Thermal management is crucial to the safe operation and the achievement of optimal performance of electric vehicle batteries. A thermal management system is responsible for maintaining the operation temperature and temperature uniformity across a battery stack. Thermal mathematical modeling was applied in examining battery thermal behaviors and thermal management. The thermal conductivity of polymer electrolyte and the thermal conductivity of composite cathode were measured. The temperature, lithium salts and lithium salt concentration dependencies of polymer electrolyte and composite cathode were studied. The thermal stability of the battery cells was studied by linear perturbation theory and numerical simulations.

 Air pollution has been named the number one health threat to American by American Lung Association. A major part of the overall air pollution (such as carbon dioxide, carbon monoxide, nitrous oxide etc.) is contributed by transportation. The California Air Resource Board has passed a revised mandate that 10% of all cars sold in the state in 2003 must be zero emission vehicles. The electric vehicle is an obvious candidate to meet such a requirement. The electric vehicle is quiet and minimizes sound pollution, and it is more energy efficient and requires less maintenance than gas powered cars. However the current lead acid battery requires long charge time but short of mile range (usually within 100 miles). Lithium polymer battery is one of batteries satisfies the long term battery criteria set by USABC for energy density, specific power, cycle life, mile range and recharge time. A lot of research efforts are underway to develop advanced electric vehicle batteries. Small-scale lithium polymer battery has been reported commercially available recently. But there are still questions unanswered about the scale up of high temperature batteries. Among them are the heat transport inside the battery cells, battery temperature uniformity, and maintaining the battery at operation temperature range. The performance, energy efficiency, safety and reliability of the battery rely on these answers. The examination of the thermal behavior and design of proper thermal management system are important topics in the battery design.

 Thermal modeling has been widely applied to exam battery thermal behavior and battery design parameters in view of the fact that a large number of cells are stacked to achieve the required energy and power of an EV battery. A lithium polymer battery is made up of a large number of thin film cells stacked in parallel, each cell includes lithium anode, polymer electrolyte (e.g. lithium triflate, lithium perchlorate, lithium imide and lithium methide etc.), composite cathode (e.g. TiS₂, V₆O₁₃, LiMn₂O₄ etc), and current collector (e.g. Al, Ni etc.). Averaged values of thermo-physical properties were used in the heat transfer equation. A thermal management system is composed of active cooling, heating and thermal insulation, they can be dealt with by the boundary conditions of the heat transfer equation. The calculations of heat transfer equation can be performed using alternating directional implicit finite difference methods.

 The heat generation term includes ohmic heating, overpotentials, and entropy change (assuming no change in the heat capacity of the system and no phase change). It depends on the temperature, state of charge and current fraction. Coupled electrochemical and thermal equations can usually be solved in one dimension and single cell battery. It is not practical to solve coupled equations for a large scale multi-cell stack. Either a constant heat generation rate was used or an averaged value under isothermal condition was assumed in the literatures of thermal modeling. The heat generation term could also be obtained from the difference of theoretical cell open circuit potential and experimental discharge curve. However none of these methods related the heat generation rate to the temperature directly, and it can be seen later that it is this temperature dependency that causes the thermal instability. In this study, the heat generation rate is associated to the temperature through local current fraction and temperature dependent ionic conductivity of polymer electrolyte.

 The polymer electrolyte, consists poly(ethylene) oxide and appropriate lithium salt concentration, is the cell component with the lowest thermal conductivity. The heat conduction in the polymer can play a dominant role in determining the thermal characteristics of the battery. However the thermal conductivities of polymer electrolyte and composite cathode have not been reported in the literature. Most published thermal modeling used estimated values or the values of similar species (e.g. TiO₂ instead of TiS₂). As it can be seen from the experimental results that error as large as one order of magnitude was introduced in the modeling. Most polymer electrolyte operates at elevated temperature to achieve desirable high ionic conductivity. The ionic conductivity changes several orders of magnitude from room temperature to the melting temperature of lithium (180° C). Despite intensive studies of temperature and lithium salt concentration dependencies of ionic conductivity, the dependencies of thermal conductivity of polymer electrolyte were little known. In this study, experimental measurement of the thermal conductivity of poly(ethylene oxide)-lithium salt electrolytes and composite cathodes (TiS₂, V₆O₁₃) were conducted by a guarded heat flow meter. The temperature effects and lithium salt concentration effects on polymer electrolyte were studied.

