Modeling method for electric-thermal coupling model of single lithium battery

Abstract

The invention discloses an electric-thermal coupling model modeling method of a single lithium battery. The method comprises the following steps: S1, constructing a second-order RC equivalent circuit model of the single lithium battery; s2, performing parameter identification on the second-order RC equivalent circuit model by utilizing the battery experiment data at different environment temperatures through a least square method to obtain second-order RC model parameters at different temperatures; s3, constructing a double-state thermal model of the single lithium battery; s4, parameter identification is carried out on the double-state thermal model through battery experiment data; s5, performing dynamic coupling on the second-order RC equivalent circuit model and the double-state thermal model to obtain an electric-thermal coupling model; and the battery information of the single lithium battery in the whole discharging process can be calculated in a loop iteration manner through the electric-thermal coupling model. According to the method, the second-order RC equivalent circuit model and the double-state thermal model are dynamically coupled to obtain the electric-thermal coupling model, so that the electric and thermal characteristics of the battery can be considered at the same time, and high-precision monitoring and evaluation of the performance of the single lithium battery are realized.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium battery modeling, and in particular to a method for modeling an electric-thermal coupling model of a single lithium battery. Background Art

[0002] With the rapid development of electric vehicles, energy storage systems and portable electronic devices, the stability and reliability of lithium-ion batteries as their core energy supply units have become the focus of the industry. The performance of lithium-ion batteries is not only affected by electrical conditions such as charge and discharge rate and cycle number, but is also closely related to ambient temperature.

[0003] If the heat generated by the battery during operation cannot be effectively managed, it will not only cause the battery temperature to rise, affecting the electrochemical performance of the battery, but may also cause safety issues such as thermal runaway or even explosion. Therefore, a deep understanding of the electrical and thermal characteristics of the battery and their interaction mechanism is of great significance for optimizing battery design, improving the performance of the battery management system (BMS), and ensuring the safe operation of the battery system.

[0004] Traditional battery performance evaluation methods mainly focus on the study of electrical characteristics, and estimate key parameters such as the remaining capacity and internal resistance of the battery by simulating the voltage response of the battery by establishing an equivalent circuit model. However, these methods often ignore the significant impact of temperature changes on battery performance. In fact, key parameters such as the internal resistance, open circuit voltage, and capacity of the battery all change with temperature, and this change presents complex nonlinear characteristics. Therefore, models that only consider electrical characteristics have certain limitations in predicting the actual performance of the battery.

[0005] In order to more comprehensively describe the performance of batteries, researchers have begun to try to incorporate thermal characteristics into battery models in recent years. Thermal models can simulate the heat generation, transfer, and dissipation process of batteries during operation, thereby predicting the temperature distribution and change trend of the battery. However, most early thermal models were based on steady-state assumptions and ignored the dynamic thermal behavior of batteries during charging and discharging. In addition, these models are usually independent of electrical models and fail to fully consider the coupling relationship between electrical and thermal characteristics. This separate modeling method cannot accurately reflect the actual performance of batteries under complex working conditions.

[0006] In order to overcome the limitations of traditional methods, the existing technology has begun to explore the electro-thermal coupling modeling method. The electro-thermal coupling model aims to simultaneously consider the electrical and thermal characteristics of the battery, as well as the interaction mechanism between them. By integrating electrical and thermal models, the electro-thermal coupling model can more accurately predict the performance of the battery under different operating conditions, including key indicators such as voltage response, temperature change, and remaining capacity. This plays a vital role in optimizing the battery management system, improving battery life, and ensuring the safe operation of the battery system. Therefore, how to design an electro-thermal coupling model that can simultaneously consider the electrical and thermal characteristics of the battery is a technical problem that needs to be solved urgently. Summary of the invention

[0007] In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is: how to provide a modeling method for an electric-thermal coupling model of a single lithium battery, dynamically couple the second-order RC equivalent circuit model and the two-state thermal model to obtain an electric-thermal coupling model, so that the electrical and thermal characteristics of the battery can be considered at the same time, thereby achieving high-precision monitoring and evaluation of the performance of the single lithium battery.

