Estimation method of low-temperature thermoelectric performance of lithium-ion batteries based on fractional-order thermoelectric model

Abstract

The present invention discloses a method for estimating the low-temperature thermoelectric performance of a lithium-ion battery based on a fractional-order thermoelectric model. First, a fractional-order thermal diffusion model (FOTDM) of a lithium-ion battery under low-temperature conditions is established based on non-standard thermal diffusion theory. Second, an equivalent circuit model of the lithium-ion battery is constructed. Then, a fractional-order thermoelectric coupling model is established based on the fractional-order thermal diffusion model (FOTDM) and the equivalent circuit model. Finally, a least-squares optimization algorithm is used to identify the fractional-order derivative order (FDO) and electrical performance parameters of the fractional-order thermoelectric coupling model (FOTEM) at different SOCs of the battery. After analyzing the proposed fractional-order thermoelectric coupling model (FOTEM) using operating conditions under a low-temperature environment, it is found that the fractional-order thermoelectric coupling model (FOTEM) has high accuracy under static operating conditions, dynamic operating conditions, and liquid heating conditions. The simulation accuracy of temperature and voltage in the fractional-order thermoelectric coupling model (FOTEM) is better than that of traditional thermoelectric coupling models.

Description

Technical Field

[0001] The present invention relates to a battery management system, and in particular to a method for estimating the low-temperature thermoelectric performance of a lithium-ion battery based on a fractional-order thermoelectric model. Background Art

[0002] Lithium-ion batteries (LIBs) are increasingly popular energy storage devices in electric vehicles, offering advantages such as high operating voltage, high output power, and long charge-discharge cycles. However, performance degradation of LIBs at low temperatures can reduce their available capacity, fast-charging speed, and energy efficiency. The cycle life, peak power, and available capacity of LIBs are closely related to battery temperature. Detailed research on the thermoelectric properties of LIBs at low temperatures is essential for developing a rational battery heating method and thermal management system (TMS).

[0003] In order for TMS to accurately and effectively simulate the temperature characteristics of lithium-ion batteries (LIBs) in low-temperature environments, it is crucial to establish an accurate thermal model. The commonly used thermoelectric coupling model has a simple structure and is easy to implement in engineering. The model parameters evaluated experimentally are usually used to analyze the effectiveness of temperature estimation in the parameter integration method. When the established electrical and thermal models are imperfect, the thermoelectric coupling model will affect the simulation and analysis of the battery temperature due to the lack of accurate characterization of the battery dynamics. The electrochemical thermal model characterizes the kinetic behavior of the battery by combining internal chemical reactions with thermal behavior. High-precision electrochemical thermal models usually require a large amount of calculation in the control system. Black box models are also often used to estimate the state parameters of lithium-ion batteries (LIBs), and their estimation effect is closely related to the number of calculation samples.

[0004] The thermodynamics of lithium-ion batteries (LIBs) are highly nonlinear and time-varying. In order to facilitate the establishment of thermal models, the thermal diffusion behavior inside the battery is usually simplified. Electrodes exhibit porosity and self-similarity at the microscale, a phenomenon that is usually ignored when establishing battery thermal models. Three heat transfer modes tend to coexist in porous electrodes. The heat transfer rate of the battery does not fully conform to a single characteristic. During the loading of the working current, the composite heat transfer mode will cause a hysteresis effect in heat propagation. The heat transfer of porous electrodes is not a standard thermal diffusion behavior. In low-temperature environments, the thermal hysteresis process of the electrode is more prominent. The temperature distribution of lithium-ion battery (LIB) modules is more uneven. Traditional thermal diffusion models are more difficult to characterize the non-standard thermal diffusion of electrodes at low temperatures. The inaccurate characterization of the temperature characteristics of lithium-ion batteries (LIBs) will affect the analysis of electrical characteristics. Over time, this phenomenon will cause the simulated thermoelectric behavior of the battery to deviate from its true value. In response to the above problems, this application proposes a solution. Summary of the Invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a fractional-order thermoelectric model that can more accurately and stably simulate the thermoelectric performance of lithium-ion batteries in low-temperature environments.

