# Evaluation of Present Accelerated Temperature Testing and Modeling of Batteries
## 1 Introduction  
The large-scale commercialization of lithium-ion batteries has enabled a great number of applications ranging from consumer electronic devices to electric vehicles and energy storage systems. However, the safety and reliability of lithium-ion batteries have been a concern, due to the numerous incidents of fires, explosions, and the rapid capacity fade [1; 2; 3; 4]. Testing is generally required to help qualify a battery in terms of safety and reliability in its targeted application. Safety testing can be conducted by following standards from organizations, such as the United Nations (UN), Underwriters Laboratories (UL), and International Electrotechnical Commission (IEC), which require that lithium-ion batteries be subjected to various mechanical, electrical, and thermal conditions. However, reliability testing, which is the focus of this paper, has for the most part been developed by battery manufacturers and device companies themselves without a widely recognized guidance document. For reliability testing of lithium-ion batteries, the capacity retention capability is usually examined intermediately by cycling or storing batteries for a certain number of cycles or amount of time. Degradation occurring during cycling and storage is called \"cycle aging\" and \"calendar aging\", respectively. However, lifetime of lithium-ion batteries comprised of cycle and calendar aging can be fairly long. For example, cells in a LiFePO\({}_{4}\)-based battery pack retired from an electric vehicle still possess an average capacity of 83% and a standard deviation of 16% of the nominal capacity, which was used in a southern city of China for more than three years with the mileage of 32,500 km [5]. The reliability testing of lithium-ion batteries under normal conditions is thus considerably time-consuming. To shorten testing time, accelerated testing is performed by increasing the loading levels on the products [6] in excess of normal conditions. There must be a method to extrapolate the data to predict reliability over the intended usage and storage conditions [7], requiring a model to be fitted to the accelerated testing data. Loading conditions (e.g., stress factors) that contribute to the calendar aging of lithium-ion batteries include ambient temperature and state of charge (SOC), whereas ambient temperature, SOC operation range, and charge/discharge current (C-rate) contribute to the cycle aging process [8; 9]. The accelerated life test plan should consider some or all these stress factors. Accelerated temperature testing has been extensively used owing to its simplicity of implementation and significant effect on degradation. The assumption is that elevated temperature can accelerate the failure mechanisms of lithium-ion batteries. For instance, [PERSON] et al. [10; 11] stored lithium-ion batteries at 25-65 \({}^{\circ}\)C, and [PERSON] et al. [12] cycled lithium-ion batteries at 40-70 \({}^{\circ}\)C. However, the failure mechanisms that were accelerated by temperature were not discussed by these papers. Lithium-ion battery degradation is mainly caused by solid electrolyte interface (SEI) layer growth, lithium plating, and particle cracks in the electrodes [13]. [PERSON] et al. [14] evaluated the effect of different temperatures on the electrode polarizations and found that low temperature (\(T<25\)\({}^{\circ}\)C) facilitates lithium plating, whereas SEI layer growth is accelerated at high temperature (\(T>25\)\({}^{\circ}\)C) The result suggested that the failure mechanisms changed at different temperature ranges. Designing an appropriate accelerated test plan thus requires comprehensive understanding of failure mechanisms at different stress levels. The Arrhenius model has been used numerously to simulate the effect of temperature on degradation and predict the reliability of lithium-ion batteries. [PERSON] et al. [10; 11] applied this model to predict the calendar life of lithium-ion batteries at various temperatures, regardless that the Arrhenius model did not fit well to all experimental data.