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Thermal-electrochemical coupled simulations for cell-to-cell imbalances in lithium-iron-phosphate based battery packs
Applied Thermal Engineering 123 (2017) 584–591
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Thermal-electrochemical coupled simulations for cell-to-cell imbalances in lithium-iron-phosphate based battery packs Hsuan-Han Huang a, Hsun-Yi Chen a,⇑, Kuo-Chi Liao a,⇑, Hong-Tsu Young b, Ching-Fei Lee c, Jhen-Yang Tien c a
Department of Bio-Industrial Mechatronics Engineering, National Taiwan University, Taiwan, ROC Department of Mechanical Engineering, National Taiwan University, Taiwan, ROC c Phoenix Silicon International Corporation, Taiwan, ROC b
h i g h l i g h t s Electric circuit of the pack is incorporated to evaluate thermally-driven imbalance. Temperature and current deviation of a large complex battery pack are investigated. Deviation among the cell capacity is aggravated with larger temperature gradients.
a r t i c l e
i n f o
Article history: Received 24 February 2017 Revised 19 May 2017 Accepted 20 May 2017 Available online 25 May 2017 Keywords: Lithium-iron-phosphate based battery Thermal-electrochemical model Thermal management Finite element analysis
a b s t r a c t A thermal-electrochemical coupled model framework considering mass balance, charge balance, reaction kinetics, and energy balance is developed to evaluate thermally-driven imbalance among cells of a commercialized lithium-iron-phosphate battery pack consisting of a combination of series and parallel connections. Current distribution and joule heat generation of copper alloy sheets connecting several cells within a battery pack are also considered in the simulation. A running management built in MATLAB, R2010a (2010) is applied to deliver the coupling of the thermal-electrochemical model, among different modulus of COMSOL Multiphysics 5.0 (2014). Simulated voltage variation and temperature distribution of an individual cell during charge/discharge are validated with the corresponding experiments. The developed model is further applied to study the non-uniform temperature distribution and electrical imbalance among cells within the 4S6P LFP battery pack. Simulation results show that thermal imbalance could magnify the deviation of discharge current and capacity among individual cells and may accelerate the capacity losses of the cells within a battery pack. Our model can facilitate understanding of the impact of electrical imbalance on the battery pack and assist thermal management systems. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The lithium-ion battery is a popular type of rechargeable batteries for portable electronics, with high energy density, no memory effect, and slow degradation. (Scrosati and Garche [3]) The lithium-iron-phosphate (LFP) battery with lithium iron phosphate as cathode material is of low cost, high power output, environmentally benign, and features intrinsic thermal safety. (Huang et al. [4]) This battery chemistry thus ranks among the most promising lithium-ion batteries that target hybrid electric vehicle (HEV) and electric vehicle (EV) markets, and rechargeable LFP battery packs are widely used as energy storage by automobile industries and ⇑ Corresponding authors. E-mail addresses: [email protected] (H.-Y. Chen), (K.-C. Liao). http://dx.doi.org/10.1016/j.applthermaleng.2017.05.105 1359-4311/Ó 2017 Elsevier Ltd. All rights reserved.
[email protected]
in uninterruptible power supply (UPS) systems. However, one of the crucial limitations for the LFP battery pack is its operating temperature, which may strongly restrict the voltage, capacity, power, and cycle life. Overheating and non-uniform temperature distribution of the battery pack could lead to degradation and failure of cells. Thermal management of the battery pack is therefore essential for its long term performance and safety. In order to analyze the thermal effects on the performance of batteries, Kumaresan et al. [5] developed thermalelectrochemical models coupling mass balance, charge balance, reaction kinetics, energy balance and heat transfer equations, and temperature dependences of transport and kinetic parameters are considered. In practice, the thermal-electrochemical coupled analysis can be used to obtain the optimal operating conditions such as pack temperature. Since thermal management needs to be carefully examined when new battery packs are developed,
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many studies proposed various cooling strategies to achieve more uniform temperature distribution. Xu and He [6] asserted that the heat dissipation of battery packs could be significantly enhanced with different arrangements of the cells and the air inlet/outlet. Wang et al. [7] and Chen et al. [8] investigated various cooling approaches to guarantee the batteries operated within the optimal temperature range as well as to provide effective solutions for the cooling system. Yang et al. [9] studied the thermal performances of battery pack to advise the appropriate arrangement of cylindrical cells for the efficient cooling system. Lan et al. [10] and Xu et al. [11] developed a novel cooling system based on aluminum minichannel tubes applied to the battery module and investigated its efficacy on the mitigation of thermal runaway. Rather few studies investigate the influences of temperature deviations on the cell-to-cell current distribution of a battery pack. Bandhauer et al. [12] revealed that electrical imbalance could lead to serious battery failures if thermal runaway is induced. Guo and White [13] developed a thermal resistance model, coupling the so-called single particle model, energy balance equation, and basic circuit constraints, to simulate electrical and thermal behaviors among batteries connected in parallel configuration. Although the electrochemical behavior and heat generation among individual cells were considered, temperature of each cell was assumed to be uniform in the study. Moreover, even though the predicted temperature of the battery pack during charge/discharge cycles is consistent with experimental data, the individual cells show minute variations in electrical behaviors due to the relatively limited temperature deviation. Yang et al. [14] investigated the unbalanced cell discharging stemmed from a temperature difference between two parallel-connected cells via simulations and experiments, with an assumption of different initial temperatures at the beginning of the discharging process. A larger current is observed within the cell of higher temperature in the early discharging stage. On the contrary, the cooler cell experiences a smaller operating current. The unbalanced discharging current induced by the temperature difference between two parallel connected cells exacerbates the imbalance phenomenon. This imbalance discharge current may thus aggravate the capacity deviation between two parallel-connected cells and accelerate the capacity losses of the battery pack. In the past, many researches overlooked the thermally-driven imbalance among the cells and its potential risk of thermal runaway and assumed the electrochemical behaviors and heat generation among individual cells of a battery pack to be identical. The thermal-electrochemical coupled analysis is thus applied in the present study to investigate effects of the non-uniform temperature distribution and thermally-driven electrical imbalance among cells on the performance of a commercialized battery pack consisting of a combination of series and parallel connections. The developed model framework enables us to examine the operating current, temperature distribution and heat generation among individual cells and the impact of thermally-driven imbalances on a large complex battery pack serving for practical applications.