[0006] Technical solution: The method for estimating the low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model described in the present invention specifically includes the following steps:

[0007] S1: Based on the non-standard thermal diffusion theory, a fractional-order thermal diffusion model (FOTDM) for lithium-ion batteries under low temperature conditions is established;

[0008] S2: Construct an equivalent circuit model of a lithium-ion battery;

[0009] S3: Establish a fractional-order thermoelectric coupling model FOTEM based on the fractional-order thermal diffusion model FOTDM and the equivalent circuit model;

[0010] S4: Identify the fractional derivative order FDO and electrical performance parameters of the fractional-order thermoelectric coupling model FOTEM at different battery SOCs based on the least squares optimization algorithm.

[0011] As a preference, the fractional-order heat diffusion equation based on nonstandard heat diffusion theory in S1 is:

[0012]

[0013] Where t is the charge and discharge time of the battery; T is the temperature of the lithium-ion battery; x, y, and z are the distances of the lithium-ion battery in the x-axis, y-axis, and z-axis directions, respectively; c is the overall equivalent specific heat capacity of the battery components; ρ is the overall equivalent density of the battery components; 、 and are the thermal conductivities of lithium-ion batteries in the x-axis, y-axis, and z-axis directions; q is the heat generation rate.

[0014] Preferably, the heat generation rate q is calculated according to the theory proposed by Bernardi, and the expression is as follows:

[0015]

[0016] Where q is the heat generation rate; V represents the volume of the lithium-ion battery; I represents the operating current of the lithium-ion battery; represents the open circuit voltage of the lithium-ion battery; U represents the terminal voltage of the lithium-ion battery; T represents the temperature of the lithium-ion battery.

[0017] As a preference, the finite difference expression of the battery fractional order thermal diffusion model FOTDM in S1 is:

[0018]

[0019] Where W is the weighted term of the historical temperature variable, ; is the total duration, is the time interval; is the fractional derivative order of the fractional thermal diffusion model FOTDM.

[0020] Preferably, the thermophysical parameters of the fractional-order thermal diffusion model FOTDM of lithium-ion batteries in S1 are calculated using a weighted average method, and the expressions are as follows:

[0021]

[0022] in, 、 、 and They are the equivalent density, equivalent volume, equivalent specific heat capacity and equivalent mass of each layer of lithium-ion battery components; and Represent the heat transfer area and thickness of each layer of components respectively; V and m represent the volume and mass of the lithium-ion battery respectively; c is the overall equivalent specific heat capacity of the battery components; ρ is the overall equivalent density of the battery components; 、 and are the thermal conductivity of lithium-ion batteries in the x-axis, y-axis, and z-axis directions respectively; is the thermal conductivity of each layer of material in the lithium-ion battery; i is the number of layers that make up the lithium-ion battery.

[0023] Preferably, the electrical characteristics of the lithium-ion battery in S2 are characterized by a second-order resistance-capacitance RC model, and the state space expression of the equivalent circuit model is as follows:

[0024]

[0025] in is a differential operator; and It is a polarized capacitor; and is the polarization resistance; and They are and The terminal voltage; Represents ohmic resistance; I represents the operating current of the lithium-ion battery.

[0026] Preferably, the coupling process of the fractional-order thermoelectric coupling model in S3 includes the following steps:

[0027] S3.1: Collect the battery's operating current I, time item, and open circuit voltage , calculated from the mixed pulse test ohmic resistance , Identifying the electrical performance parameters of lithium-ion batteries through optimization algorithms: polarization capacitance in equivalent circuit models and and polarization resistance and ;

[0028] S3.2: Importing the identified electrical performance parameters of the lithium-ion battery into an electrical model of the lithium-ion battery to calculate the terminal voltage U of the lithium-ion battery;

[0029] S3.3: Substitute the calculated terminal voltage U into the heat generation equation proposed by Bernardi to calculate the heat generation rate of the lithium-ion battery;

[0030] S3.4: Load the heat generation rate of the lithium-ion battery calculated in S3.3 into the fractional order thermal diffusion model (FOTDM) of the lithium-ion battery to simulate the temperature;

[0031] S3.5: Use the temperature obtained from the simulation in S3.4 to adjust the electrical performance parameters of the lithium-ion battery;

[0032] S3.6: The electrical performance parameters of lithium-ion batteries at different states of charge (SOC) are continuously updated, and the historical weight terms of the lithium-ion battery temperature are gradually updated and loaded into the fractional-order thermal diffusion model (FOTDM) of the lithium-ion battery. Finally, the fractional-order thermoelectric coupling model (FOTEM) of the lithium-ion battery is established.

