This article presents an electro-thermal model of a prismatic lithium-ion cell, integrating physics-based models for capacity and resistance estimation. A 100 Ah prismatic cell with LFP-based chemistry was selected for analysis. A comprehensive experimental campaign was conducted to determine electrical parameters and assess their dependencies on temperature and C-rate. Capacity tests were conducted to characterize the cell’s capacity, while an OCV test was used to evaluate its open circuit voltage. Additionally, Hybrid Pulse Power Characterization tests were performed to determine the cell’s internal resistive-capacitive parameters. To describe the temperature dependence of the cell’s capacity, a physics-based Galushkin model is proposed. An Arrhenius model is used to represent the temperature dependence of resistances. The integration of physics-based models significantly reduces the required test matrix for model calibration, as temperature-dependent behavior is effectively predicted. The electrical response is represented using a first-order equivalent circuit model, while thermal behavior is described through a nodal network thermal model. Model validation was conducted under real driving emissions cycles at various temperatures, achieving a root mean square error below 1% in all cases. Furthermore, a comparative study of different cell cooling strategies is presented to identify the most effective approach for temperature control during ultra-fast charging. The results show that side cooling achieves a 36% lower temperature at the end of the charging process compared to base cooling.

Lithium-ion batteries are highly affected by calendar ageing effects, which can lead to capacity loss even when the battery is not used at all. The current literature proposes plenty of semi-empirical models to predict the calendar ageing of the lithium-ion batteries, which are mostly based on Arrhenius functions for temperature dependency, exponential models for state of charge dependency and power laws for time dependency. Those models are easy to calibrate, and they provide a sufficiently precise prediction of capacity loss over time. However, it might be difficult to find a physical meaning to the parameters determined in these models, due to their lumped nature and the optimization process used. Therefore, in this work a semi-empirical model able to predict the capacity degradation over time with physically meaningful parameters is proposed. The dependency on temperature is considered by a pre-exponential factor whereas the dependency on state of charge is considered by a power law coefficient. A two-step constrained optimization process is considered to calibrate the model parameters. The model allows to predict the capacity loss over a wide range of different temperature and state of charge conditions, and it is calibrated for 4 different cell chemistries: LMO-NMC, LFP, NCA, and NMC. It was found that the worst storing condition is given by the highest temperature and state of charge conditions. The capacity degradation is provided over a period of 50 years. Two end-of-life conditions were analyzed: a loss of capacity of 20 % as representative of an end-of-life condition for automotive applications, and a loss of capacity of 50 % as an end-of-life condition for deep-space applications. In both cases, it was observed that NMC provided the best performance (the slowest ageing over time) for storing temperatures below 15 degrees C and storing state of charge below 10 %, whereas for temperatures higher than 15 degrees C and state of charge higher than 10 %, the LFP chemistry resulted to be the most longevous.

Adequate cell temperature estimation in lithium-ion batteries becomes crucial for state of charge (SOC) observation and safety purposes. The diagnosis of individual cell temperature in multicell battery packs depends on the number of temperature sensors available and the thermal dynamics of the system. This paper explores the potential of single value decomposition (SVD) of thermal distribution on battery packs in order to retain the critical information and minimize the number of states, but also the number of sensors required. The algorithm proposes a thermal lumped model to identify the thermal dynamics of the pack under different control actions and atmospheric conditions, and uses a Kalman filter to update the model states with temperature readings. Experimental tests were carried out to in a prototype with 20 cylindrical 21700 Li-Ion cell, equipped with several thermocouples and recording thermal images every 5 s. Results show that combining SVD with dynamic models and observers, the temperature distribution of the pack can be predicted with negligible errors.