Positive electrode reaction þ
Li1x FePO4 þ xLi þ xe $ LiFePO4
ð1Þ
Negative electrode reaction þ
Lix C6 $ 6C þ xLi þ xe
ð2Þ
Total reaction
Li1x FePO4 þ Lix C6 $ LiFePO4 þ 6C
ð3Þ
During the charge process, the reactions proceed from the lefthand side to the right-hand side and lithium ions deintercalate from the positive electrode and intercalate into the negative electrode, while the reverse reaction takes place during the discharge process. The LFP battery domain that the one-dimensional electrochemical model considered includes the aforementioned three components and is described as three sequentially extended lines. Since there are other physical phenomena in addition to the aforementioned electrochemical reactions, during charge and discharge processes an electrochemical model on the basis of coupled mass balance, charge balance, and reaction kinetics constitution laws is adapted here to simulate the electrochemical behavior of the LFP battery. This model consists of diffusion phenomena in the concentrated electrolyte and the solid phase electrodes, Ohm’s law for the potential distribution, and the conservation of charge and mass. Moreover, the solid phase porous electrodes filled with the electrolyte and the diffusion mechanism in the electrodes are described by the porous electrode theory, which considers each electrode as a number of spherical particles with the surface area represents the porous electrode active surface area. Governing equations and boundary conditions illustrating the isothermal charge and discharge processes of a lithium-ion battery are listed in Table 1 to describe general dynamics of a battery system and are used to predict the behaviors of lithium-ion batteries during charge and discharge procedures (Doyle et al. [16]). To describe the effect of heat generation from cell to pack level and formation of thermal hot spots within the battery pack, a three-dimensional thermal model is coupled to the electrochemical model. Performances of the LFP cell, such as the output voltage and storage capacity, are significantly influenced by its operating temperature. However, the heat generation of the LFP cell is in turn controlled by the electrochemical reactions occurring in the cell during charge and discharge processes and thus affects the
Table 1 Equations used in the thermal-electrochemical model. Equations
Boundary conditions
Electrochemical model Separator i2 @t þ @ c ¼ D @x 2 z m F @x þ þ @g sþ tþ I RT @c ¼ þ @x j F nmþ þ zþ mþ @x 2
@c @t
rc ¼ 0 at x ¼ 0 and d þ ds þ dþ i2 ¼ I at x ¼ d and ds rU1 ¼ rI at x ¼ 0 and d þ ds
Electrodes
2. Mathematical model
@c @t @g @x
Since highly conductive current collectors such as aluminum and copper foils are utilized to ensure homogeneous current distribution, the electrochemical behavior of the cylindrical cell can be reasonably assumed to be one dimension along the radial/thickness direction (Newman and Alyea [15]). The one-dimensional electrochemical model applying to the LFP battery here considers three components: the graphite negative electrode, separator, and lithium-iron-phosphate positive electrode. The chemical reactions in the LFP battery that our electrochemical model considered are as follows:
ajn ð1t þ Þ i2 @t þ @ c ¼ D @x 2 z m F @x þ mþ þ þ sþ Ii2 i2 RT @c ¼ r þ j þ F nmþ þ zþtþmþ @x 2
s1 @i2 ajn ¼ nF @x
a a aF I ¼ Fðka Þ c ðkc Þ a ðcmax cÞac caa exp aRT ðg UÞ a F a ðg UÞ exp RT Thermal model
qC p dT ¼ rðkrTÞ þ Q rxn þ Q rec þ Q ohm dt Q rxn ¼ FaJðU1 U2 UÞ Q rec ¼ FaJ @U @T
Q rxn ¼ reff ðrU1 Þ2 þ jeff ðrU2 Þ2 þ
2jeff RT F
ð1 tþ ÞrðlncÞrU2
krT ¼ hðT 1 TÞ at t ¼ Rz ¼ 0 and L
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operating temperature. Heat is released accompanying with the electrochemical reaction and subsequently leads to temperature increase of the battery. In our model framework, the dependence of the physicochemical properties is described by the Arrhenius equation. Energy balance equations and boundary conditions listed in Table 1 are used to describe the spatial distribution of temperature (Gu and Wang [17]). The heat generation due to electrochemical reactions and joule heating is assessed based on electrochemical model, and then applied in the heat transfer equations to evaluate the temperature distributions. The average temperature of the corresponding active materials is then fed back to update the electrochemical model through temperaturedependent physicochemical properties. The thermal and electrochemical behaviors of the battery systems are thus partially coupled by the aforementioned processes. Geometry of the LFP cell applied in the thermal model includes the mandrel, active material, and outer cases. An air domain with a size of one cubic meter around the cell is constructed, and surfaces of this domain are set to be open-boundary conditions. Natural convection condition is considered and applied to the surface of the cell. Temperature deviations among cells are usually observed within the battery pack in practical applications, and the operating voltage of individual cells could be strongly temperaturedependent. Performances of the battery pack are therefore influenced by the thermal environment which might cause the electrical imbalance and thus lead to the failure. In order to evaluate the electrical imbalance and temperature deviation among individual cells, an electric circuit model coupled with the thermalelectrochemical model is further incorporated to evaluate the divergent driving currents of individual cells (Guo and White [13]). Current and voltage of cells within the battery pack follow Kirchhoff’s circuit laws of electrical circuits. The internal resistance of the cell depends on various factors, such as size, material compositions, chemical properties, degree of ageing, temperature, and the discharge current. In spite of the complexity of internal resistance, the total resistance of a cell R within a battery pack consisting of a combination of series and parallel connections can be determined by the current and voltage using the following equation
R¼
V ocp V cell Icell
ð4Þ
where V ocp denotes the open circuit potential calculated by subtracting the open circuit potential of the anode from the open circuit potential of the cathode, V cell is the working voltage, and Icell is the applied current of the cell. Values of material parameters employed in the thermalelectrochemical model are acquired from experimental measurements as well as references listed in Table 2. The initial concentration of individual electrodes applied in this model play an important role in describing the voltage profiles and cell capacity. Our previous work used a proper estimation method of the initial concentration of electrodes which can avoid artificial tuning of parameters so as to improve the accuracy of simulation results (Huang et al. [18], Kumaresan et al. [19]). Performances of the LFP battery under various discharge rates are investigated with the aforementioned model. Numerical solutions of the thermalelectrochemical model are obtained by using the commercial finite element software COMSOL Multiphysics 5.0 [2]. In this study, a running management is built in MATLAB, R2010a [1] and is applied to transfer the coupling parameters of the thermal-electrochemical model such as operating current, heat generation, and temperature of individual cell connected in different configuration within the battery pack among different modules of COMSOL Multiphysics 5.0 [2]. A flow chart of simulation procedures is illustrated in Fig. 1. 3. Experiments A high-energy-type LFP cell (40,138) with the nominal capacity of 18 Ah and the nominal voltage of 3.3 V, manufactured by Phoenix Silicon International Corporation (PSI) and commercially applied to UPS systems, is investigated here. To examine electrochemical behaviors of the LFP cell under different C rates, discharge of the cell was conducted under constant currents of 0.2C, 1C, and 2C rates until a cut-off voltage of 2.1 V was reached over the operating duration at environmental temperature of about 32 °C. To further investigate the thermal behavior of the battery pack, a 4S6P system produced by PSI is selected for our study. Discharge
Table 2 Parameters used in the thermal-electrochemical model. Description
Negative electrode
Positive electrode
Separator
Unit
Remarks
Thickness Cell cross section area Initial salt concentration Max solid phase concentration Particle radius Solid phase volume Electrolyte phase volume fraction Reaction rate constant k (ka/kc) Charge transfer coefficient a (aa/ac) Conductivity Li-diffusivity Density Transport number Equilibrium potential Temperature derivative of equilibrium Heat capacity Thermal conductivity
1.01e4 4.27e1 14,470 31,507 1.25e5 0.471 0.357 2.00e11/2.00e11 0.5/0.5 100 Function of T 1450
1.60e4
1.58e05
a
700 21,190 8.00e6 0.297 0.444 1.11e11/3.63e11 0.5/0.5 91 Function of T 2250
1000
m m2 mol/m3 mol/m3 m
Heat capacity Thermal conductivity a b c d
Experimental measurements. Estimated values. COMSOL Multiphysics 5.0 [2]. Kumaresan et al. [19].