[0033] Preferably, the state of charge (SOC) of the lithium-ion battery in S3.6 is calculated as follows:

[0034]

[0035] in is the rated capacity of the lithium-ion battery.

[0036] Preferably, S4 specifically includes the following steps:

[0037] S4.1: Use the least squares optimization algorithm to iteratively optimize the initial terminal voltage to obtain the optimal equivalent circuit model parameter set and the final estimated terminal voltage of the fractional-order thermoelectric coupling model (FOTEM) of the lithium-ion battery;

[0038] S4.2: Initialize the fractional derivative order FDO of the fractional thermoelectric coupling model FOTEM, and import the thermophysical parameters and heat generation rate of the lithium-ion battery into the fractional thermoelectric coupling model FOTEM to calculate the estimated temperature;

[0039] S4.3: Substitute the estimated temperature and the measured temperature into the optimization function of the least squares optimization algorithm for error iteration and optimization;

[0040] S4.4: After multiple optimization iterations, the optimal estimated temperature and fractional derivative order FDO of the fractional thermoelectric coupled model FOTEM are determined.

[0041] Preferably, the optimization function of the least squares optimization algorithm in S4.3 is expressed as follows:

[0042]

[0043] in, is the objective function of the equivalent circuit model; is the objective function of the fractional-order thermal diffusion model FOTDM; is the measured voltage; is the estimated voltage of the equivalent circuit model; is the measured temperature; is the estimated temperature of the fractional order thermal diffusion model FOTDM; is the simulated continuous temperature.

[0044] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0045] 1. The temperature and voltage simulation accuracy of the fractional-order thermoelectric coupling model FOTEM is better than that of the traditional thermoelectric coupling model. FOTEM can track the actual temperature and voltage of the battery more quickly and simulate the temperature field more accurately.

[0046] 2. The fractional-order thermoelectric coupling model FOTEM uses all variables in the historical time to calculate transient temperature. Compared with traditional thermoelectric coupling models, FOTEM has higher real-time simulation stability;

[0047] 3. Fractional-order thermoelectric coupling model FOTEM As a high-order extension of the traditional thermoelectric coupling model, FOTEM has a wider range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is the second-order resistance-capacitance RC model of the lithium-ion battery in the present invention.

[0049] Figure 2 This is the coupling process between the second-order resistance-capacitance RC model and the fractional-order thermal diffusion model FOTDM in the present invention.

[0050] Figure 3 This is the parameter identification of the second-order resistance-capacitance RC model and the fractional-order thermal diffusion model FOTDM in the present invention.

[0051] Figure 4 It is a testing platform for the lithium-ion battery LIB in the present invention.

[0052] Figure 5 The figure shows the distribution of temperature test points of the battery module in the present invention.

[0053] Figure 6 Test data (0°C) of the lithium-ion battery module HPPC in the present invention: (a) test voltage; (b) test temperature.

[0054] Figure 7 FOTEM identification results of the fractional-order thermoelectric coupling model of the lithium-ion battery model in the present invention (0°C): (a) simulated temperature; (b) simulation error of temperature.

[0055] Figure 8 These are the identification results of the fractional derivative order FDO under different temperatures and states of charge (SOC) in the present invention.

[0056] Figure 9 FOTEM identification results of the fractional-order thermoelectric coupling model of the lithium-ion battery model in the present invention (0°C): (a) voltage simulation result; (b) voltage simulation error.

[0057] Figure 10 Temperature simulation of the fractional-order thermoelectric coupling model FOTEM in the present invention at -20°C: (a) temperature; (b) temperature error.

[0058] Figure 11 This is the voltage simulation of the fractional-order thermoelectric coupling model FOTEM in the present invention at -20°C.

[0059] Figure 12 The temperature simulation results of different test points of constant current in the present invention under -20°C environment: (a) temperature; (b) temperature root mean square error.

[0060] Figure 13 The simulation effect of DST in the -20°C environment in the present invention: (a) simulated temperature; (b) simulated voltage.

[0061] Figure 14 The temperature simulation effects of different test points under the DST working condition at -20°C in the present invention: (a) temperature; (b) temperature root mean square error. DETAILED DESCRIPTION

[0062] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0063] Example 1

[0064] The present invention describes a method for estimating the low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model, which specifically includes the following steps:

[0065] S1: Based on the non-standard thermal diffusion theory, a fractional-order thermal diffusion model (FOTDM) of lithium-ion batteries under low temperature conditions is established.

