  i$T V V F F V

(5)

The term i$TðDS=FÞ in Eq. (5) is positive (DS < 0) or negative (DS > 0) during the discharge or charge, respectively. The internal resistance of a unit cell varies by variation in temperature and SOC. Thus, it should be measured under various temperatures and SOC [9]. Using the experimental data of the commercial Li-ion battery (SONY-US18650) presented in Ref. [9], Ri can be estimated as [27]

8 < 2:258  106 SOC0:3952 ; Ri ¼ 1:857  106 SOC0:2787 ; : 1:659  106 SOC0:1692 ;

T ¼ 20  C T ¼ 30  C T ¼ 40  C

(6)

The structure of a thin-film flat Li-ion unit cell is similar to SONYUS18650, thus in this paper, the Ri value presented in Eq. (6) is used to design the proposed Li-ion battery pack including thin-film flat Li-ion unit cells. It was shown DS over a temperature range between about 20  C and 40  C is almost independent of the temperature [9]. In this temperature range, DS only depends on SOC which can be approximated as [9]

8 < 99:88SOC  76:67; DSz þ30; : 20;

0  SOC  0:77 0:77 < SOC  0:87 0:87 < SOC  1

(7)

Please cite this article in press as: Fathabadi H, High thermal performance lithium-ion battery pack including hybrid activeepassive thermal management system for using in hybrid/electric vehicles, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.04.046

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4. Calculation of temperature distribution A commercial Li-ion battery pack including twenty battery units and two cooling ducts mounted at both ends is shown in Fig. 1 [14,36]. The battery units have been connected in series to increase the battery voltage, and each battery unit consists of 10 thinflat Li-ion unit cells connected in parallel to provide appropriate current [35]. The open circuit voltage and electric capacity of each battery unit are 3.6 V and 20 A h because the open circuit voltage and electric capacity of a unit cell are 3.6 V and 2 A h. Consequently, these parameters for the Li-ion battery pack consisting of 20 battery units are 72 V and C0 ¼ 20 A h, respectively. Graphite, Cu, Graphite, electrolyte, LiCoO2, Al, LiCoO2, and separator are the seven layers which are used to perform a thin-flat Li-ion unit cell. The dimensions of a thin-flat Li-ion unit cell are 730 mm (thickness)  16 cm (wide)  23 cm (tall) [35]. The cover thickness of a battery unit is 0.7 mm, thus the final dimensions of a battery unit are 8 mm (thickness)  16 cm (wide)  23 cm (tall). Tables 2 and 3 represent the proposed battery pack configuration and the thickness of each layer of a thin-flat Li-ion unit cell [35]. The top view of the proposed battery pack is shown in Fig. 2. The proposed battery pack includes activeepassive cooling media. Cooling/heating is performed by using the PCM/EG composite as passive cooling/heating media and flowing air through the distributed ducts as active cooling media. PCM/EG composite volume increases during the melting process, so a volume expansion receptacle has been installed beside the battery pack. The proposed battery pack design is shown in detail in Fig. 3. As shown in Figs. 2 and 3, for x and y, we have 2 mm  x  162 mm, 0  y  230 mm, and each duct consists of 8 small mini ducts with the dimensions of 20 mm  1.5 mm. Figs. 2 and 3 show that the PCM/EG composite used in the proposed battery pack acts as a separator layer for the two thin-flat Li-ion unit cells located on the both sides of each battery unit, so the temperature distributions in the seven layers of a thin-flat Li-ion unit cell and also in the PCM/EG composite which plays eighth layer role are the solution of the following partial equation [9,14,35,36]:

Table 2 Configuration of the commercial Li-ion battery pack used in hybrid/electric vehicle. Battery Number of unit cells per battery unit Number of battery units in the pack Cell surface area [cm2] Electric capacity of each unit cell [A h] Electric capacity of each battery unit [A h] Open-circuit voltage of each unit cell [V] Cut-off state of charge [%]

10 20 368 2 20 3.6 20

v2 T v2 T q_ 1 vT þ þ ¼ a vt vx2 vy2 k

(8)

Replacing q_ from Eq. (5) in Eq. (8), results that

1 vT DS$i R $i2 þ T i a vt k$F k

V2 T ¼

(9)