Function of SOC Function of SOC 700 1.58
Copper 385 400
c c c c
m/s
b,c c
Function of SOC 7.50e11
S/m m2/s kg/m3
c c c c
0.363 Function of SOC Function of SOC 716 1.04
a b
c c
J/(kg K) W/(m K)
d
Aluminum
Unit
Remarks
875 238
J/(kg K) W/(m K)
c
1978
c
c
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Fig. 1. A flow chart of simulation procedures in this study.
Fig. 2. Arrangement of temperature measuring points in (a) front view (T1 and T2), (b) side view (T3) of the 4S6P LFP battery pack.
of the 4S6P LFP battery pack, consisting of a combination of four in series and six in parallel connection, with the interconnectors of copper alloy sheets was conducted under various C rates until a cut-off voltage of 2.5 V was reached over the operating duration. A higher cut-off voltage is applied for the pack in practical operation to prevent individual cells from over discharge. Temperatures within the pack were measured using twenty-one thermocouples attached to the surface of cells and interconnectors during charging and discharging under different C rates. However, in order to effectively compare the temperature differences among individual cells, only three representative measuring points (indicated as T1, T2, and T3) with relatively large temperature differences distributed at the middle cylindrical surfaces of the cell are reported here as shown in Fig. 2. To ensure the fidelity of the temperature measurements, the charge and discharge protocols were followed by a relaxation period to ensure a uniform starting temperature between the batteries before next experimental processes. 4. Results and discussion Voltage profiles of the LFP cell under 0.2, 1, 2C discharge procedures at an ambient temperature of about 32 °C were experimentally measured, as shown in Fig. 3(a) (in symbols). The voltage plateaus around 3.3 V were observed and the discharge capacity of the cell was slightly declined from 18 Ah to 17 Ah along with the increase of the discharge rates. The corresponding surface temperatures were measured using a thermocouple positioned at the half height of the cylindrical cell to make the measurement more representable of the average cell temperature, and are shown in Fig. 3(b) (in symbols). More rapid temperature rise of the cell was observed at higher discharging rate. Validity of the application of our thermal-electrochemical model to the LFP cell under several discharge rates is examined by comparing simulated temperature
Fig. 3. (a) Discharge voltage profiles; (b) temperature evolutions of the LFP cell under various rates at an ambient temperature of about 32 °C based on the experiments (in symbols) and the simulations (in lines).
behavior of the cell with the corresponding measurements. Discharge voltage profiles of the cell under various rates based on the simulations are shown in Fig. 3(a) (in lines). The discharge voltage profiles based on the simulations match fairly well with those based on the corresponding experiments, in particular, the simulated voltage plateaus are closely matched. The predicted
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temperature evolutions (in lines) during discharge are also in fair agreement with experimental data, as demonstrated in Fig. 3(b). For the 4S6P LFP battery pack, experimental measurements shown in Fig. 4(a) and (b) (in symbols) illustrate the inhomogeneous temperature distribution and evolution history at 2C discharge rate until a cut-off voltage of 2.5 V was reached at the ambient temperatures of 20 °C and 32 °C, respectively. At the initial stage of discharge, temperatures of all three measuring points are fairly close and increase in a similar fashion. Temperature deviations of the three measuring spots in the pack at either ambient temperature are observed after 400 s of discharge. Due to the arrangements of cells and upward flow of heated air, temperature measured at T1 is higher than that of T2. Temperature at T3 of the pack is cooler because the upward flow of air is drawn from the side while the pack bottom is enclosed. Temperature rise throughout the process of 2C discharge is about 17 °C under the ambient temperature of 20 °C, while the temperature rise is about 22 °C under the ambient temperature of 32 °C. In spite of the larger discharging temperature rise under higher ambient temperature, temperature deviations within the pack are similar at either ambient temperature. According to the present experimental measurements, the non-uniformity of temperatures among the cells within
the pack may be less dependent on the ambient temperature than other operating conditions, such as discharge rate, connection configurations of the pack, cell arrangements, and cooling conditions. Simulated temperatures of the pack at the ambient temperatures of 20 °C and 32 °C are validated with the corresponding experiments, as shown in Fig. 4(a) and (b) (in lines). It is observed that simulated temperatures under the ambient temperatures of 20 °C are rather underestimated comparing with the experimental measurements. On the contrary, simulated temperatures under the ambient temperatures of 32 °C are in better agreement with the corresponding experiments. This discrepancy may be due to the fact that the parameters used in the thermal-electrochemical model are based on measurements at an ambient temperature of about 32 °C, and there is a temperature dependency of these parameters. In addition to the temperature evolution histories, the simulation results shown in Fig. 5 also illustrate the spatial temperature deviations within the pack. In the case of the ambient temperature
Fig. 5. Temperature distribution of the pack after 1600-s discharge based on the simulations.
Fig. 4. Temperature evolutions of the pack under 2C rate at an ambient temperature of (a) 20 °C and (b) 32 °C based on the experiments (in symbols) and the simulations (in lines).
Fig. 6. Distributions of the internal resistance of individual cells within the pack after 1600-s discharge based on the simulations.
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of 32 °C, temperature deviations in the pack can be clearly observed. Distributions of the corresponding internal resistance of individual cells within the pack after 1600-s discharge are shown in Fig. 6. The corresponding temperature differences among the parallel-connected cells are up to 3 °C, which leads to higher internal resistance of the cells with lower temperature. Since the parallel-connected cells have equivalent output voltage and the internal resistance of the colder cells rise more significantly, operating current of the cells with higher temperature increases in order to offset the effect of temperature difference on its internal resistance. This temperature imbalance in turn results in decrease
of the discharging current through the cells with lower temperature. This vicious temperature rising circle causes considerably more heating at certain region of the pack, and aggravates temperature nonuniformity within the pack compared to a constant current loading. At the later stage of the discharge process, cells with higher temperature approaches to the fully discharged state faster and thus experience a smaller current as the internal resistances increase rapidly [20]. Discharge capacities of the cell with higher temperatures could exhaust at faster rate and thus restrict the overall available capacity and power of the pack. The simulated temperature and current evolution histories of the cells at the bottom row of the pack (labeled as 1a to 1f
Fig. 7. (a) Simulated temperature evolutions; (b) simulated current evolution histories of the cells of 1a to 1f under 2C discharge rate and an ambient temperature of 32 °C.