[0066] The fractional-order heat diffusion equation based on nonstandard heat diffusion theory is:

[0067]

[0068] Where t is the charge and discharge time of the battery; T is the temperature of the lithium-ion battery; x, y, and z are the distances of the lithium-ion battery in the x-axis, y-axis, and z-axis directions, respectively; c is the overall equivalent specific heat capacity of the battery components; ρ is the overall equivalent density of the battery components; 、 and are the thermal conductivities of lithium-ion batteries in the x-axis, y-axis, and z-axis directions; q is the heat generation rate.

[0069] The heat generation rate q is calculated according to the theory proposed by Bernardi and is expressed as follows:

[0070]

[0071] Where q is the heat generation rate; V represents the volume of the lithium-ion battery; I represents the operating current of the lithium-ion battery; represents the open circuit voltage of the lithium-ion battery; U represents the terminal voltage of the lithium-ion battery; T represents the temperature of the lithium-ion battery.

[0072] The finite difference expression of the battery fractional-order thermal diffusion model FOTDM is:

[0073]

[0074] Where W is the weighted term of the historical temperature variable, ; is the total duration, is the time interval; is the fractional derivative order of the fractional thermal diffusion model FOTDM.

[0075] The thermophysical parameters of the fractional-order thermal diffusion model (FOTDM) of lithium-ion batteries are calculated using the weighted average method, and the expressions are as follows:

[0076]

[0077] in, 、 、 and They are the equivalent density, equivalent volume, equivalent specific heat capacity and equivalent mass of each layer of lithium-ion battery components; and Represent the heat transfer area and thickness of each layer of components respectively; V and m represent the volume and mass of the lithium-ion battery respectively; c is the overall equivalent specific heat capacity of the battery components; ρ is the overall equivalent density of the battery components; 、 and are the thermal conductivity of lithium-ion batteries in the x-axis, y-axis, and z-axis directions respectively; is the thermal conductivity of each layer of material in the lithium-ion battery; i is the number of layers that make up the lithium-ion battery.

[0078] S2: Construct an equivalent circuit model of a lithium-ion battery.

[0079] like Figure 1 As shown, the electrical characteristics of lithium-ion batteries are characterized by a second-order resistance-capacitance RC model, and the state space expression of the equivalent circuit model is as follows:

[0080]

[0081] in is a differential operator; and It is a polarized capacitor; and is the polarization resistance; and They are and The terminal voltage; Represents ohmic resistance; I represents the operating current of the lithium-ion battery.

[0082] S3: If Figure 2 As shown in FIG, a fractional-order thermoelectric coupling model is established based on the fractional-order thermal diffusion model FOTDM and the equivalent circuit model. The coupling process includes the following steps:

[0083] S3.1: If Figure 3 The working current I, time item, and open circuit voltage of the battery are collected as shown , calculated from the mixed pulse test ohmic resistance , Identifying the electrical performance parameters of lithium-ion batteries through optimization algorithms: polarization capacitance in equivalent circuit models and and polarization resistance and ;

[0084] S3.2: Importing the identified electrical performance parameters of the lithium-ion battery into an electrical model of the lithium-ion battery to calculate the terminal voltage U of the lithium-ion battery;

[0085] S3.3: Substitute the calculated terminal voltage U into the heat generation equation proposed by Bernardi to calculate the heat generation rate of the lithium-ion battery;

[0086] S3.4: Load the heat generation rate of the lithium-ion battery calculated in S3.3 into the fractional order thermal diffusion model (FOTDM) of the lithium-ion battery to simulate the temperature;

[0087] S3.5: Use the temperature obtained from the simulation in S3.4 to adjust the electrical performance parameters of the lithium-ion battery;

[0088] S3.6: The electrical performance parameters of lithium-ion batteries at different states of charge (SOCs) are continuously updated, and the historical weight terms of the lithium-ion battery temperature are gradually updated and loaded into the fractional-order thermal diffusion model (FOTDM) of the lithium-ion battery. Finally, a fractional-order thermoelectric coupling model (FOTEM) of the lithium-ion battery is established. The state of charge (SOC) of the lithium-ion battery is calculated as follows:

[0089]

[0090] in is the rated capacity of the lithium-ion battery.