SOC of a battery is defined as [35]

SOC ¼ 1 

I$t C0

(10)

where t is the discharge duration and for the proposed battery pack C0 ¼ 20 A h. When simulation starts (t ¼ 0), we have SOC ¼ 1 and thus, the battery is full charge. Substituting SOC ¼ 1 and T ¼ Ti ¼ 20  C (ambient temperature) in Eqs. (6) and (7) results that Ri ¼ 2.258  106 U m3 and DS ¼ 20 J mol1 K1. By substituting the computed values of Ri, DS, i ¼ I=V and F ¼ 96,485 C mol1 in Eq. (9), it can be summarized as

   2 20$ VI 2:258  106 $ VI v2 T v2 T 1 vT  T þ ¼ a vt 96; 485$k k vx2 vy2

(11)

As mentioned above, the temperature distributions in the seven layers of each thin-flat Li-ion unit cell and also in the PCM/EG composite, which plays eighth layer role for only the two thin-flat Li-ion unit cells located on the both sides of each battery unit, can be obtained by solving Eq. (11). Thermal conductivity (k) of the PCM/EG composite and each layer of the thin-flat Li-ion unit cells presented in Tables 1 and 4 are used for solving Eq. (11). The value of i ¼ I=V depends on simulation conditions (discharge rate) which will be explained in Section 5. Since the ambient temperature is Ti ¼ 20  C, so the initial condition for solving Eq. (11) is

cx; cy;

Tðx; y; 0Þ ¼ Ti ¼ 20  C

(12)

The boundary conditions are also necessary to solve Eq. (11). These conditions can be found by considering the effects of the PCM/EG composite used in battery pack (passive cooling system) and the Table 3 Thickness of a Li-ion unit cell layers extracted from US18650 LithiumIon Battery Manual, Sony Co. [36].

Fig. 1. Schematic of the battery pack with 20 battery units and two surrounding cooling ducts.

Thickness of cell layers [mm] Graphite Cu Graphite Electrolyte LiCoO2 Al LiCoO2 Separator

120 20 120 40 180 20 180 50

Total thickness of a unit cell [mm]

730

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Fig. 2. Top view of the proposed battery pack including activeepassive cooling/heating media.

Fig. 3. Battery pack design including the proposed hybrid activeepassive thermal management system.

proposed distributed cooling ducts (active cooling system) because the unit cells and the battery pack are exposed to the ambient via the proposed active/passive cooling system and the battery pack container. The temperature variation of the air flowing through the each duct can be obtained from following equation [35]:

mc

DTair dm cDTair  h$DSduct $ðTL:Wall þ TR:Wall  2Tair Þ ¼ 0 þ Dt dt (13)

_ ¼ dm=dt and DSduct ¼ WDy Substituting m ¼ rair $ DV, DV ¼ ADy, m in Eq. (13) results that

r$A$Dy$c

DTair _ DTair h$W$Dy$ðTL:Wall þTR:Wall 2Tair Þ ¼ 0 þ mc Dt (14)

where W is the duct depth (W ¼ 160 mm) and A is the crosssectional area of each duct (A ¼ 160 mm  1.5 mm ¼ 240 mm2). For the mass of the air flowing through the duct, we have Table 4 Thermalephysical properties for the different layers of the Li-ion unit cell [36].

_ ¼ m

dm dy ¼ rair $A$ ¼ rair $A$VAir dt dt

(15)

Substituting Eq. (15) in Eq. (14) results that

DTair þ rair $A$VAir $cDTair Dt  h$W$Dy$ðTL:Wall þ TR:Wall  2Tair Þ ¼ 0

r$A$Dy$c

(16)

Transient response of Eq. (16) disappears after passing enough time and the steady state appears in the duct. In this case, the first term of Eq. (16) can be ignored and thus, Eq. (16) is simplified as

DTair ¼

hW

rair $A$VAir $c

ðTL:Wall þ TR:Wall  2Tair ÞDy

(17)

Eq. (17) explicitly shows the effect of the fluid flow (air natural convection) in the numerical simulations. Eq. (17) can be numerically solved by using the following boundary condition:

Tair ðyÞjy¼0 ¼ Tairinput ¼ Ti ¼ 20  C

(18)

Property

Cu

Graphite

Electrolyte

LiCoO2

Al

Separator

After finding Tair(y) as a numerical solution of Eq. (17), the boundary conditions for Eq. (11) can be obtained as

k [W m1  C1] r [kg m3] c [J kg1  C1]

398 8930 386

1.04 1347 1437

0.59 1223 1375

4 2700 715

237 2710 902

0.35 1400 1551

 vTðx; y; tÞ h ¼ 1 jTð2; y; tÞ  Tair ðyÞj  vx k x¼2 mm

(19)

Please cite this article in press as: Fathabadi H, High thermal performance lithium-ion battery pack including hybrid activeepassive thermal management system for using in hybrid/electric vehicles, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.04.046

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H. Fathabadi / Energy xxx (2014) 1e10

and

 vTðx; y; tÞ  vx

¼ x¼162 mm

h2 jTð162; y; tÞ  Tair ðyÞj k

(20)

where h1 and h2 are the local heat transfer coefficients at x ¼ 2 mm and x ¼ 162 mm, respectively. Using these boundary conditions and the initial condition presented by Eq. (12), the temperature distributions in PCM/EG composite and each layer of the unit cells are calculated by numerically solving Eq. (11). Above explanation can be summarized as follows. The temperature distributions in the PCM/EG composite and each layer of the unit cells are calculated by solving Eq. (11) while the temperature distribution of fluid flow (air natural convection) in each cooling duct is calculated by solving Eq. (17) and furthermore, the solution of Eq. (17) is used as the boundary condition for solving Eq. (11). 5. Calculations and simulation results To provide same conditions for comparing the results of this work with other works [14,35], the values of the parameters of the proposed hybrid activeepassive cooling system are considered as:  Active cooling system: air as fluid, natural convection, air velocity VAir ¼ 0.01 m s1, heat transfer coefficient h ¼ 37.5 W m2  C1, ambient temperature Ti ¼ 20  C (same as conditions in Refs. [14,35]).  The discharge rate of the battery pack is considered as 2C0 ¼ 40 A h which means the battery will be fully discharged after half hour. The discharge current of the battery pack is considered as IB ¼ 40 A, thus the discharge current of each unit cell is I ¼ ðIB =10Þ ¼ 4 A. All simulations start for a fully charged battery (SOC ¼ 1) and ends after 24 min when the battery SOC reaches 0.2 (same as conditions in Refs. [14,35]).  Passive cooling system: PCM/EG composite, k ¼ 16.6 W m1  C1, ambient temperature Ti ¼ 20  C.

5.1. Simulation method and results for temperature distribution As mentioned in Section 4, the dimensions of a thin-flat Li-ion unit cell are 730 mm (thickness)  16 cm (wide)  23 cm (tall), so the volume of a middle unit cell of each battery unit is V ¼ Vmiddle ¼ 26.864 cm3 while by considering Fig. 3, the volume of the unit cells located on the left or right side of each battery unit is V ¼ VSide ¼ 100.464 cm3. Substituting I ¼ 4 A in Eq. (11) and converting it to discrete form results following difference equation:

Tðx þ 2Dx; y; tÞ  2Tðx þ Dx; y; tÞ þ Tðx; y; tÞ ðDxÞ2 þ

Ri ¼

5.2. Simulation method and results for voltage distribution The voltage of one unit cell of the proposed battery pack can be found as

VL ¼ EOC  r$I ¼ EOC 

Tðx; y þ 2Dy; tÞ  2Tðx; y þ Dy; tÞ þ Tðx; y; tÞ ðDyÞ2

  20$ V4 1 Tðx; y; t þ DtÞ  Tðx; y; tÞ Tðx; y; tÞ  ¼ a Dt 96; 485$k  2 2:258  106 $ V4  k