Fig. 8. (a) Simulated temperature evolutions; (b) simulated current evolution histories of the cells of 1a to 1f under 2C discharge rate and an ambient temperature of 32 °C with cyclic operation.
Table 3 Discharge rate, discharge capacity and temperature of the cells of 1a to 1f under 2C rate and ambient temperature of 32 °C at the end of discharge based on the simulations. Cell
1a
1b
1c
1d
1e
1f
Discharge rate (C) Discharge capacity (Ah) Temperature (°C)
2.062 18.24 47.72
1.946 18.17 49.90
1.885 18.11 50.42
1.849 18.10 50.00
1.954 18.17 49.63
2.104 18.27 48.88
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Table 4 Discharge rate, discharge capacity and temperature of the cells of 1a to 1f under 2C rate and ambient temperature of 32 °C at the end of discharge of the cyclic operation based on the simulations. Cell
1a
1b
1c
1d
1e
1f
Discharge rate (C) Discharge capacity (Ah) Temperature (°C)
2.206 18.38 50.25
1.907 18.06 51.52
1.634 18.05 53.04
1.827 18.13 52.48
1.944 18.18 51.64
2.195 18.30 50.44
indicated in Fig. 6) under 2C discharge rate and an ambient temperature of 32 °C are shown in Fig. 7(a) and (b), respectively. Table 3 lists the corresponding discharge capacity, temperature, and discharge rate at the end of discharge and demonstrates that the deviations among these six cells are about 2%, 3 °C, and 12%, respectively. On the contrary, in the case of the ambient temperature of 20 °C, temperature differences among the parallelconnected cells are less than 1 °C and thus the discharge rate and discharge capacity are relatively uniform. In order to investigate the effects of thermally-driven current imbalance on the performance of the pack, a cyclic charge and discharge process, which might occur in practical applications such as a self-guided vehicle widely adopted in various industries, is performed to achieve larger heat accumulation. These aforementioned apparatus with the intelligent control system can be charged automatically for continuous operations, while accumulated heat of the pack could become hazardous to their cycling life. The pack was simulated under five cycles consisting of 200-s charge and 200-s discharge under 2C rate followed by a fully discharge. Fig. 8 (a) and (b) shows the temperature and current evolution histories of the pack during this thermal accumulation process, respectively. During the designed cyclic operation, temperature deviations among cells gradually increase and thus the cells with higher temperatures heat up considerably more than the cells with lower temperatures. At the early stage of the final discharge process, it is observed that the cells with higher temperature experience larger current due to the fact that the internal resistance of cells decreases with increasing temperature. As the discharging process is further carried out, the cells with higher temperature approaches the fully discharged state faster than those with lower temperatures. As shown in Table 4, after cyclic operations deviations of discharge capacity among the parallel-connected cells are doubled comparing to the direct discharge process at ambient temperature of 32 °C, where larger temperature deviations are observed. The doubled deviation of discharge capacity demonstrates the increasing possibility of overcharge and thermal runaway hazards during cyclic operations. On the other hand, a sudden boost of the current could lead to undesired side reactions and in turn increase internal resistance of the LFP battery. Capacity losses of the cells could be thus influenced by the current deviation induced by the nonuniform temperature distribution. Simulation results of the thermal-electrochemical model adopted in this study demonstrate that thermally-driven pack imbalances could directly affect long term performance and stability of the battery pack. However, cell degradation mechanisms and processes, which may accelerate the cell deterioration and thus amplified the pack imbalances in practical continuous applications, are not considered in the current model. The influence of thermally engendered current imbalances among the parallel-connected cells might be more detrimental in applications where the pack is operated under fluctuating currents within a narrow range of SOC. Such a scenario is commonly found in the applications such as hybrid electric vehicles that do not have sufficient time to balance cells. Our simulation suggests that it is crucial to consider thermally-driven pack imbalances in larger packs as the temperature deviations may exist throughout the
battery pack, warranting careful pack design and cooling strategies for higher performance and safety. 5. Conclusions In this paper, the impacts of electrical imbalance and nonuniform temperature distribution among cells during charge/ discharge on the performances of a 4S6P LFP battery pack are studied. The battery system is simulated by the thermalelectrochemical model coupled with current conservation equations, which accounts for the electrical behaviors among cells within the pack. A running management built in MATLAB, R2010a [1] is applied to communicate the coupling parameters of the thermal-electrochemical model such as operating current, heat generation and temperature of the battery cells connected in various configurations among different modulus of COMSOL Multiphysics 5.0 [2]. Simulations of the discharge voltage and temperature distribution of a single cell under various C rates are validated with the corresponding experimental measurements. Simulations of the 4S6P pack under 2C discharge are also conducted. Temperatures of the selected measuring points within the pack based on the experiments and our simulations are in fair agreement. This numerical approach is further applied to investigate the influences of temperature deviations on the pack. When significant temperature deviations exist in the battery pack, cells with lower temperature would have higher internal resistance and vice versa. In turn, some of the cells with higher temperature are driven by higher current, which causes these hotter sections to increase faster in temperature. Variation of discharge capacity among the parallel-connected cells is aggravated while larger temperature gradients are observed. The thermally-driven pack imbalances such as variation of discharge capacity and current imbalance observed in this study could be much more server in practical applications, since factors including cell degradation, fluctuating loading, and vibrating environment are not considered in our model. The developed model framework, which incorporates temperature deviations and its impact on the thermally-driven pack imbalances, can assist the design of the pack in charge/discharge control and thermal management systems. Acknowledgements This work is funded by Ministry of Science and Technology, Taiwan, and Phoenix Silicon International Corporation under Grant MOST1032622E002035CC2 and MOST1042622E002018CC2. References [1] MATLAB (R2010a), MATLAB User Manual, Release 7.10.0, USA, 2010. [2] COMSOL Multiphysics 5.0, Burlington, MA, USA, 2014. [3] B. Scrosati, J. Garche, Lithium batteries: status, prospects and future, J. Power Sources 195 (9) (2010) 2419–2430. [4] H. Huang, S.C. Yin, L.F. Nazar, Approaching theoretical capacity of LiFePO4 at room temperature at high rates, Electrochem. Solid-State Lett. 4 (10) (2001). [5] K. Kumaresan, G. Sikha, R.E. White, Thermal model for a li-ion cell, J. Electrochem. Soc. 155 (2) (2008) 164–171. [6] X.M. Xu, R. He, Review on the heat dissipation performance of battery pack with different structures and operation conditions, Renew. Sustain. Energy Rev. 29 (2014) 301–315.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Thermal-electrochemical coupled simulations for cell-to-cell imbalances in lithium-iron-phosphate based battery packs Hsuan-Han Huang a, Hsun-Yi Chen a,⇑, Kuo-Chi Liao a,⇑, Hong-Tsu Young b, Ching-Fei Lee c, Jhen-Yang Tien c a
Department of Bio-Industrial Mechatronics Engineering, National Taiwan University, Taiwan, ROC Department of Mechanical Engineering, National Taiwan University, Taiwan, ROC c Phoenix Silicon International Corporation, Taiwan, ROC b
h i g h l i g h t s Electric circuit of the pack is incorporated to evaluate thermally-driven imbalance. Temperature and current deviation of a large complex battery pack are investigated. Deviation among the cell capacity is aggravated with larger temperature gradients.