[0091] S4: Identify the fractional derivative order and electrical performance parameters of the battery at different SOCs based on the least squares optimization algorithm, specifically including the following steps:

[0092] S4.1: Use the least squares optimization algorithm to iteratively optimize the initial terminal voltage to obtain the optimal equivalent circuit model parameter set and the final estimated terminal voltage of the fractional-order thermoelectric coupling model (FOTEM) of the lithium-ion battery;

[0093] S4.2: Initialize the fractional derivative order FDO of the fractional thermoelectric coupling model FOTEM, and import the thermophysical parameters and heat generation rate of the lithium-ion battery into the fractional thermoelectric coupling model FOTEM to calculate the estimated temperature;

[0094] S4.3: Substitute the estimated temperature and the measured temperature into the optimization function of the least squares optimization algorithm to perform error iteration and optimization. The optimization function of the least squares optimization algorithm is expressed as follows:

[0095]

[0096] Among them, among them, is the objective function of the equivalent circuit model; is the objective function of the fractional-order thermal diffusion model FOTDM; is the measured voltage; is the estimated voltage of the equivalent circuit model; is the measured temperature; is the estimated temperature of the fractional order thermal diffusion model FOTDM; is to simulate continuous temperature;

[0097] S4.4: After multiple optimization iterations, the optimal estimated temperature and fractional derivative order FDO of the fractional thermoelectric coupled model FOTEM are determined.

[0098] Example 2

[0099] A ternary lithium-ion battery was used for experimental testing. The anode component of the battery was graphite and the cathode component was LiNi 1 / 3Mn 1 / 3 Co 1 / 3 O2, the calibration parameters of the ternary lithium-ion battery are shown in Table 1:

[0100] Table 1: Calibration parameters for ternary lithium-ion batteries

[0101] Parameter name Calibration value Test conditions Battery capacity 51Ah Ambient temperature: 25°C, discharge current: 1C, discharge cut-off voltage: 2.8V Operating voltage range 2.2-4.2V Ambient temperature: -20°C ≤ 5°C Calibration voltage 3.635V Ambient temperature: 25°C, SOC: 40% Operating temperature (charging) -20-55°C - Operating temperature (discharge) -30-55°C - Battery size 26.72*91.4*148.3mm

[0102] like Figure 4 As shown, it is a test platform for ternary lithium-ion battery modules, including an ARBIN test system and auxiliary channels. The environmental chamber is used to adjust the ambient temperature. The water cooling system is used to provide coolant for the cooling plate and heat the ternary lithium-ion battery. The battery charge and discharge test system, environmental chamber and water cooling equipment are all controlled by the workstation.

[0103] Ten single ternary lithium-ion batteries are connected in series through bolt assemblies. The temperature data of the ternary lithium-ion batteries are collected by thermocouples in the auxiliary channel. The position of the thermocouples in the ternary lithium-ion battery module is as follows: Figure 5 As shown, the thermocouple is arranged at the center of the side of each single ternary lithium-ion battery.

[0104] The ternary lithium-ion battery module was tested at various discharge currents and temperatures. The battery module was discharged to 0% SOC, and then a segmented current was applied to the ternary lithium-ion battery module until the SOC rose to 100%. Then, a constant current was applied to the ternary lithium-ion battery module at different discharge rates. The charging and discharging parameter settings are shown in Table 2:

[0105] Table 2: Charging and discharging parameter settings

[0106] Ambient temperature (°C) Stage charging current (A) Stage charging voltage (V) Discharge rate (C) Discharge cut-off voltage (V) 0 Stage 1: 17.8 Stage 1: 3.74 0.5 / 1 / 2 2.80 0 Stage 2: 12.7 Phase 2: 3.80 0.5 / 1 / 2 2.80 0 Phase 3: 10.7 Stage 3: 3.92 0.5 / 1 / 2 2.80 0 Stage 4: 7.9 Phase 4: 4.05 0.5 / 1 / 2 2.80 0 Phase 5: 5.3 Phase 5: 4.16 0.5 / 1 / 2 2.80 0 Phase 6: 2.4 Stage 6: 4.20 0.5 / 1 / 2 2.80 -10 Stage 1: 4 Stage 1: 3.71 0.5 / 1 / 1.5 2.50 -10 Phase 2:3 Stage 2: 3.82 0.5 / 1 / 1.5 2.50 -10 Phase 3:2 Stage 3: 3.94 0.5 / 1 / 1.5 2.50 -10 Phase 4: 1.5 Phase 4: 4.08 0.5 / 1 / 1.5 2.50 -10 Phase 5:1 Phase 5: 4.16 0.5 / 1 / 1.5 2.50 -20 Stage 1: 4 Stage 1: 3.71 0.5 / 1 2.30 -20 Phase 2:3 Stage 2: 3.82 0.5 / 1 2.30 -20 Phase 3:2 Stage 3: 3.94 0.5 / 1 2.30 -20 Phase 4: 1.5 Phase 4: 4.08 0.5 / 1 2.30 -20 Phase 5:1 Phase 5: 4.16 0.5 / 1 2.30