Eq. (21) is solved by writing one M-file code in Matlab environment and plotting the numerical results as a temperature distribution curve. By assuming D x ¼ 0.01 cm, Dy ¼ 0.01 cm, D t ¼ 0.01 s, considering V ¼ Vmiddle ¼ 26.864  106 m3 for the middle unit cells and V ¼ VSide ¼ 100.464  106 m3 for the two unit cells located on the left and right side of each battery unit, replacing k ¼ 16.6 W m1  C1 from Table 1 in Eq. (21) for the PCM/EG composite (only for the two unit cells located on the left and right side of each battery unit), substituting k from Table 4 in Eq. (21) for each layer of the thin-flat Li-ion unit cells, utilizing the boundary conditions presented in Eqs. (19) and (20), and using the initial condition presented in Eq. (12), the temperature distribution with in the battery pack is calculated and then is plotted. The time passage is expressed by variation of the SOC because according to Eq. (10), the SOC linearly decreases in the case of the constant discharge current. During the discharge process, for new values of SOC, the new values of Ri and DS are found from Eqs. (6) and (7) and are replaced in Eq. (21) to find the new temperature data. The temperature data obtained from solving Eq. (21) are plotted for the midline of the battery pack at (y ¼ 115 mm, x ¼ 81 mm). Curve (a) in Fig. 4 shows the temperature distribution at the midline of the proposed battery pack, after 24 min when the battery SOC reaches 20% (SOC ¼ 0.2). This curve explicitly represents ultra uniform temperature distribution among the battery units (excluding the two battery units mounted at both ends), a maximum temperature dispersion less than 0.02  C (DTMax  0.02  C), and the maximum observed temperature TMax ¼ 26.5  C. The maximum observed temperature in the two battery units located at both ends is TMax ¼ 26.4  C and the maximum temperature dispersion is less than 0.4  C. The intermediate plunges in the temperature distribution show the temperature of air in the cooling ducts. For providing a comparison, the temperature distribution of the latest related work [35], which only uses active cooling system including the same number of the distributed cooling ducts (19 ducts) with the same size (A ¼ 160 mm  1.5 mm ¼ 240 mm2), is shown as curve (b) in Fig. 4. For that work, the curve (b) shows that the maximum temperature dispersion of all middle battery units is less than 0.05  C (DTMax  0.05  C) with a maximum observed temperature TMax ¼ 31  C. For the two battery units located at both ends, the maximum observed temperature is TMax ¼ 30.8  C with a maximum temperature dispersion less than 0.8  C.

(21)

Ri $I V

(22)

As shown in Fig. 4, the temperature distribution of the proposed battery pack when the battery SOC reaches SOC ¼ 0.2 is between 20  C and 30  C. For the unit cells temperature in the range between 20  C and 30  C, Ri can be estimated using Eq. (6) as

  1:857  106 SOC0:2787  2:258  106 SOC0:3952 ðTðx; y; tÞ  20Þ þ 2:258  106 SOC0:3952 10

(23)

Please cite this article in press as: Fathabadi H, High thermal performance lithium-ion battery pack including hybrid activeepassive thermal management system for using in hybrid/electric vehicles, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.04.046

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7

Fig. 4. Temperature distribution at the midline of the proposed battery pack, after 24 min when the battery SOC reaches 20% (SOC ¼ 0.2). Discharge process starts from SOC ¼ 1 and ends to SOC ¼ 0.2 with the discharge rate of 2C0 ¼ 40 A h. Curve (a). This work: Proposed activeepassive cooling system (active: air, natural convection, the cross-sectional area of each duct 160 mm  1.5 mm, VAir ¼ 0.01 m s1, h ¼ 37.5 W m2  C1, Ti ¼ 20  C) and (passive: PCM/EG composite, k ¼ 16.6 W m2  C1). Curve (b). The latest work: Active cooling system (air, natural convection, the cross-sectional area of each duct 160 mm  1.5 mm, VAir ¼ 0.01 m s1, h ¼ 37.5 W m2  C1, Ti ¼ 20  C) [35].

