Internal Electrical Resistance Research Articles

The multi-variable stepwise algorithm for internal short circuit detection in a serial battery pack with inconsistent state of health

Internal short circuit of cells is one of the main causes of thermal runaway in electric vehicle battery systems. Therefore, one of the most effective ways to prevent thermal runaway is to detect and identify internal short-circuit lithium-ion batteries before thermal runaway using a battery management system. This paper investigates the detection and identification of internal short circuits in batteries by proposing a multi-variable stepwise analysis (MSA) method. The MSA method is proposed for detecting and identifying faulty batteries by combining horizontal and vertical comparison methods and aging cells' ohmic internal resistance variation characteristics. A less consistent pack containing aging cells was designed to perform internal short-circuit experiments. Based on setting the appropriate threshold and moving the window frame horizontally, comparing the deviation degree of the ohmic internal resistance of each cell in the battery pack and the average ohmic internal resistance of the normal battery, the aging battery in the battery pack can be effectively identified. State of health (SOH) is the percentage remaining of the battery's actual maximum capacity value. The deviation degree of ohmic internal resistance of aging batteries with SOH of 92% and 80% is maintained at more than 15% and 45%. For early internal shorts with an equivalent internal short-circuit resistance of 100 Ω, the internal short-circuit detection time is 3896 s. For the short circuit in the middle and later periods (<10Ω), the MSA algorithm can achieve rapid internal short-circuit detection within the 50 s window, reducing the risk of thermal runaway. The results verified that the method could effectively identify aging cells within the battery pack and detect internal short circuits for other cells, reducing false positives and effectively preventing thermal runaway.

Research on rapid extraction of internal resistance of lithium battery based on short-time transient response

Unlike laboratory measurements and online parameter observations based on long-term continuous operation data, offline fast measurement of battery parameters is widely used for convenient and accurate acquisition of battery parameters in battery production and maintenance processes. However, too short allowable measurement time in engineering results in a small amount of dynamic information that the algorithm can obtain and unclear initial state values, making it difficult to improve the accuracy of the algorithm. This paper employs a local coordinate system established in the vicinity of the measurement moment to extract the transient behavior of battery terminal voltage response under excitation current, and investigates the characterization capability of these transients on ohmic and polarization internal resistance of batteries at different time points. Moreover, based on an equivalent circuit model, it evaluates how initial values of transient voltage affect accuracy in calculating internal resistance. Through customized working condition verification, the selection principles for rapid identification of time points and the basic requirements for excitation conditions have been determined. Comparative verification of online parameter identification results based on continuous time series demonstrates that the fast identification algorithm can accurately identify Ohmic internal resistance and effectively characterize the variation law of battery polarization.

A novel state of health prediction method for battery system in real-world vehicles based on gated recurrent unit neural networks

State of health (SOH) is crucial to battery management system. However, SOH accuracy and reliability is difficult to be guaranteed owing to complex ageing mechanisms and driving conditions. This paper proposes a novel battery SOH prediction method based on gated recurrent unit (GRU) neural network for real-world vehicles. Firstly, real-vehicle operating data is extracted as well as cleaned and sliced to improve data reliability, then the Kalman filter and recursive least squares method are used to identify the ohmic internal resistance (OIR). The GRU neural network is established to realize the battery SOH prediction, and the average relative error of final validation set is less than 0.65 %. To further validate the reliability and applicability of the prediction method, four other vehicles data are set as input, and the SOH results indicate that all average relative errors are still within 4 %. This study demonstrates the feasibility of using OIR as a health factor for real-world vehicles, and also provides a new solution for accurately predicting battery SOH for real-world vehicles.

Soft Coiled Pneumatic Actuator with Integrated Length-Sensing Function for Feedback Control

SPIRA Coil actuators are formed from thin sheets of PET plastic laminated into a coil shape that unfurls like a “party horn” when inflated, while many soft actuators require large pressures to create only modest strains, SPIRA Coils can easily be designed and fabricated to extend over dramatic distances with relatively low working pressures. Internal metalized PET strips separate in the extended portion of the actuator, creating an electrical circuit with a resistance that corresponds to the actuator length. This paper presents and experimentally validates easy-to-use design models for the actuators’ self-retracting spring stiffness, its pneumatic extension force, and its internal length-sensing electrical resistance. Testing of the self-sensing capabilities demonstrates that the embedded sensor can be used to determine the actuator length with virtually no hysteresis. Feedback control with the resistance-based sensing resulted in length-control errors within 5% of the extended actuator length (i.e., 3 cm of 60 cm).