a r t i c l e
i n f o
Article history: Received 24 February 2017 Revised 19 May 2017 Accepted 20 May 2017 Available online 25 May 2017 Keywords: Lithium-iron-phosphate based battery Thermal-electrochemical model Thermal management Finite element analysis
a b s t r a c t A thermal-electrochemical coupled model framework considering mass balance, charge balance, reaction kinetics, and energy balance is developed to evaluate thermally-driven imbalance among cells of a commercialized lithium-iron-phosphate battery pack consisting of a combination of series and parallel connections. Current distribution and joule heat generation of copper alloy sheets connecting several cells within a battery pack are also considered in the simulation. A running management built in MATLAB, R2010a (2010) is applied to deliver the coupling of the thermal-electrochemical model, among different modulus of COMSOL Multiphysics 5.0 (2014). Simulated voltage variation and temperature distribution of an individual cell during charge/discharge are validated with the corresponding experiments. The developed model is further applied to study the non-uniform temperature distribution and electrical imbalance among cells within the 4S6P LFP battery pack. Simulation results show that thermal imbalance could magnify the deviation of discharge current and capacity among individual cells and may accelerate the capacity losses of the cells within a battery pack. Our model can facilitate understanding of the impact of electrical imbalance on the battery pack and assist thermal management systems. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The lithium-ion battery is a popular type of rechargeable batteries for portable electronics, with high energy density, no memory effect, and slow degradation. (Scrosati and Garche [3]) The lithium-iron-phosphate (LFP) battery with lithium iron phosphate as cathode material is of low cost, high power output, environmentally benign, and features intrinsic thermal safety. (Huang et al. [4]) This battery chemistry thus ranks among the most promising lithium-ion batteries that target hybrid electric vehicle (HEV) and electric vehicle (EV) markets, and rechargeable LFP battery packs are widely used as energy storage by automobile industries and ⇑ Corresponding authors. E-mail addresses: [email protected] (H.-Y. Chen), (K.-C. Liao). http://dx.doi.org/10.1016/j.applthermaleng.2017.05.105 1359-4311/Ó 2017 Elsevier Ltd. All rights reserved.
[email protected]
in uninterruptible power supply (UPS) systems. However, one of the crucial limitations for the LFP battery pack is its operating temperature, which may strongly restrict the voltage, capacity, power, and cycle life. Overheating and non-uniform temperature distribution of the battery pack could lead to degradation and failure of cells. Thermal management of the battery pack is therefore essential for its long term performance and safety. In order to analyze the thermal effects on the performance of batteries, Kumaresan et al. [5] developed thermalelectrochemical models coupling mass balance, charge balance, reaction kinetics, energy balance and heat transfer equations, and temperature dependences of transport and kinetic parameters are considered. In practice, the thermal-electrochemical coupled analysis can be used to obtain the optimal operating conditions such as pack temperature. Since thermal management needs to be carefully examined when new battery packs are developed,
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many studies proposed various cooling strategies to achieve more uniform temperature distribution. Xu and He [6] asserted that the heat dissipation of battery packs could be significantly enhanced with different arrangements of the cells and the air inlet/outlet. Wang et al. [7] and Chen et al. [8] investigated various cooling approaches to guarantee the batteries operated within the optimal temperature range as well as to provide effective solutions for the cooling system. Yang et al. [9] studied the thermal performances of battery pack to advise the appropriate arrangement of cylindrical cells for the efficient cooling system. Lan et al. [10] and Xu et al. [11] developed a novel cooling system based on aluminum minichannel tubes applied to the battery module and investigated its efficacy on the mitigation of thermal runaway. Rather few studies investigate the influences of temperature deviations on the cell-to-cell current distribution of a battery pack. Bandhauer et al. [12] revealed that electrical imbalance could lead to serious battery failures if thermal runaway is induced. Guo and White [13] developed a thermal resistance model, coupling the so-called single particle model, energy balance equation, and basic circuit constraints, to simulate electrical and thermal behaviors among batteries connected in parallel configuration. Although the electrochemical behavior and heat generation among individual cells were considered, temperature of each cell was assumed to be uniform in the study. Moreover, even though the predicted temperature of the battery pack during charge/discharge cycles is consistent with experimental data, the individual cells show minute variations in electrical behaviors due to the relatively limited temperature deviation. Yang et al. [14] investigated the unbalanced cell discharging stemmed from a temperature difference between two parallel-connected cells via simulations and experiments, with an assumption of different initial temperatures at the beginning of the discharging process. A larger current is observed within the cell of higher temperature in the early discharging stage. On the contrary, the cooler cell experiences a smaller operating current. The unbalanced discharging current induced by the temperature difference between two parallel connected cells exacerbates the imbalance phenomenon. This imbalance discharge current may thus aggravate the capacity deviation between two parallel-connected cells and accelerate the capacity losses of the battery pack. In the past, many researches overlooked the thermally-driven imbalance among the cells and its potential risk of thermal runaway and assumed the electrochemical behaviors and heat generation among individual cells of a battery pack to be identical. The thermal-electrochemical coupled analysis is thus applied in the present study to investigate effects of the non-uniform temperature distribution and thermally-driven electrical imbalance among cells on the performance of a commercialized battery pack consisting of a combination of series and parallel connections. The developed model framework enables us to examine the operating current, temperature distribution and heat generation among individual cells and the impact of thermally-driven imbalances on a large complex battery pack serving for practical applications.