Substituting Eq. (23) in Eq. (22) results that

ð1:857106 SOC0:2787 2:258106 SOC0:3952 Þ 10

VL ¼ EOC 

ðTðx; y; tÞ  20Þ þ 2:258  106 SOC0:3952 $I V

Since each battery unit consists of ten unit cells connected in parallel, so the voltage of each unit cell or the related battery unit at the end of the discharge cycle (after 24 min) can be calculated by substituting V ¼ 26.864  106 m3, EOC ¼ 3.6 V, I ¼ 4 A, and the obtained temperature data for the midline of the battery pack after 24 min when the battery SOC reaches 0.2 shown in Fig. 4 (T(8.1 cm , 11.5 cm, 24 min)) in Eq. (24). Thus, we have

(24)

The proposed cooling ducts and the PCM/EG composite, which have been added to the battery pack, increase the battery pack volume. The percent of the increase in the battery pack volume is defined as

DVvolume % ¼ 100

DVvolume Vvolume

(27)

For the proposed battery pack including activeepassive cooling media, which is shown in Figs. 2 and 3, DVvolume% can be computed as

ð1:857106 0:20:2787 2:258106 0:20:3952 Þ 10

VL ¼ 3:6 

DVol:% ¼ 100

ðTð8:1; 11:5; 24Þ  20Þ þ 2:258  106 0:20:3952 $4 26:864  106

164 mm  230 mm  268:5 mm  20  160 mm  230 mm  8 mm ¼ 72% 20  160 mm  230 mm  8 mm

The voltage data at the end of the discharge cycle obtained from Eq. (25) are plotted which is shown in detail in Fig. 5. It can be easily seen that the voltage distribution in the proposed battery pack shown in Fig. 5 is ultra uniform. The percent of the voltage regulation is defined as

DV% ¼ 100

VMax  VMin Vave

(26)

For the proposed battery pack design the voltage regulation percent is about 0.85%.

(25)

(28)

The main function of PCM is absorbing heat during the phase change process (melting point is Tm ¼ 58.9  C), so for showing the PCM/EG composite effect, the simulation has been repeated for the various ambient temperatures as shown in Fig. 6. It can be clearly seen that the PCM/EG composite melting starts at ambient temperature of 51  C and ends at 54  C. It can be seen that the battery units temperature does not increase during the melting process. It is worth noting that the proposed battery pack operates in the appropriate/ recommended temperature range (below 60  C) for ambient temperature until 55  C as shown in Fig. 6. In fact, high melting enthalpy of PCM/EG composite together with melting of the PCM/EG

Please cite this article in press as: Fathabadi H, High thermal performance lithium-ion battery pack including hybrid activeepassive thermal management system for using in hybrid/electric vehicles, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.04.046

8

H. Fathabadi / Energy xxx (2014) 1e10

Fig. 5. Voltage of each battery unit at the end of the discharge process when the battery SOC reaches 0.2 (after 24 min).

composite (average melting point is Tm ¼ 58.9  C) absorbs produced heat during the phase change process, and thus prevents temperature rise in the battery units during the melting process. A comparison between the battery temperatureeambient temperature characteristics (battery units temperature versus ambient temperature) of the proposed battery pack and the latest work [35] is shown in Fig. 7. Although the proposed battery packs in this work and [35] both use the same active cooling system consisting of the air ducts with the same number and size, following differences can be easily distinguished:  The temperature curve of this work (blue curve) is under the other curve (red curve). In fact, using PCM/EG composite as passive cooling system adds the mass of the PCM/EG composite (mPCM) to the battery pack and thus, this decreases the rate of increase in the battery pack temperature. In other words, the PCM/EG composite absorbs a large amount of the heat produced by the battery pack (QPCM) during the discharge process which can be obtained as

QPCM ¼ mPCM $cPCM $DT

Fig. 7. Maximum temperature of the battery units versus ambient temperature for the proposed battery pack (blue curve) and other work (red curve) [35]. Discharge process starts from SOC ¼ 1 and ends to SOC ¼ 0.2 with the discharge rate of 2C0 ¼ 40 A h. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

As mentioned in Section 2, the idea of using PCMs for passive thermal management of devices is to use of the latent heat of a phase change, usually between the solid and the liquid state. A phase change involves a large amount of latent energy at small temperature changes. In the proposed battery pack, when ambient temperature reaches 51  C, the PCM/EG composite used in the battery pack begins to melt and thus, it needs to absorb a large amount of the heat produced by the battery pack to provide the latent heat which is necessary for phase change from the solid to the liquid state. During the phase change between the solid and the liquid state, the battery pack temperature remains constant (about 58  C). When ambient temperature reaches 54  C, the phase change becomes complete and the whole PCM/EG composite changes to liquid. After completing the phase change, increase in ambient temperature increases the battery pack temperature again. The amount of the heat absorbed by the PCM/EG composite during the phase change can be calculated as

(29) Qf ¼ mPCM $Lf

 The temperature curve of this work is flat for the ambient temperature in the range of [51  C, 54  C]. In other words, the battery pack temperature remains constant in this range of the ambient temperature.