Narrow middle channel design in counter-flow microfluidic fuel cell with flow-through electrodes

Output performance of counter-flow microfluidic fuel cell is hampered by its significant internal ohmic resistance. In this work, narrow middle channel design is introduced to the counter-flow microfluidic fuel cell with flow-through electrodes to ease the internal ohmic resistance issue and realize increased fuel utilization and improved power density simultaneously. Systematically numerical investigations are performed to validate the feasibility and evaluate the prospect of the narrow middle channel design. Meanwhile, in-depth analyses are provided to explore the mechanisms behind the distinctive cell characteristics. Corresponding results demonstrate that the width of the middle channel in the counter-flow microfluidic fuel cell with flow-through electrodes can be safely reduced from the commonly used 1–2 mm–0.3 mm without reactant crossover and obvious increase in the energy consumption for the pumping of the reactant streams. Superiority of the narrow middle channel design is more significant in the high reactant concentration and high flow rate case where an increase of 30.29 % is observed in the peak power density when the middle channel width reduces from 1 mm to 0.3 mm under the reactant concentrations of 4 M and flow rate of 120 μLmin−1.

Error theory study on EKF-based SOC and effective error estimation strategy for Li-ion batteries

Accurate state-of-charge (SOC) estimation is crucial for ensuring the safe and reliable operation of battery management systems (BMS). Among the various algorithms used for SOC estimation in real-vehicle BMS, the extended Kalman filter (EKF) algorithm holds significance due to its adherence to optimal estimation principles and its property of insensitivity to initial values. By studying the relationship between error sources and SOC estimation errors, it becomes possible to develop targeted measures for enhancing the accuracy of SOC estimation based on the EKF. From a probabilistic perspective, this paper derives theoretical equations that establish the connection between SOC estimation errors and various error sources, including measured voltage, measured current, open circuit voltage curve, capacity, ohmic internal resistance, and polarization resistance. Furthermore, the paper analyzes the relationship among multiple error sources in generating SOC estimation errors. Building upon the outcomes of this theoretical analysis, a joint SOC estimation method that combines the EKF with Ampere-hour counting (AHC) is employed to identify errors. In scenarios where simultaneous faults occur in the current and voltage sensors, they are identified based on the slope and Euclidean distance of the two SOC trajectories, respectively. Subsequently, sensor faults correction and SOC compensation are implemented by leveraging simplified equations involving capacity and SOC increments and measured voltage and SOC estimation errors. In addition to addressing sensor faults, the paper also considers battery model parameter errors. By incorporating customized current pulse profile and theoretical equations relating to error sources and SOC estimation errors, a comprehensive error estimation of model parameters is achieved, capable of handling single and multiple errors. The derived simplification bridges the gap between error sources and SOC estimation errors, offering a novel approach for parameter sensitivity analysis and a theoretical foundation for quantifying these errors. The experimental results demonstrate the effectiveness and rapidity of the proposed method for identifying and correcting sensor faults and model parameter errors.

Sensitivity analysis of proton exchange membrane fuel cells based on fixed frequency impedance

Durability is a major constraint to the commercialization of proton exchange membrane fuel cells (PEMFC). An accurate evaluation of the internal state of the fuel cell is necessary to develop a reasonable control strategy. Impedance is one of the important parameters to characterize the internal state of the fuel cell. Making full use of the impedance parameter is of great importance to extend the fuel cell life. The internal sensitivity of the fuel cell is investigated when the reaction parameters are altered. The characteristic frequency is determined to be 2000Hz by the correspondence between the electrochemical impedance spectroscopy and the equivalent circuit model. This frequency is also where the ohmic internal resistance is located. At different current densities, the cooling water temperature and the air stoichiometric ratio are varied. By measuring the variation of the impedance, the change of state inside the stack can be known. The optimal external parameters of the stack reaction can be determined. This study has important implications for making full use of impedance as a characterization parameter and for more rational control of fuel cell systems. Fixed frequency impedance will play an auxiliary role in water and heat management.