[0008] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0009] A method for modeling an electric-thermal coupling model of a single lithium battery, comprising:

[0010] S1: Construct a second-order RC equivalent circuit model of a single lithium battery;

[0011] S2: The parameters of the second-order RC equivalent circuit model are identified by using the least squares method using the battery experimental data at different ambient temperatures to obtain the second-order RC model parameters at different temperatures;

[0012] S3: Construct a two-state thermal model of a single lithium battery;

[0013] S4: Parameter identification of the two-state thermal model using battery experimental data;

[0014] S5: Dynamically couple the second-order RC equivalent circuit model and the two-state thermal model to obtain an electro-thermal coupling model; the electro-thermal coupling model can be used to iteratively calculate battery information of a single lithium battery during the entire discharge process.

[0015] Preferably, in step S1, the formula of the second-order RC equivalent circuit model is expressed as:

[0016]

[0017] Where: x(t) represents the battery SOC at time t; U p and U sThey represent the polarization voltage of the two RC parallel circuits of the battery; η is the coulomb efficiency; C b Indicates battery capacity; I b Indicates the battery current; U ocv represents the open circuit voltage of the battery; R0 represents the ohmic resistance; R p and R s Represents polarization resistance; C p and C s represents polarized capacitance; T represents ambient temperature;

[0018] Discretize the continuous state space expression of the second-order RC equivalent circuit model, and obtain the state space expression of the second-order RC equivalent circuit model in discrete time domain:

[0019]

[0020] Where: Δt represents the sampling period; k represents the sampling time point.

[0021] Preferably, in step S2, after the second-order RC model parameters at different temperatures are identified, a three-dimensional relationship between the second-order RC model parameters and the temperature and SOC is established according to the fitting method and the interpolation method, so that the second-order RC model parameters at the corresponding temperature can be directly obtained by looking up the table according to the current temperature and SOC of the single lithium battery.

[0022] Preferably, in step S2, in step S2, the battery experimental data includes data obtained through a battery capacity test experiment;

[0023] The experimental steps of the battery capacity test experiment include:

[0024] S201: Place the experimental target battery in an incubator, adjust the incubator temperature to 25°C, and leave for 3 hours;

[0025] S202: Set the charging program to constant current-constant voltage charging, the charging voltage is 4.2V, the charging current is a standard charging current rate of 0.5C; define the stop condition when full, and leave it for 3 hours after full;

[0026] S203: adjusting the temperature of the incubator to the experimental target temperature and leaving it for 6 hours;

[0027] The experimental target temperatures include 35℃, 25℃, 15℃, 5℃ and -5℃;

[0028] S204: setting the discharge program to constant current discharge, with a current ratio of 0.5C, and defining a stop condition at the end of the discharge;

[0029] S205: Repeat steps S201 to S204 several times, and calculate an average value of the battery capacities measured several times.

[0030] Preferably, in step S2, in step S2, the battery experimental data includes data obtained through an intermittent pulse discharge test experiment;

[0031] The experimental steps of the intermittent pulse discharge test experiment include:

[0032] S211: Place the experimental target battery in an incubator, adjust the incubator temperature to 25°C, and leave for 3 hours;

[0033] S212: The charging program is set to constant current-constant voltage charging. The charging and cut-off conditions are consistent with those in the capacity test experiment. After being fully charged, the charging is left for 3 hours.

[0034] S213: adjusting the temperature of the incubator to the experimental target temperature and leaving it for 6 hours;

[0035] The experimental target temperatures include 35℃, 25℃, 15℃, 5℃ and -5℃;

[0036] S214: Set the discharge program to constant current discharge, the current rate to 1C, the discharge time to 6 minutes, and the protection condition to the cut-off voltage to 2.5V. This step reduces the battery SOC by 10%;

[0037] S215: leaving the single lithium battery for 1 hour;

[0038] S216: Steps S214 to S215 are cycled ten times, at which point the total discharge capacity of the experimental target battery is 100% capacity.

[0039] Preferably, in step S2, the current rate C of the single lithium battery charge and discharge rate The calculation formula is:

[0040]

[0041] Where: i b Indicates the battery charging and discharging current; C b Indicates the battery capacity.