[0107] In one cycle of the hybrid pulse power characterization HPPC experiment, the LIB was first discharged at a constant current rate of 1C for 10 seconds, then the ternary lithium-ion battery LIB was charged at a constant current rate of 0.7C for 10 seconds, and the battery was disconnected for 600 seconds, and then discharged at a rate of 1C until the SOC decreased by 10%.

[0108] The ohmic resistance of the ternary lithium-ion battery can be calculated from the voltage drop during the HPPC charge and discharge process, and its expression is as follows:

[0109]

[0110] in and are the current and voltage drop during discharge, respectively; and are the current and voltage drop during charging, respectively.

[0111] In order to demonstrate the performance of the fractional-order thermoelectric coupling model FOTEM in the dynamic charge and discharge process, a dynamic stress test DST was established to load the battery with a short constant current discharge to prevent the battery module from overcharging at low temperature and high SOC.

[0112] like Figure 6 As shown, the voltage response and temperature under the dynamic stress test DST test conditions are shown. The fully charged ternary lithium-ion battery LIB model is placed in a preheated environmental chamber for 5 hours, and the ternary lithium-ion battery module is tested according to the low-temperature dynamic stress test DST operating conditions.

[0113] During the test, the thermal convection expression of the ternary lithium-ion battery under natural cooling is as follows:

[0114]

[0115] in, Indicates the heat exchange parameters of air; Indicates the temperature of the natural environment; 、 and is the distance of the battery in three dimensions.

[0116] The liquid heating system of the ternary lithium-ion battery module is generally composed of a water cooling system, coolant, cooling plate, etc. The continuity equation of the liquid heating flow field is expressed as follows:

[0117]

[0118] in, 、 、 and are the density, inflow temperature, heat transfer coefficient and specific heat capacity of the fluid respectively; is the viscosity of the coolant; P is the static pressure of the coolant; v is the flow velocity.

[0119] The heat exchange expression of the cooling plate is as follows:

[0120]

[0121] in, is the density of the cooling plate; is the specific heat capacity of the cooling plate; 、 and is the thermal conductivity in three-dimensional space.

[0122] The calculated thermophysical parameters of the ternary lithium-ion battery are shown in Table 3. The open circuit voltage at different temperatures was obtained through experimental testing, and the calculated coefficients About 0.27.

[0123] Table 3: Thermophysical performance parameters of ternary lithium-ion batteries

[0124] Components Calibrated capacity (J / (kg·K)) Thermal conductivity (W / m·K) <![CDATA[Density (kg / cm 3 )]]> Dynamic viscosity Temperature influence coefficient (m·V / K) Battery 2146.88 31.4-0.98 2.93 - 0.27

[0125] like Figure 7 As shown, the identification result of the ternary lithium-ion battery module point 1 is displayed. Figure 7 The temperature change corresponds to the discharge process temperature at 100% SOC in the hybrid pulse power characteristic HPPC. The entire discharge process lasts 40 seconds. The estimation error of the fractional-order thermoelectric coupling model FOTEM is within 0.08 K, and the optimal fractional derivative order FDO of the fractional-order thermoelectric coupling model FOTEM is equal to 1.58.

[0126] like Figure 8 As shown in the figure, the identification results of the fractional derivative order FDO at different temperatures and SOCs are shown. When the ambient temperature is 0℃, the fractional derivative order FDO at 10% SOC is 1.40. As the SOC increases, the fractional derivative order FDO will gradually increase.

[0127] As the ambient temperature decreases, the fractional derivative order FDO gradually increases. At an ambient temperature of -20°C, the fractional derivative order FDO increases from 1.54 to 1.74. The change in the fractional derivative order FDO reflects that the porous electrode exhibits stronger nonstandard thermal diffusion at lower ambient temperatures.

[0128] The final parameters determined by the second-order RC model are used to calculate the simulated voltage, such as Figure 9 As shown in the figure, the simulation error of ECM is within 0.03V.