High-performance tellurium-free thermoelectric module for moderate temperatures using α-MgAgSb/Mg2(Si,Sn)

α-MgAgSb is a promising thermoelectric material with an average figure of merit above unity between room temperature and 573 K, making it attractive for low temperature waste heat recovery or temperature regulation applications. We demonstrate here the first α-MgAgSb/Mg2(Si,Sn)-based thermoelectric module, where Mg2(Si,Sn) was chosen as n-type counterpart due to its excellent thermoelectric properties, low weight, abundant, and eco-friendly constituents. By using this new material combination, a maximum conversion efficiency of 6.4% and maximum power of 0.68 W were achieved for a temperature difference of 275 K, superior to commercially available (Bi,Te,Sb)-based thermoelectric modules. The Constant Property Model was used to check the validity of the measurement results and to identify room for further improvement. The characterization of the prototype shows a relatively good match between measurement and calculation for most of the thermoelectric module performance parameters; however, the measured internal electrical resistance is around 10% higher than the predicted values, indicating opportunities for further enhancement.

Environmentally-Friendly Electroplating Process Using Solid Electrolyte Membranes

The automobile is a very broad industry, and consists of tens of thousands of parts. Many parts of automobile employ surface treatment to provide several functions such as electronic and anti-corrosion properties. Among several surface treatment process, plating is an important elemental technology for automobile industry. For the industrial perspective, interest in SDGs significantly increases, and efforts to reduce environmental impact are highly urgent. Recently, we have developed novel electroplating process, solid electrodeposition (SED), which is based on ion transfer through solid electrolyte membrane1). This process has unique deposition characteristics that the metal film can be deposited only on the contact area between cathode and the membrane, in a fashion similar to stamping deposition. The SED process has an advantage for reducing amounts of waste effluent and CO2 gas. Moreover, this process has a potential of high deposition rate due to utilization of thin electrolyte membrane, providing lower electrical resistance between electrodes1), 2). Therefore, in the environmental and economical perspective, we believe that SED is promising process to metallize the substrate surface as an alternative to the conventional electroplating, especially in the field of electronics manufacturing. In this study, we report on SED system in details and characterization of deposited copper and nickel films. We also introduce copper fine patterning technique combined with SED using hard mask. Figure 1 shows schematic of the present SED system. The head part composed of anode plate, electrolyte solution and membrane are placed on substrate under controlled temperature and pressure. The membrane mainly plays a role of selective cation transfer from electrolyte solution to the substrate, although a small amounts of electrolyte solution can also be transferred due to pressure difference between internal head part and atmosphere. This solution uniformly spread to the interface between membrane and substrate so that uniform metal deposition is continuously proceeded without adhering the membrane with the substrate. Additionally, the SED system allows one to shorten the distance between electrodes because membrane can act as a diaphragm. Therefore, the power consumption is smaller than that of conventional electroplating, owing to decrease in an internal electrical resistance, providing the decrease of exhaust CO2 gas. The deposited film has relatively uniform thickness as shown in Figure 2, the result of which is due to the short distance between electrodes as well as uniform current feeding to deposit metal films through the back side of the cathode. The deposited copper and nickel films are crystalline and highly conductive, the quality of which are being enough for application of the SED process in the current electronics device manufacturing. By combining the SED process with the conventional screen printing technique, copper circuit patterns with line width of below 50 μm could also be successfully fabricated.1) Akamatsu, S. Nakano, K. Kimura, Y Takashima, T. Tsuruoka, H. Nawafune, Y. Sato, J. Murai, H. Yanagimoto, ACS Appl. Mater. Interfaces, 13, 13896-13906 (2021)2) Narui, Y. Hoshi, I. Shitanda, M. Itagaki, H. Yanagimoto, M. Hiraoka and H. Iisaka, E01-920, 232nd ECS Meeting. Figure 1

Modelling and Experimental Validation of the Flow and Mixing Processes in a Microfluidic Membraneless X-Cell with Flowing Vanadium Electrolytes