(30)

 Furthermore, it can be seen that the battery units temperature remains in the appropriate/recommended temperature range (below 60  C) for ambient temperature until 55  C while it is 48  C for other works [35].

Fig. 6. Temperature distribution of the battery units for various ambient temperatures.

Please cite this article in press as: Fathabadi H, High thermal performance lithium-ion battery pack including hybrid activeepassive thermal management system for using in hybrid/electric vehicles, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.04.046

H. Fathabadi / Energy xxx (2014) 1e10 Table 5 Comparison between the parameters of the proposed battery pack in this work and the latest related works [14,35]. Discharge process starts from SOC ¼ 1 and ends to SOC ¼ 0.2 with the discharge rate of 2C0 ¼ 40 A h, and at Ti ¼ 20  C. Parameter

This work

[35]

[14]

Thermal management system Convection Maximum observed temperature in middle battery units (TMax) [ C] Maximum temperature dispersion in middle battery units (DTMax) [ C] Maximum observed temperature in battery units located at both ends of the battery pack (TMax) [ C] Maximum temperature dispersion in battery units located at both ends of the battery pack (DTMax) [ C] The percent of the voltage regulation (DV%) The percent of the increase in the volume of the battery pack (DVol.%)

Activeepassive Natural 26.5

Active Natural 31

Active Forced 36

0.02

0.05

0.2

26.4

30.8

35

0.4

0.8

1

0.85

1.98

>2

72

17.81

22.5

Table 5 represents a comparison between the parameters of the designed activeepassive cooling/heating media in this work and the two latest works [14,35]. The comparison explicitly proves higher thermal performance of the proposed hybrid activeepassive thermal management system compared to other works although one of the other works uses forced convection [14]. By considering Figs. 4, 5 and 7 and Table 5, some contributions and advantages of the proposed battery pack can be summarized as:  Uniform temperature and voltage distributions.  The maximum observed temperature in each battery unit is less than other works.  The maximum temperature dispersion in each battery is less than other works.  Natural convection (there is no need for extra devices such as fan).  The proposed battery pack design has the best thermal performance for various ambient temperatures until 55  C (for other works it is only 48  C). 6. Conclusion In this study, a novel Li-ion battery pack design including hybrid activeepassive thermal management system for using in hybrid/ electric vehicles was proposed. Air flow in the proposed distributed ducts and PCM/EG composite were used as active and passive cooling/heating components, respectively. Thermal analysis of the proposed battery pack design was carried out, and the temperature distribution in the proposed battery pack consisting of 20 battery units, 19 distributed ducts and PCM/EG composite was calculated by numerical solving of the related partial differential equations. The internal resistance, temperature/voltage distributions among the battery units, and battery temperatureeambient temperature characteristic were calculated and plotted. The numerical solutions and simulations were repeated for various ambient temperatures and it was shown that the battery pack has the high thermal performance and remains in the recommended temperature range (below 60  C) for ambient temperature until 55  C. Natural convection together with uniform voltage/temperature distributions, negligible temperature dispersion in each battery unit, the maximum observed temperature in each battery unit less than that in other available battery packs, and the best thermal performance for ambient temperatures until 55  C are some advantages of the proposed battery pack. Simulation and numerical results validated

9

the theoretical results. The temperature curves and parameters of the proposed battery pack were compared with other works which clearly proved the benefits of the proposed battery pack design.

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Please cite this article in press as: Fathabadi H, High thermal performance lithium-ion battery pack including hybrid activeepassive thermal management system for using in hybrid/electric vehicles, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.04.046