In this study, a methodology for the energy analysis of a lithium-ion battery module cooled by a serpentine cooling plate is proposed. A novel lumped electro-thermal model of a cooled module is calibrated and validated: thermal nodes are assigned to the Li-ion cells, the cooling plate, the thermal pad, and the coolant. The model is experimentally characterized and validated, and a maximum root mean square error equal to 1.44 % for the electrical model is obtained; all the errors of the thermal models are kept below the 2 %. The proposed approach allows to identify, with a low computational cost and reduced calculation time, the thermal evolution of the nodes depending on the environmental and operating conditions considered. This aspect is of fundamental importance to identify hot spots in the module and to prevent possible dangerous events such as thermal runaway. To highlight these advantages, an extended fast-charging parametric study of the module is carried out, considering 240 simulations, varying 4 parameters (ambient temperature, required electric power, temperature and coolant volumetric flow) and monitoring 3 variables (peak temperature in the module at the end of the charging process, thermal gradient, and time spent in the optimal temperature range), allowing to identify the combinations of operating parameters that permit the rapid charging of the module under optimal conditions. Furthermore, the energy analysis provides an estimation of the charging efficiency of the cells, which is around 90 % for every considered thermal boundary. The heat generated by the cells, the heat dissipated into the coolant and the heat absorbed by the other module components are estimated. In a 4C charge 80 % of total heat is dissipated into the coolant, while this quantity increases to 95 % in a 1C charge. The reduced computational time and cost make this model suitable both for cooling system design and for control strategies development.

This work proposes a novel approach for state of health estimation of lithium-ion cells by developing a capacity fade model with temperature and Ah throughput dependencies. Two accelerated life cycle testing datasets are used for model calibration: a multi discharge rate dataset of an NMC/graphite cylindrical cell and a multi temperature dataset for an LCO/graphite pouch cell. The multi discharge rate dataset has been recorded at 23 °C and for 4 discharge-rates (C/4, C/2, 1C and 3C). The multi-temperature dataset considers the accelerated ageing of the cells at 4 temperatures (10, 25, 45 and 60 °C). An Arrhenius model is chosen for describing the temperature dependency while a power law model is chosen for cycle (Ah throughput) dependency. The model shows a good agreement with experimental data in each analyzed condition, allowing a precise description of the capacity degradation over time. From the single-temperature analysis, it is found that the activation energy decreases with respect to the C-rate: this is due to the fact that at higher C-rates, the irreversible chemical phenomena accelerate, leading to an overall faster ageing of the cell. From the multi-temperature analysis, the power law coefficient shows a quadratic dependency relative to temperature: a minimum for the power law coefficient is found corresponding to 25 °C, due to the fact that both for lower and higher temperatures, the ageing mechanisms are accelerated. Finally, an analysis of the impact of fast charging on cell ageing, in different charging scenarios is provided: the fast degradation of the cells at very low temperatures highlights the importance of an appropriate cooling of the battery during charging operations. This empirical methodology can be easily integrated in battery management system algorithms due to the easiness of the calibration and the low calculation time.

This article proposes a novel methodology for the definition of an optimized immersion cooling fluid for lithium-ion battery applications aimed to minimize maximum temperature and temperature gradient during most critical battery operations. The battery electric behavior is predicted by a first order equivalent circuit model, whose parameters are experimentally determined. Thermal behavior is described by a nodal network, assigning to each node thermal characteristics. Hence, the electro-thermal model of a battery is coupled with a thermal management model of an immersion cooling circuit developed in MATLAB/Simulink. A first characterization of the physical properties of an optimal dielectric liquid is obtained by means of a design of experiment. The optimal values of density, thermal conductivity, kinematic viscosity, and specific heat are defined to minimize the maximum temperature and temperature gradient during a complete discharge of the battery at 2.5C. Through a statistical analysis, it is also possible to recognize which effects among those previously mentioned are statistically relevant for this analysis. With the optimized fluid, a second design of experiment is carried out to define an optimized design of the module (in terms of distance between cells, and staggered angle), in relation to the operating conditions (volumetric flow and discharge rate). Once the optimal design has been identified, a final comparative study is carried out between different fluids used in immersion cooling systems, whose characteristics have been found in the literature, to find which of the fluids analyzed comply with the maximum temperature and maximum gradient conditions set for this study.