[0129] like Figure 10 As shown, the temperature simulation effect at -20°C is shown. At lower temperatures, the discharge time and available capacity of the battery are significantly reduced. At a discharge rate of 0.5C, the maximum error of the fractional-order thermoelectric coupling model FOTEM is about 0.43K, and the error of the integer-order thermoelectric coupling model IOTEM is 1.21K. At a discharge rate of 1C, the maximum error of the fractional-order thermoelectric coupling model FOTEM is 0.62K.

[0130] like Figure 11As shown in the figure, the voltage simulation effect at -20°C is shown. The accuracy of the fractional-order thermoelectric coupling model FOTEM is higher than that of the integer-order thermoelectric coupling model IOTEM. The maximum root mean square error RMSE of the fractional-order thermoelectric coupling model FOTEM at -20°C is 0.046V.

[0131] like Figure 12 As shown in Figure 3, the temperature changes of the ternary lithium-ion battery LIB at different test points at -20°C are shown. Due to its history weighting term, the fractional-order thermoelectric coupling model FOTEM can effectively simulate the thermal hysteresis effect of the ternary lithium-ion battery LIB.

[0132] However, the integer-order thermoelectric coupling model IOTEM lacks the description of the self-similar characteristics of the porous electrode, which leads to an increase in the cumulative error of the simulated temperature, with the maximum root mean square error (RMSE) of 0.59 K at -20 °C.

[0133] like Figure 13 Figure 2 shows the temperature simulation results of DST at -20°C. When the discharge time exceeds 1050 seconds, the temperature fluctuates in a small range.

[0134] like Figure 14 Figures (a) and (b) show the temperature simulation results and simulation errors of the fractional-order thermoelectric coupling model FOTEM at five test points. Compared with the integer-order thermoelectric coupling model IOTEM, the fractional-order thermoelectric coupling model FOTEM can more accurately simulate the thermal behavior of the DST. The maximum root mean square error (RMSE) at -20°C is 0.065K. The maximum root mean square error (RMSE) of the voltage at -20°C is 0.02V.

[0135] The results show that the fractional-order thermoelectric coupling model FOTEM has high accuracy under static conditions, dynamic conditions, and liquid heating conditions. The simulation accuracy of temperature and voltage in the fractional-order thermoelectric coupling model FOTEM is better than that of the traditional thermoelectric coupling model.

Claims

1. A method for estimating the low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model, characterized by: The specific steps include: S1: Based on the non-standard thermal diffusion theory, a fractional-order thermal diffusion model (FOTDM) for lithium-ion batteries under low temperature conditions is established; S2: Construct an equivalent circuit model of a lithium-ion battery; S3: Establish a fractional-order thermoelectric coupling model FOTEM based on the fractional-order thermal diffusion model FOTDM and the equivalent circuit model; S4: Identify the fractional derivative order FDO and electrical performance parameters of the fractional-order thermoelectric coupling model FOTEM at different battery SOCs based on the least squares optimization algorithm.

2. The method for estimating low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model according to claim 1, characterized in that: The fractional-order heat diffusion equation based on nonstandard heat diffusion theory in S1 is: Where t is the charge and discharge time of the battery; T is the temperature of the lithium-ion battery; x, y, and z are the distances of the lithium-ion battery in the x-axis, y-axis, and z-axis directions, respectively; c is the overall equivalent specific heat capacity of the battery components; ρ is the overall equivalent density of the battery components; 、 and are the thermal conductivities of lithium-ion batteries in the x-axis, y-axis, and z-axis directions; q is the heat generation rate.

3. The method for estimating low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model according to claim 2, characterized in that: The heat generation rate q is calculated according to the theory proposed by Bernardi and is expressed as follows: Where q is the heat generation rate; V represents the volume of the lithium-ion battery; I represents the operating current of the lithium-ion battery; represents the open circuit voltage of the lithium-ion battery; U represents the terminal voltage of the lithium-ion battery; T represents the temperature of the lithium-ion battery.

4. The method for estimating low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model according to claim 1, characterized in that: The finite difference expression of the battery fractional-order thermal diffusion model FOTDM in S1 is: Where W is the weighted term of the historical temperature variable, ; is the total duration, is the time interval; is the fractional derivative order of the fractional thermal diffusion model FOTDM; c is the overall equivalent specific heat capacity of the battery constituent materials; ρ is the overall equivalent density of the battery constituent materials; 、 and are the thermal conductivities of lithium-ion batteries in the x-axis, y-axis, and z-axis directions; q is the heat generation rate.