Positive electrode reaction þ
Li1x FePO4 þ xLi þ xe $ LiFePO4
ð1Þ
Negative electrode reaction þ
Lix C6 $ 6C þ xLi þ xe
ð2Þ
Total reaction
Li1x FePO4 þ Lix C6 $ LiFePO4 þ 6C
ð3Þ
During the charge process, the reactions proceed from the lefthand side to the right-hand side and lithium ions deintercalate from the positive electrode and intercalate into the negative electrode, while the reverse reaction takes place during the discharge process. The LFP battery domain that the one-dimensional electrochemical model considered includes the aforementioned three components and is described as three sequentially extended lines. Since there are other physical phenomena in addition to the aforementioned electrochemical reactions, during charge and discharge processes an electrochemical model on the basis of coupled mass balance, charge balance, and reaction kinetics constitution laws is adapted here to simulate the electrochemical behavior of the LFP battery. This model consists of diffusion phenomena in the concentrated electrolyte and the solid phase electrodes, Ohm’s law for the potential distribution, and the conservation of charge and mass. Moreover, the solid phase porous electrodes filled with the electrolyte and the diffusion mechanism in the electrodes are described by the porous electrode theory, which considers each electrode as a number of spherical particles with the surface area represents the porous electrode active surface area. Governing equations and boundary conditions illustrating the isothermal charge and discharge processes of a lithium-ion battery are listed in Table 1 to describe general dynamics of a battery system and are used to predict the behaviors of lithium-ion batteries during charge and discharge procedures (Doyle et al. [16]). To describe the effect of heat generation from cell to pack level and formation of thermal hot spots within the battery pack, a three-dimensional thermal model is coupled to the electrochemical model. Performances of the LFP cell, such as the output voltage and storage capacity, are significantly influenced by its operating temperature. However, the heat generation of the LFP cell is in turn controlled by the electrochemical reactions occurring in the cell during charge and discharge processes and thus affects the
Table 1 Equations used in the thermal-electrochemical model. Equations
Boundary conditions
Electrochemical model Separator i2 @t þ @ c ¼ D @x 2 z m F @x þ þ @g sþ tþ I RT @c ¼ þ @x j F nmþ þ zþ mþ @x 2
@c @t
rc ¼ 0 at x ¼ 0 and d þ ds þ dþ i2 ¼ I at x ¼ d and ds rU1 ¼ rI at x ¼ 0 and d þ ds
Electrodes
2. Mathematical model
@c @t @g @x
Since highly conductive current collectors such as aluminum and copper foils are utilized to ensure homogeneous current distribution, the electrochemical behavior of the cylindrical cell can be reasonably assumed to be one dimension along the radial/thickness direction (Newman and Alyea [15]). The one-dimensional electrochemical model applying to the LFP battery here considers three components: the graphite negative electrode, separator, and lithium-iron-phosphate positive electrode. The chemical reactions in the LFP battery that our electrochemical model considered are as follows:
ajn ð1t þ Þ i2 @t þ @ c ¼ D @x 2 z m F @x þ mþ þ þ sþ Ii2 i2 RT @c ¼ r þ j þ F nmþ þ zþtþmþ @x 2
s1 @i2 ajn ¼ nF @x
a a aF I ¼ Fðka Þ c ðkc Þ a ðcmax cÞac caa exp aRT ðg UÞ a F a ðg UÞ exp RT Thermal model
qC p dT ¼ rðkrTÞ þ Q rxn þ Q rec þ Q ohm dt Q rxn ¼ FaJðU1 U2 UÞ Q rec ¼ FaJ @U @T
Q rxn ¼ reff ðrU1 Þ2 þ jeff ðrU2 Þ2 þ
2jeff RT F
ð1 tþ ÞrðlncÞrU2
krT ¼ hðT 1 TÞ at t ¼ Rz ¼ 0 and L
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operating temperature. Heat is released accompanying with the electrochemical reaction and subsequently leads to temperature increase of the battery. In our model framework, the dependence of the physicochemical properties is described by the Arrhenius equation. Energy balance equations and boundary conditions listed in Table 1 are used to describe the spatial distribution of temperature (Gu and Wang [17]). The heat generation due to electrochemical reactions and joule heating is assessed based on electrochemical model, and then applied in the heat transfer equations to evaluate the temperature distributions. The average temperature of the corresponding active materials is then fed back to update the electrochemical model through temperaturedependent physicochemical properties. The thermal and electrochemical behaviors of the battery systems are thus partially coupled by the aforementioned processes. Geometry of the LFP cell applied in the thermal model includes the mandrel, active material, and outer cases. An air domain with a size of one cubic meter around the cell is constructed, and surfaces of this domain are set to be open-boundary conditions. Natural convection condition is considered and applied to the surface of the cell. Temperature deviations among cells are usually observed within the battery pack in practical applications, and the operating voltage of individual cells could be strongly temperaturedependent. Performances of the battery pack are therefore influenced by the thermal environment which might cause the electrical imbalance and thus lead to the failure. In order to evaluate the electrical imbalance and temperature deviation among individual cells, an electric circuit model coupled with the thermalelectrochemical model is further incorporated to evaluate the divergent driving currents of individual cells (Guo and White [13]). Current and voltage of cells within the battery pack follow Kirchhoff’s circuit laws of electrical circuits. The internal resistance of the cell depends on various factors, such as size, material compositions, chemical properties, degree of ageing, temperature, and the discharge current. In spite of the complexity of internal resistance, the total resistance of a cell R within a battery pack consisting of a combination of series and parallel connections can be determined by the current and voltage using the following equation
R¼
V ocp V cell Icell
ð4Þ
where V ocp denotes the open circuit potential calculated by subtracting the open circuit potential of the anode from the open circuit potential of the cathode, V cell is the working voltage, and Icell is the applied current of the cell. Values of material parameters employed in the thermalelectrochemical model are acquired from experimental measurements as well as references listed in Table 2. The initial concentration of individual electrodes applied in this model play an important role in describing the voltage profiles and cell capacity. Our previous work used a proper estimation method of the initial concentration of electrodes which can avoid artificial tuning of parameters so as to improve the accuracy of simulation results (Huang et al. [18], Kumaresan et al. [19]). Performances of the LFP battery under various discharge rates are investigated with the aforementioned model. Numerical solutions of the thermalelectrochemical model are obtained by using the commercial finite element software COMSOL Multiphysics 5.0 [2]. In this study, a running management is built in MATLAB, R2010a [1] and is applied to transfer the coupling parameters of the thermal-electrochemical model such as operating current, heat generation, and temperature of individual cell connected in different configuration within the battery pack among different modules of COMSOL Multiphysics 5.0 [2]. A flow chart of simulation procedures is illustrated in Fig. 1. 3. Experiments A high-energy-type LFP cell (40,138) with the nominal capacity of 18 Ah and the nominal voltage of 3.3 V, manufactured by Phoenix Silicon International Corporation (PSI) and commercially applied to UPS systems, is investigated here. To examine electrochemical behaviors of the LFP cell under different C rates, discharge of the cell was conducted under constant currents of 0.2C, 1C, and 2C rates until a cut-off voltage of 2.1 V was reached over the operating duration at environmental temperature of about 32 °C. To further investigate the thermal behavior of the battery pack, a 4S6P system produced by PSI is selected for our study. Discharge
Table 2 Parameters used in the thermal-electrochemical model. Description
Negative electrode
Positive electrode
Separator
Unit
Remarks
Thickness Cell cross section area Initial salt concentration Max solid phase concentration Particle radius Solid phase volume Electrolyte phase volume fraction Reaction rate constant k (ka/kc) Charge transfer coefficient a (aa/ac) Conductivity Li-diffusivity Density Transport number Equilibrium potential Temperature derivative of equilibrium Heat capacity Thermal conductivity
1.01e4 4.27e1 14,470 31,507 1.25e5 0.471 0.357 2.00e11/2.00e11 0.5/0.5 100 Function of T 1450
1.60e4
1.58e05
a
700 21,190 8.00e6 0.297 0.444 1.11e11/3.63e11 0.5/0.5 91 Function of T 2250
1000
m m2 mol/m3 mol/m3 m
Heat capacity Thermal conductivity a b c d
Experimental measurements. Estimated values. COMSOL Multiphysics 5.0 [2]. Kumaresan et al. [19].