Most of the equivalent circuit battery models available in the literature have been developed specifically for one cell and require extensive measurements to calibrate cell electrical parameters in different operating conditions. In this work, a generalized equivalent circuit model for lithium-iron phosphate batteries is proposed, which only relies on the nominal capacity, available in the cell datasheet. Using data from cells previously characterized, a generalized zeroth-order model is developed. This novel approach allows to avoid time-consuming and expensive experiments and reduces the test matrix. In spite of not relying on detailed data on the dependence of the electrical parameters with respect to state of charge, c-rate and temperature, the model provides an excellent description of the electrical behavior for both low-energy and high-energy cells, the error being always kept below 2 %. The internal resistance of the cell is expressed as a function of a new characteristic coefficient, which is typical of this lithium-ion battery chemistry. This coefficient is fitted to an exponential function of the temperature, which is physically meaningful, as the internal resistance has an Arrhenius-like behavior with respect to temperature. This model, due to its simplicity and flexibility, is particularly useful for control-oriented applications, and for off-line analyses.

In this study an analysis of the employment of nanoparticles and nano encapsulated phase change materials for battery cooling is provided. By using a previously validated electro-thermal model of a lithium-ion battery module, the effect of 5 different nanoparticles and 6 different nano encapsulated phase change materials is estimated. The analysis is provided for a battery module charge process at 4C, with a coolant mass flow of 2 l/ min and with ambient and fluid temperature equal to 20 degrees C. The concentration of the nanofluid is varied between 0.01 % and 5 %. By increasing the concentration, a beneficial effect is observed on the battery cooling, in terms of maximum temperature achieved during the charge process and heat dissipated into the coolant. Among the 30 different combinations of nanoparticles and nano encapsulated phase change materials analyzed in this work, it is concluded that the best results in terms of dissipated heat and maximum temperature are obtained for copper oxide (CuO) combined with octadecane. In this case, at 20 degrees C, a reduction of the maximum temperature of about 2 degrees C is obtained with a volume fraction equal to 5 %, with respect to the case in which there are no nanoparticles. Furthermore, the total heat dissipated in the coolant is increased by 28 %. Finally, the study proposes a design of experiment to evaluate the performance of a phase change material for battery cooling. For this analysis, 4 variables are considered (concentration, melting temperature, heat of fusion and characteristic temperature range) and the effect on the maximum temperature and on the temperature spatial difference is observed: it is found that the thermal evolution of the cells is mostly affected by melting temperature and concentration.

This paper deals with the experimental characterization and electro-thermal modelling of lithium-ion batteries. This aspect is of considerable importance to be able to understand the phenomena of heat generation and thermal behavior of a lithium-ion battery. Electrical parameters need to be characterized to properly estimate the elec-trical losses inside the battery and, thus, the total heat generation. The testing methodology is based on capacity test, open circuit voltage tests, and hybrid power pulse characterization tests. It highlights the dependency of each parameter on state of charge, current and temperature. A first order equivalent circuit model is used to simulate the electric behavior of the cell. Extrapolation physical models are used to accurately estimate capacity (Peukert model) and resistive parameters (Arrhenius model) for points outside the considered test matrix. The thermal behavior of the cell is modeled using a nodal network, assigning volume, heat capacity and heat gen-eration to the nodes. The main output of the research is the development of a completely generalized method-ology that can be adapted to any other chemistry, format, or capacity; furthermore, this methodology can be applied also in case of limited test matrix points, due to the implementation of extrapolation physical models for electrical parameters. The model is validated with a scaled real driving emission cycle. Finally, a case study for the fast charging of a battery module is presented, to highlight the great potential of the model, not only for on-line estimation, but also for off-line studies, being the charging operation one of the most critical from the thermal management point of view. From this analysis, it is found that a stand-alone cell can be charged for a longer time at 6C - a 5.42% more time-, with respect to the hottest cell in the considered battery module configuration.