Microfluidic devices are characterized by submillimeter channel cross-sections and tiny flow rates, typically below 100 µL/min. This results in rather small Reynolds numbers that maintain the flow laminar and steady, preventing chaotic mixing from turbulence [1-4]. This orderly flow can be used to remove the ionomeric membrane in redox flow batteries, generating membraneless microfluidic cells with low internal electric resistance. These devices could be manufactured at a lower cost than their macro counterparts. However, without a membrane, the mixing region where the electrolytes come into contact must be accurately controlled to avoid unwanted interface deflections leading to increased cross-contamination of liquid and species.In this work, we compare experimental and CFD realizations of the flow in a membraneless microfluidic flow channel [5], including in the simulations the effect of viscosity variations across the positive and negative vanadium electrolytes. The apparatus includes a microfluidic control system that uses piezoelectric pumps and valves for flow regulation, an X-cell as flow channel, and small tanks with discharged positive (VIV) and negative (VIII) electrolytes. We use a UV/Visible spectrometer to measure the amount of mixing at the outlet of the cell [6]. This allows us to validate the CFD model against the experimentally measured cross-contamination and liquid transfer. To our knowledge, these results are unique in using spectrometry data to quantify the mixing ratio of VIII/VIV, and provide valuable data to validate CFD models that could later be used to engineer the flow in membraneless microfluidic vanadium redox flow batteries. Acknowledgments This work has been partially funded by FEDER/Ministerio de Ciencia, Innovación y Universidades – Agencia Estatal de Investigación Projects PID2019-106740RB-I00 and RTC-2017-5955-3/AEI/10.13039/501100011033, and by Grant IND2019/AMB-17273 of the Comunidad de Madrid.

Study on aging and external short circuit mechanisms of Li-ion cells with different electrode thicknesses

Thermal runaway is one of the challenges associated with the widespread use of Li-ion batteries. The thermal runaway characteristics of Li-ion batteries are closely associated with the electrode materials, electrode structure design and degree of cycling deterioration. The energy density of Li-ion cells can be efficiently increased by expanding the electrode thickness, but cycle and thermal performance will be deteriorated with the increase of electrode thickness. The cycle performance and aging mechanisms of cells with different electrode thicknesses during cycling has been investigated in present research. Afterwards, the external short-circuit was conducted on aged cells to explore the effect of electrode thickness on cell thermal runaway behavior. The results showed that the ohmic internal resistance and polarization internal resistance of the thick-electrode cell increased continuously with cycling, and the capacity faded significantly. The increase in Li+ migration distance in a thick electrode will make the state of charge (SOC) distribution uneven along the thick direction. The thick electrode cell had the largest absolute temperature rise and temperature rise rate when it was short-circuited, which were 104.07 °C and 1.89 °C/s, respectively. The temperature of the area near the negative electrode of the cell was higher than that of the center and the positive electrode. The micro structure of electrode by SEM revealed that cycling can cause thick electrode material to crack, resulting in capacity loss. When thermal runaway developed, thick electrodes had the highest absolute temperature rise and temperature rise rate. As the current density increased, the thermal runaway would aggravate the damage to the positive electrode material, and the separator would close and shrink, thereby cutting off the reaction between the positive and negative electrodes.

Online modeling of the LiFePO4 power battery based on the data supervisory mechanism

The establishment of the accurate lithium-ion power battery model is an important basis to realize the reliable state estimation of the lithium-ion power battery, and also a necessary work to develop the battery management system. However, the existing modeling algorithms lack the data supervision mechanism for the online modeling, and cannot guarantee the stability and clear physical meaning of the model parameters used in the Battery Management System (BMS), which may lead to the breakdown of the BMS state estimation algorithm and major security risks. Therefore, the data supervisory mechanism is designed to solve the problem and a lithium-ion power battery online modeling method based on it is proposed in this paper. Experimental results on the LiFePO4 power battery demonstrate the effective of the proposed online modeling method and lay a foundation for the subsequent state estimation of the LiFePO4 power battery. As the ambient temperature increases from 10 °C to 40 °C, the average value and the standard deviation of the LiFePO4 power battery ohmic internal resistance decrease 25.88 % and 83.33 % respectively. Meanwhile, the Mean Absolutely Error (MAE), the Root Mean Square Error (RMSE) and the Maximum Absolute Error (Max-AE) of the terminal voltage decrease 31.91 %, 30.43 % and 58.06 % respectively.