Function of SOC Function of SOC 700 1.58
Copper 385 400
c c c c
m/s
b,c c
Function of SOC 7.50e11
S/m m2/s kg/m3
c c c c
0.363 Function of SOC Function of SOC 716 1.04
a b
c c
J/(kg K) W/(m K)
d
Aluminum
Unit
Remarks
875 238
J/(kg K) W/(m K)
c
1978
c
c
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Fig. 1. A flow chart of simulation procedures in this study.
Fig. 2. Arrangement of temperature measuring points in (a) front view (T1 and T2), (b) side view (T3) of the 4S6P LFP battery pack.
of the 4S6P LFP battery pack, consisting of a combination of four in series and six in parallel connection, with the interconnectors of copper alloy sheets was conducted under various C rates until a cut-off voltage of 2.5 V was reached over the operating duration. A higher cut-off voltage is applied for the pack in practical operation to prevent individual cells from over discharge. Temperatures within the pack were measured using twenty-one thermocouples attached to the surface of cells and interconnectors during charging and discharging under different C rates. However, in order to effectively compare the temperature differences among individual cells, only three representative measuring points (indicated as T1, T2, and T3) with relatively large temperature differences distributed at the middle cylindrical surfaces of the cell are reported here as shown in Fig. 2. To ensure the fidelity of the temperature measurements, the charge and discharge protocols were followed by a relaxation period to ensure a uniform starting temperature between the batteries before next experimental processes. 4. Results and discussion Voltage profiles of the LFP cell under 0.2, 1, 2C discharge procedures at an ambient temperature of about 32 °C were experimentally measured, as shown in Fig. 3(a) (in symbols). The voltage plateaus around 3.3 V were observed and the discharge capacity of the cell was slightly declined from 18 Ah to 17 Ah along with the increase of the discharge rates. The corresponding surface temperatures were measured using a thermocouple positioned at the half height of the cylindrical cell to make the measurement more representable of the average cell temperature, and are shown in Fig. 3(b) (in symbols). More rapid temperature rise of the cell was observed at higher discharging rate. Validity of the application of our thermal-electrochemical model to the LFP cell under several discharge rates is examined by comparing simulated temperature
Fig. 3. (a) Discharge voltage profiles; (b) temperature evolutions of the LFP cell under various rates at an ambient temperature of about 32 °C based on the experiments (in symbols) and the simulations (in lines).
behavior of the cell with the corresponding measurements. Discharge voltage profiles of the cell under various rates based on the simulations are shown in Fig. 3(a) (in lines). The discharge voltage profiles based on the simulations match fairly well with those based on the corresponding experiments, in particular, the simulated voltage plateaus are closely matched. The predicted
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temperature evolutions (in lines) during discharge are also in fair agreement with experimental data, as demonstrated in Fig. 3(b). For the 4S6P LFP battery pack, experimental measurements shown in Fig. 4(a) and (b) (in symbols) illustrate the inhomogeneous temperature distribution and evolution history at 2C discharge rate until a cut-off voltage of 2.5 V was reached at the ambient temperatures of 20 °C and 32 °C, respectively. At the initial stage of discharge, temperatures of all three measuring points are fairly close and increase in a similar fashion. Temperature deviations of the three measuring spots in the pack at either ambient temperature are observed after 400 s of discharge. Due to the arrangements of cells and upward flow of heated air, temperature measured at T1 is higher than that of T2. Temperature at T3 of the pack is cooler because the upward flow of air is drawn from the side while the pack bottom is enclosed. Temperature rise throughout the process of 2C discharge is about 17 °C under the ambient temperature of 20 °C, while the temperature rise is about 22 °C under the ambient temperature of 32 °C. In spite of the larger discharging temperature rise under higher ambient temperature, temperature deviations within the pack are similar at either ambient temperature. According to the present experimental measurements, the non-uniformity of temperatures among the cells within
the pack may be less dependent on the ambient temperature than other operating conditions, such as discharge rate, connection configurations of the pack, cell arrangements, and cooling conditions. Simulated temperatures of the pack at the ambient temperatures of 20 °C and 32 °C are validated with the corresponding experiments, as shown in Fig. 4(a) and (b) (in lines). It is observed that simulated temperatures under the ambient temperatures of 20 °C are rather underestimated comparing with the experimental measurements. On the contrary, simulated temperatures under the ambient temperatures of 32 °C are in better agreement with the corresponding experiments. This discrepancy may be due to the fact that the parameters used in the thermal-electrochemical model are based on measurements at an ambient temperature of about 32 °C, and there is a temperature dependency of these parameters. In addition to the temperature evolution histories, the simulation results shown in Fig. 5 also illustrate the spatial temperature deviations within the pack. In the case of the ambient temperature
Fig. 5. Temperature distribution of the pack after 1600-s discharge based on the simulations.
Fig. 4. Temperature evolutions of the pack under 2C rate at an ambient temperature of (a) 20 °C and (b) 32 °C based on the experiments (in symbols) and the simulations (in lines).
Fig. 6. Distributions of the internal resistance of individual cells within the pack after 1600-s discharge based on the simulations.
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of 32 °C, temperature deviations in the pack can be clearly observed. Distributions of the corresponding internal resistance of individual cells within the pack after 1600-s discharge are shown in Fig. 6. The corresponding temperature differences among the parallel-connected cells are up to 3 °C, which leads to higher internal resistance of the cells with lower temperature. Since the parallel-connected cells have equivalent output voltage and the internal resistance of the colder cells rise more significantly, operating current of the cells with higher temperature increases in order to offset the effect of temperature difference on its internal resistance. This temperature imbalance in turn results in decrease
of the discharging current through the cells with lower temperature. This vicious temperature rising circle causes considerably more heating at certain region of the pack, and aggravates temperature nonuniformity within the pack compared to a constant current loading. At the later stage of the discharge process, cells with higher temperature approaches to the fully discharged state faster and thus experience a smaller current as the internal resistances increase rapidly [20]. Discharge capacities of the cell with higher temperatures could exhaust at faster rate and thus restrict the overall available capacity and power of the pack. The simulated temperature and current evolution histories of the cells at the bottom row of the pack (labeled as 1a to 1f
Fig. 7. (a) Simulated temperature evolutions; (b) simulated current evolution histories of the cells of 1a to 1f under 2C discharge rate and an ambient temperature of 32 °C.
