Despite various advantages lithium-ion battery LIB offers as a favorable candidate for electric vehicles, they however face certain challenges due to dramatic increase of impedance at low temperature and lithium deposition which overall affects battery performance. Internal or external heating of lithium-ion batteries before charging or discharging is usually done in cold weather until it reaches the effective operating temperature.
Internal heating however is preferred due to uniform temperature distribution coupled with higher efficiency when compared to external heating strategy. In order to ensure high efficiency and less damage to battery lifetime when using internal heating strategy, it is essential to build a high-fidelity electro-thermal coupled model for voltage estimation and prediction of temperature evolution of lithium-ion battery.
In a recent article of Jiang et al. (2016) which was published in journal, Applied Energy, a low-temperature electro-thermal coupled model was investigated based on electrochemical mechanism which was developed to accurately capture both electrical and thermal behaviors of batteries.
Several modelling strategies such as black box, electrochemical model and equivalent electrical circuit (RQ, Warburg and RC elements) model in predicting voltage performance of LIBs have been studied but equivalent electrical circuit has more advantage over others in terms of good compromise between computation time, parameterization effort and simulation accuracy.
However, at low temperature, a general equivalent electrical circuit has lower accuracy. Further, sluggish charge-transfer kinetics, decreased solid-state lithium-ion diffusivity, reduced electrolyte conductivity and strong existence of mutual coupling between various influencing factors are founded in the battery at low temperature, resulting in highly non-linear characteristic of model parameters. Hence, most models developed to describe low-temperature performance of LIBs are complicated and highly sensitive to temperature.
The authors proposed a low-temperature electro-thermal coupled model, reduced electro-thermal coupled model based on frequency-dependent FD equation where it was experimentally validated under different temperature, current frequency and current amplitude conditions with simulation results implemented to show good agreement with the experimental data.
In their experiments, three different kinds of batteries consisting of graphite anode and cathode materials; LiNi1/3Co1/3Mn1/3O2 (NCM), LiFePO4 (LFP) battery and LiCoC2 (LCO) battery were used. Electrochemical impedance spectroscopy were conducted using electrochemical workstation over a temperature range of -15°C to 6°C with intervals of 3°C at 50% state of charge SOC. Verification experiments for voltage performance were done using sinusoidal alternating current with various sets of frequencies, temperature and amplitude, and using dynamic varying current profile such as urban dynamometer driving schedule UDDS for NCM batteries while verification experiments for thermal behavior was carried out under sinusoidal alternating current conditions including constant frequency constant current CFCC and constant frequency variable current CFVC.
For electro-thermal coupled model, various resistance and capacitance RC elements was used to describe the kinetic process of charge transfer on cathode and anode surface, lithium-ion diffusivity in solid state and representation of lithium ion migration through passive film, and resistance and inductance elements indicates response at high frequency.
When checking the effectiveness of model reduction, influence of frequency on polarization voltage showed that different electrochemical process can be controlled by varying the sinusoidal alternating current frequency while irreversible heat within the battery can be controlled by varying the frequency. It was discovered that resistance increases and capacitance decreases with decrease in environmental temperature when observing frequency dependence of resistance and capacitance.
Results shown when considering verification at different frequencies and comparing mean value of absolute error between measured and simulated voltage showed two models, electro-thermal coupled and reduced electro-thermal coupled having similar distribution of voltage deviations. However, simulation errors of the electro-thermal coupled model are smaller than the reduced electro-thermal coupled model. But mean errors of 13.8mV and 15.6mV respectively and maximum relative errors of less than 1.76% and 1.77% of electro-thermal and reduced electro-thermal coupled model were observed indicating that present model can accurately emulate voltage behavior of lithium-ion batteries despite slight difference at various frequency.
Comparison between experimental data and simulation results at four different temperatures with battery subjected to sinusoidal alternating current excitation of 10A and 500Hz for 1361s showed that mean errors and maximum relative errors of presented model gradually increase with decrease in temperature indicating nonlinearity at lower temperature. Mean errors of electro-thermal and reduced electro-thermal coupled models are less than 16.15mV and 26.7mV respectively and maximum relative error less than 1.88% and 2.12% at four different temperatures.
Battery subjected to different sinusoidal alternating current excitation with CFCC consisting of 50 Hz-5A and 50 kHz-10A showed temperature errors less than 1.5°C and 1.58°C respectively which confirms accurate thermal behavior of LIBs predicted by models under various conditions.
Simulation results and measurements with maximum sinusoidal alternating current amplitude showed good agreement observed for a variety of current rates at -15°C where mean errors and maximum relative errors were less than 1.62mV and 18.4mV, 1.76% and 1.85% for electro-thermal and reduced electro-thermal coupled respectively.
With battery subjected to sinusoidal alternating current excitation of 500Hz and 5 kHz, electro-thermal and reduced electro-thermal coupled models gave maximum error of 1.32°C and 1.79°C at CFVC conditions. Temperature trend are nicely consistent with measured ones indicating that the proposed models exhibit high accuracy in evaluating battery temperature under various conditions.
Comparing with the equivalent electrical circuit model, Thevenin model and exponential function, the reduced equivalent electrical circuit model, based on the FD equation, cannot only accurately describe electrochemical characteristic within the battery, but also precisely predict the impedance in wide frequency ranges with a lower computational effort. Furthermore, the effectiveness and adaptability of the proposed methodology for model reduction is verified based on the highly consistent results between simulation and experiments using batteries with three different cathode materials from different manufacturers. It is also concluded that there is superior adaptability of the new FD equation.
The model verification when considering UDDS profile gave mean voltage error and maximum relative voltage error at 24.25mV and 2.65% respectively indicating good agreement between simulation results and experimental data.
This study proposed reduced electro-thermal coupled model with maximum relative voltage error and temperature error of 2.65% and 1.79°C respectively fulfils requirement of engineering applications. It also offers lower computational effort, lower complexity under various conditions and its characterization of state of health for LIBs which can be used in application of on-board battery management system.