Combined State of Charge and State of Energy Estimation for Echelon-Use Lithium-Ion Battery Based on Adaptive Extended Kalman Filter

To ensure the safety and reliability of an echelon-use lithium-ion battery (EULIB), the performance of a EULIB is accurately reflected. This paper presents a method of estimating the combined state of energy (SOE) and state of charge (SOC). First, aiming to improve the accuracy of the SOE and SOC estimation, a third-order resistor-capacitance equivalent model (TRCEM) of a EULIB is established. Second, long short-term memory (LSTM) is introduced to optimize the Ohmic internal resistance (OIR), actual energy (AE), and actual capacity (AC) parameters in real time to improve the accuracy of the model. Third, in the process of the SOE and SOC estimation, the observation noise equation and process noise equation are updated iteratively to make adaptive corrections and enhance the adaptive ability. Finally, an SOE and SOC estimation method based on LSTM optimization and an adaptive extended Kalman filter (AEKF) is established. In simulation experiments, when the capacity decays to 90%, 60% and 30% of the rated capacity, regardless of whether the initial value is consistent with the actual value, the values of the SOE and SOC estimation can track the actual value with strong adaptive ability, and the estimated error is less than 1.19%, indicating that the algorithm has a high level of accuracy. The method presented in this paper provides a new perspective for estimating the SOE and SOC of a EULIB.

Machine learning-based state of health prediction for battery systems in real-world electric vehicles

Carbon dioxide emission reduction is a significant benefit of electric vehicles. State of health prediction is essential to ensure the safety and reliability of the battery system, which is a key part of electric vehicles. This paper proposes a novel state of health prediction strategy based on ohmic internal resistance and long short-term memory networks. Driving conditions are extracted based on the current and speed of real-world vehicles. Combining the equivalent circuit model and Kalman filter, the parameter identification of the power battery system is performed. Ohmic internal resistance is selected as the health state characterization parameter. According to the ohmic internal resistance results obtained from the identification, Pearson correlation analysis is used to obtain the parameters with the highest correlation to the ohmic internal resistance. These parameters are used as input samples for the long short-term memory network to get the evaluation value of health status. The model is trained and tested using data from different operating conditions and vehicles. The root mean square errors of the model outputs are below 0.02 Ω, demonstrating the method's effectiveness. The proposed method is expected to have considerable application in advanced battery management systems.

Synthesis and Fabrication of Graphite/WO3 Nanocomposite-Based Screen-Printed Flexible Humidity Sensor

The resistive type of graphite/WO3 nanocomposite-based humidity sensor is fabricated through screen printing on a flexible polyethylene terephthalate substrate. Three different nanocomposite-based humidity sensors have been fabricated and analyzed for their humidity-sensing characteristics. The structure elucidation of the nanocomposite was carried out using x-ray diffraction, Fourier-transform infrared spectroscopy, and scanning electron microscopy. By exposing the printed humidity sensor to relative humidity ranging from 11% to 97% at room temperature, its capabilities were studied. The relative resistance, sensitivity, dynamic response, and hysteresis were determined for all three devices, and they showed maximum responses towards relative humidity changes with the highest sensitivity of ≈ 60.8% and excellent hysteresis curves (maximum change of ≈ 1%). The screen-printed flexible humidity sensor exhibited less than a 5% change in the internal electrical resistance when subjected to various bending angles.

State of energy estimation of the echelon-use lithium-ion battery based on Takagi–Sugeno fuzzy optimization

Owing to the degradation of an echelon-use lithium-ion battery (EULIB), the Ohmic internal resistance (OIR) and actual capacity (AE) have both changed greatly, and the state of energy (SOE) can more accurately represent the state of a EULIB than the state of charge (SOC) because of the working voltage. To improve the accuracy and adaptability of SOE estimation, in the paper, we study the energy state estimation of a EULIB. First, the four-order resistor–capacitance equivalent model of a EULIB is established, and an unscented transformation is introduced to further improve the estimation accuracy of the SOE. Second, a EULIB’s SOE is estimated based on adaptive unscented Kalman filter (AUKF), and the OIR and AE of a EULIB are estimated based on the AUKF. Third, a Takagi–Sugeno fuzzy model is introduced to optimize the OIR and AE of the EULIB, and the SOE estimation method is established based on an adaptive dual unscented Kalman filter (ADUKF). Through simulation experiments, verification, and comparison, energy decayed to 80%, 60%, and 40% of the rated energy, respectively, even with a large initial error; with the initial value of the SOE starting at 100%, 60%, or 20%, the estimated SOE can track the actual value. It can be seen that the method has a strong adaptive ability, and the estimation accuracy error is less than 1.0%, indicating that the algorithm has high accuracy. The method presented in this paper provides a new perspective for SOE estimation of EULIBs.