 The thermal conductivities of lithium triflate polymer electrolytes were found to be of similar value to the poly(ethylene oxide) matrix, and to be relatively constant for the electrolytes with various concentrations of the lithium salt. The thermal conductivities of poly(ethylene oxide)-lithium salt, including lithium perchlorate, triflate, imide, and methide, vary from 0.12 to 0.22 W/mK over the temperature ranging from 25° C to 150° C. Unlike the ionic conductivity of the polymer electrolytes, the thermal conductivity only slightly increases with the temperature below glass transition and decreases after glass transition (the polymer electrolyte undergoes phase transition from crystalline structure to amorphous structure at about 60 – 80° C). The results can be explained by phonon transmission (lattice vibration) being the dominant heat transport mechanism, with the ionic transport of heat being minor. Further, unlike ionic conductivity, the thermal conductivity of the PEO-lithium salt electrolytes decreases with increasingly amorphous structure according to the order: PEO-LiClO₄, PEO-LiCF₃SO₃, PEO-LiN(CF₃SO₂)₂, and PEO-LiC(CF₃SO₂)_3, due to the scattering of phonons in the disordered regions of the amorphous structure.

 The thermal conductivity of composite cathode (consists of PEO lithium triflate salt, TiS₂ or V₆O₁₃, and acetylene black), from 0.2 to 0.5 W/mK over the temperature ranging from 25° C to 150° C, was found to be close to polymer electrolyte. The thermal conductivity of V₆O₁₃ composite cathode is slightly higher than that of TiS₂ composite but exhibits similar trend over temperature range. The thermal conductivity increases before glass transition temperature and change only slightly after glass transition temperature. Again, phonon scattering mechanism was proposed to explain the thermal conductivity in amorphous structure. The thermal conductivities of polymer electrolyte and composite cathode (after glass transition temperature, which is the operation temperature of most lithium polymer cells) were therefore assumed to be a constant and independent of temperature in the mathematical modeling.

Due to a number of reasons such as the existence of macroscopic defects in the polymer electrolyte, the temperature perturbation can exist in lithium polymer battery. The temperature variation will affect the ionic conductivity of polymer electrolyte and the current distribution within these cells, which in turn will change the heat generation rate and eventually affect the temperature distribution. Instability could arise from this temperature dependency. The instability is one where local perturbation to a higher temperature results in higher ionic conductivity and therefore the passage of more current in this region with attendant increase in heat generation. If this excess heat generation cannot be conducted into adjacent cooler regions, instability or the growth of the perturbation results. In this study, thermal stability of lithium polymer battery is examined by a linear perturbation analysis. The analysis suggested the battery would experience thermal instability for perturbations of small wave number, for large potential drop across the polymer electrolyte, for small polymer electrolyte thickness, density and heat capacity, and for strong temperature dependence of the ionic conductivity.

The numerical calculations were carried out for constant potential drop across the polymer electrolyte, for constant mean discharge current density and for constant mean discharge output power. The numerical simulations were approximately in agreement with the linear perturbation analysis and predicting instability at small wave numbers. However, the growth rates of the perturbations appear not to be high. Calculations were carried out to determine whether the stability of the battery could be altered by changes in materials or external cooling. Example included enhancement of the external cooling to change the heat transfer coefficient upward by one order of magnitude. Neither of these changes significantly affected the stability. Numerical calculations for small batteries showed no thermal instability.

Numerical simulation and linear perturbation have been applied to study the thermal behavior of lithium polymer battery and its stability. The study indicates that perturbation with small wave number will cause the growth of the temperature and cause thermal instability. The calculations suggest that this instability is unlikely for small but may occur for larger batteries such as those intended for use in electric vehicle. The thermal conductivity of polymer electrolyte and composite cathode were found as relatively independent of temperature by experiment. It was also found that the thermal conductivity of polymer electrolyte is insensitive for different lithium salt and salt concentration.

The thermal instability analysis is intended to study the tendency of temperature variation, the response of the battery to a small perturbation in temperature of whatever origin. In the event that the perturbation grows, the battery is described as "unstable’ even though the temperature peaks might not grow to dangerous levels. The battery is "stable’ if the perturbation diminish with time. It is not an instability of explosive in nature, and the outset that the instability examined is not that following some accidental events such as puncturing of the battery. The instability of the battery is not directly linked to the safety of the battery.

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