5. The method for estimating low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model according to claim 1, characterized in that: The thermophysical parameters of the fractional-order thermal diffusion model (FOTDM) of lithium-ion batteries in S1 are calculated using the weighted average method, and the expressions are as follows: in, 、 、 and They are the equivalent density, equivalent volume, equivalent specific heat capacity and equivalent mass of each layer of lithium-ion battery components; and Represent the heat transfer area and thickness of each layer of components respectively; V and m represent the volume and mass of the lithium-ion battery respectively; c is the overall equivalent specific heat capacity of the battery components; ρ is the overall equivalent density of the battery components; 、 and are the thermal conductivity of lithium-ion batteries in the x-axis, y-axis, and z-axis directions respectively; is the thermal conductivity of each layer of material in the lithium-ion battery; i is the number of layers that make up the lithium-ion battery.

6. The method for estimating low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model according to claim 1, characterized in that: The electrical characteristics of the lithium-ion battery in S2 are characterized by a second-order resistance-capacitance RC model. The state space expression of the equivalent circuit model is as follows: in is a differential operator; and It is a polarized capacitor; and is the polarization resistance; and They are and The terminal voltage; Represents ohmic resistance; I represents the operating current of the lithium-ion battery; is the open circuit voltage.

7. The method for estimating low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model according to claim 1, characterized in that: The coupling process of the fractional-order thermoelectric coupling model in S3 includes the following steps: S3.1: Collect the battery's operating current I, time item, and open circuit voltage , calculated from the mixed pulse test ohmic resistance , Identifying the electrical performance parameters of lithium-ion batteries through optimization algorithms: polarization capacitance in equivalent circuit models and and polarization resistance and ; S3.2: Importing the identified electrical performance parameters of the lithium-ion battery into an electrical model of the lithium-ion battery to calculate the terminal voltage U of the lithium-ion battery; S3.3: Substitute the calculated terminal voltage U into the heat generation equation proposed by Bernardi to calculate the heat generation rate of the lithium-ion battery; S3.4: Load the heat generation rate of the lithium-ion battery calculated in S3.3 into the fractional order thermal diffusion model (FOTDM) of the lithium-ion battery to simulate the temperature; S3.5: Use the temperature obtained from the simulation in S3.4 to adjust the electrical performance parameters of the lithium-ion battery; S3.6: The electrical performance parameters of lithium-ion batteries at different states of charge (SOC) are continuously updated, and the historical weight terms of the lithium-ion battery temperature are gradually updated and loaded into the fractional-order thermal diffusion model (FOTDM) of the lithium-ion battery. Finally, the fractional-order thermoelectric coupling model (FOTEM) of the lithium-ion battery is established.

8. The method for estimating low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model according to claim 7, characterized in that: The calculation method of the state of charge (SOC) of lithium-ion batteries in S3.6 is as follows: in is the rated capacity of the lithium-ion battery.

9. The method for estimating low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model according to claim 5, characterized in that: S4 specifically includes the following steps: S4.1: Use the least squares optimization algorithm to iteratively optimize the initial terminal voltage to obtain the optimal equivalent circuit model parameter set and the final estimated terminal voltage of the fractional-order thermoelectric coupling model (FOTEM) of the lithium-ion battery; S4.2: Initialize the fractional derivative order FDO of the fractional thermoelectric coupling model FOTEM, and import the thermophysical parameters and heat generation rate of the lithium-ion battery into the fractional thermoelectric coupling model FOTEM to calculate the estimated temperature; S4.3: Substitute the estimated temperature and the measured temperature into the optimization function of the least squares optimization algorithm for error iteration and optimization; S4.4: After multiple optimization iterations, the optimal estimated temperature and fractional derivative order FDO of the fractional thermoelectric coupled model FOTEM are determined.

10. The method for estimating low-temperature thermoelectric performance of lithium-ion batteries based on a fractional-order thermoelectric model according to claim 9, characterized in that: The expression of the optimization function of the least squares optimization algorithm in S4.3 is as follows: in, is the objective function of the equivalent circuit model; is the objective function of the fractional-order thermal diffusion model FOTDM; is the measured voltage; is the estimated voltage of the equivalent circuit model; is the measured temperature; is the estimated temperature of the fractional order thermal diffusion model FOTDM; is the simulated continuous temperature.

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