Impact of Individual Cell Parameter Difference on the Performance of Series-Parallel Battery Packs.

Lithium-ion power batteries are used in groups of series-parallel configurations. There are Ohmic resistance discrepancies, capacity disparities, and polarization differences between individual cells during discharge, preventing a single cell from reaching the lower limit of the terminal voltage simultaneously, resulting in low capacity and energy utilization. The effect of the parameter difference (difference in parameters) of individual cells on the performance of the series-parallel battery pack is simulated and analyzed by grouping cells with different parameters. The findings reveal that when cells are connected in series, the capacity difference is a significant factor impacting the battery pack's energy index, and the capacity difference and Ohmic resistance difference are significant variables affecting the battery pack's power index. When cells are connected in parallel, the difference in Ohmic internal resistance between them causes branch current imbalance, low energy utilization in some individual cells, and a sharp expansion of unbalanced current at the end of discharge, which is prone to overdischarge and shortens battery life. Interestingly, we found that when there is an aging cell in a series-parallel battery pack, the terminal voltage of the single battery module containing the aging single cell will decrease sharply at the end of discharge. Evaluating the change rate of battery module terminal voltage at the end of discharge can be used as a method to evaluate the aging degree of the battery module. The research results provide a reference for connecting batteries to battery packs, particularly the screening of retired power battery packs and the way to reconnect into battery packs.

A novel Co-estimation framework of state-of-charge, state-of-power and capacity for lithium-ion batteries using multi-parameters fusion method

A battery management system can intelligently manage and maintain battery systems by effectively estimating and predicting battery internal states. Owing to battery nonlinear characteristics related to various influence factors, the estimation of battery internal states should consider the available capacity and ohmic internal resistance. This paper proposes a co-estimation framework for state of charge (SOC), state of power (SOP) and battery available capacity. Firstly, the first-order equivalent model method is used to identify the battery parameters by recursive least squares algorithm with variable forgetting factor, and the SOC-OCV curve of the battery is obtained by combining the ampere-time integration method. Secondly, three Kalman filters are utilized to estimate battery SOCs and the maximum available capacity and internal resistance are estimated by a forgetting factor recursive least square algorithm. Then peak current and power are estimated under the composite constraints of the estimated capacity and internal resistance. Finally, the experimental data are collected at temperatures 25 °C and 40 °C to verify and analyze the proposed method. The results of battery state estimation indicate that the proposed framework can accurate estimation battery internal states and also provide an effective reference for the driving of powered vehicles.

Accurate Computation ERT Measurements With External Electrical Resistance

Electrical resistance tomography (ERT) is an advanced measurement technique due to low cost, rapid response, no radiation, and nonintrusiveness, but there is a natural relation between internal electrical resistance (IER) distribution and external electrical resistance (EER) relative to a detected field. The IER distribution can reconstruct all the detected objects within the field, while EER can greatly affect the measuring accuracy. So far, there is no effective method to compute the effect of EER. In this article, a general method is proposed to analytically compute all measurements in the existence of EER. Inversely, according to the interrelation between IER and EER, IER can be solved based on all available measurements. To validate the proposed method, an important parameter of solid-phase fraction (SPF) based on IER was computed in dredging engineering. Results show that the new method can compute the value of SPF more accurately than the existing method and thus can provide more accurate and practical measurements in the presence of EER.

Research on electrochemical characteristics and heat generating properties of power battery based on multi-time scales

A comprehensive understanding of the mechanisms of battery is essential for the design of thermal management systems. In this work, a second-order equivalent circuit model considering the hysteresis effect of the battery was developed, and a combined EIS and HPPC characterization method was used for parameter identification. The results showed that the combining EIS and HPPC parameter measurement methods could extract and analyze the parameters of the battery with different time scales and improve the accuracy of the model. It was found that the polarization internal resistance (R1 and R2) of the battery shows a stronger temperature dependence than the ohmic internal resistance at low temperatures, with R1 being about 170 times higher at low temperatures (10 °C) than high temperatures (50 °C). At the same temperature, τ2 was approximately 100 times larger than τ1, which was two orders of magnitude difference between τ1 and τ2. In addition, the dynamic heat generation results showed that the heat generation rate of the battery increases with decreasing temperature. At 3C discharge rate, the heat generation rate of the battery at low temperature (−10 °C) was about 1.5 times higher than at room temperature (25 °C).