Fig. 8. (a) Simulated temperature evolutions; (b) simulated current evolution histories of the cells of 1a to 1f under 2C discharge rate and an ambient temperature of 32 °C with cyclic operation.
Table 3 Discharge rate, discharge capacity and temperature of the cells of 1a to 1f under 2C rate and ambient temperature of 32 °C at the end of discharge based on the simulations. Cell
1a
1b
1c
1d
1e
1f
Discharge rate (C) Discharge capacity (Ah) Temperature (°C)
2.062 18.24 47.72
1.946 18.17 49.90
1.885 18.11 50.42
1.849 18.10 50.00
1.954 18.17 49.63
2.104 18.27 48.88
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Table 4 Discharge rate, discharge capacity and temperature of the cells of 1a to 1f under 2C rate and ambient temperature of 32 °C at the end of discharge of the cyclic operation based on the simulations. Cell
1a
1b
1c
1d
1e
1f
Discharge rate (C) Discharge capacity (Ah) Temperature (°C)
2.206 18.38 50.25
1.907 18.06 51.52
1.634 18.05 53.04
1.827 18.13 52.48
1.944 18.18 51.64
2.195 18.30 50.44
indicated in Fig. 6) under 2C discharge rate and an ambient temperature of 32 °C are shown in Fig. 7(a) and (b), respectively. Table 3 lists the corresponding discharge capacity, temperature, and discharge rate at the end of discharge and demonstrates that the deviations among these six cells are about 2%, 3 °C, and 12%, respectively. On the contrary, in the case of the ambient temperature of 20 °C, temperature differences among the parallelconnected cells are less than 1 °C and thus the discharge rate and discharge capacity are relatively uniform. In order to investigate the effects of thermally-driven current imbalance on the performance of the pack, a cyclic charge and discharge process, which might occur in practical applications such as a self-guided vehicle widely adopted in various industries, is performed to achieve larger heat accumulation. These aforementioned apparatus with the intelligent control system can be charged automatically for continuous operations, while accumulated heat of the pack could become hazardous to their cycling life. The pack was simulated under five cycles consisting of 200-s charge and 200-s discharge under 2C rate followed by a fully discharge. Fig. 8 (a) and (b) shows the temperature and current evolution histories of the pack during this thermal accumulation process, respectively. During the designed cyclic operation, temperature deviations among cells gradually increase and thus the cells with higher temperatures heat up considerably more than the cells with lower temperatures. At the early stage of the final discharge process, it is observed that the cells with higher temperature experience larger current due to the fact that the internal resistance of cells decreases with increasing temperature. As the discharging process is further carried out, the cells with higher temperature approaches the fully discharged state faster than those with lower temperatures. As shown in Table 4, after cyclic operations deviations of discharge capacity among the parallel-connected cells are doubled comparing to the direct discharge process at ambient temperature of 32 °C, where larger temperature deviations are observed. The doubled deviation of discharge capacity demonstrates the increasing possibility of overcharge and thermal runaway hazards during cyclic operations. On the other hand, a sudden boost of the current could lead to undesired side reactions and in turn increase internal resistance of the LFP battery. Capacity losses of the cells could be thus influenced by the current deviation induced by the nonuniform temperature distribution. Simulation results of the thermal-electrochemical model adopted in this study demonstrate that thermally-driven pack imbalances could directly affect long term performance and stability of the battery pack. However, cell degradation mechanisms and processes, which may accelerate the cell deterioration and thus amplified the pack imbalances in practical continuous applications, are not considered in the current model. The influence of thermally engendered current imbalances among the parallel-connected cells might be more detrimental in applications where the pack is operated under fluctuating currents within a narrow range of SOC. Such a scenario is commonly found in the applications such as hybrid electric vehicles that do not have sufficient time to balance cells. Our simulation suggests that it is crucial to consider thermally-driven pack imbalances in larger packs as the temperature deviations may exist throughout the
battery pack, warranting careful pack design and cooling strategies for higher performance and safety. 5. Conclusions In this paper, the impacts of electrical imbalance and nonuniform temperature distribution among cells during charge/ discharge on the performances of a 4S6P LFP battery pack are studied. The battery system is simulated by the thermalelectrochemical model coupled with current conservation equations, which accounts for the electrical behaviors among cells within the pack. A running management built in MATLAB, R2010a [1] is applied to communicate the coupling parameters of the thermal-electrochemical model such as operating current, heat generation and temperature of the battery cells connected in various configurations among different modulus of COMSOL Multiphysics 5.0 [2]. Simulations of the discharge voltage and temperature distribution of a single cell under various C rates are validated with the corresponding experimental measurements. Simulations of the 4S6P pack under 2C discharge are also conducted. Temperatures of the selected measuring points within the pack based on the experiments and our simulations are in fair agreement. This numerical approach is further applied to investigate the influences of temperature deviations on the pack. When significant temperature deviations exist in the battery pack, cells with lower temperature would have higher internal resistance and vice versa. In turn, some of the cells with higher temperature are driven by higher current, which causes these hotter sections to increase faster in temperature. Variation of discharge capacity among the parallel-connected cells is aggravated while larger temperature gradients are observed. The thermally-driven pack imbalances such as variation of discharge capacity and current imbalance observed in this study could be much more server in practical applications, since factors including cell degradation, fluctuating loading, and vibrating environment are not considered in our model. The developed model framework, which incorporates temperature deviations and its impact on the thermally-driven pack imbalances, can assist the design of the pack in charge/discharge control and thermal management systems. Acknowledgements This work is funded by Ministry of Science and Technology, Taiwan, and Phoenix Silicon International Corporation under Grant MOST1032622E002035CC2 and MOST1042622E002018CC2. References [1] MATLAB (R2010a), MATLAB User Manual, Release 7.10.0, USA, 2010. [2] COMSOL Multiphysics 5.0, Burlington, MA, USA, 2014. [3] B. Scrosati, J. Garche, Lithium batteries: status, prospects and future, J. Power Sources 195 (9) (2010) 2419–2430. [4] H. Huang, S.C. Yin, L.F. Nazar, Approaching theoretical capacity of LiFePO4 at room temperature at high rates, Electrochem. Solid-State Lett. 4 (10) (2001). [5] K. Kumaresan, G. Sikha, R.E. White, Thermal model for a li-ion cell, J. Electrochem. Soc. 155 (2) (2008) 164–171. [6] X.M. Xu, R. He, Review on the heat dissipation performance of battery pack with different structures and operation conditions, Renew. Sustain. Energy Rev. 29 (2014) 301–315.
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