[0042] Preferably, in step S3, the formula of the two-state thermal model is expressed as:

[0043]

[0044] Where: and Respectively represent the rate of change of battery surface temperature and core temperature; R c and R u Respectively represent the equivalent internal thermal resistance and the equivalent external thermal resistance; C s and C c They represent the surface concentrated heat capacity and the core concentrated heat capacity respectively; Q represents the heat generated inside the battery; Tamb Indicates the ambient temperature.

[0045] Preferably, in step S4, before obtaining the battery experimental data, a battery drilling preparatory experiment is first performed;

[0046] The experimental steps of the battery drilling preparation experiment include:

[0047] S401: Completely drain the battery of the experimental target to avoid short circuit during drilling;

[0048] S402: In an operating box with protective measures, drilling is performed from the center of the anode or cathode of the battery;

[0049] S403: Select a thermocouple that fits the battery size and place it in the hole. The length of the thermocouple placed inside the battery should be half the height of the battery and should be placed perpendicular to the plane where the electrodes are located.

[0050] S404: Use insulating silicone with good thermal conductivity to seal the gap between the thermocouple and the drilled hole to ensure the normal operation of the battery;

[0051] S405: Perform a charge and discharge test on the battery and compare the external characteristics before drilling to ensure that the whole process has no impact on the battery characteristics.

[0052] Preferably, in step S4, the battery experimental data includes data obtained from a battery temperature rise test experiment;

[0053] The experimental steps of the battery temperature rise test experiment include:

[0054] S411: placing the experimental target battery in an incubator, adjusting the incubator temperature to 25° C., and leaving it for 3 hours;

[0055] S412: Set the charging program to constant current-constant voltage charging, the charging voltage is 4.2V, the charging current is a standard charging current rate of 0.5C, the stop condition when full is defined, and leave it for 3 hours after full;

[0056] S413: Set the discharge program to constant current discharge with a current rate of 1C, define the stop condition at the end of discharge, and record the middle surface temperature and internal core temperature of the battery during the entire discharge process.

[0057] Preferably, in step S5, the working logic of the electric-thermal coupling model includes:

[0058] S501: Bringing the initial values ​​of various variables into the electrical-thermal coupling model;

[0059] S502: Inputting current information of a single lithium battery;

[0060] S503: Calculate each voltage value of the second-order RC equivalent circuit model when discharging starts, and update the SOC information;

[0061] S504: Calculate the heat generated Q at this time; substitute Q into the two-state thermal model to calculate the core temperature and surface temperature of the single lithium battery at the next moment;

[0062] The formula is:

[0063] Q=I×(U ocv -U t );

[0064] Where: I represents current; U t Indicates the terminal voltage of the battery; U ocv Indicates open circuit voltage;

[0065] S505: Calculate the average temperature T by core temperature and surface temperature a ; The average temperature T a Substitute into the second-order RC equivalent circuit model;

[0066] The formula is:

[0067]

[0068] S506: According to the average temperature T a The second-order RC model parameters at the next moment are obtained by looking up the table with SOC information;

[0069] S507: updating the second-order RC equivalent circuit model by using the second-order RC model parameters at the next moment, and calculating various voltage values ​​and SOC information at the next moment;

[0070] S508: Execute S504 to S507 in a loop to calculate the battery information of the single lithium battery during the entire discharge process, including SOC, various voltage values, core temperature and surface temperature.

[0071] Compared with the prior art, the electric-thermal coupling modeling method of a single lithium battery in the present invention has the following beneficial effects:

[0072] The present invention constructs a second-order RC equivalent circuit model and a two-state thermal model for a single lithium battery. First, by constructing a second-order RC equivalent circuit model, the voltage response characteristics of the battery during the charging and discharging process can be accurately captured, including key electrical parameters such as ohmic internal resistance, polarization internal resistance and polarization capacitance, which can effectively reflect the changes in the internal state of the battery. Secondly, the influence of temperature changes on battery performance is further considered in combination with the two-state thermal model. Further, by identifying the model parameters, the influence of temperature on the electrical characteristics of the battery can be quantified, including changes in internal resistance, enhancement or weakening of polarization effects, etc. Among them, the least squares method is used to identify the model parameters, which can make full use of the information in the experimental data and improve the accuracy of the model parameters. Finally, the second-order RC model parameters at different temperatures are obtained by experimental identification at different ambient temperatures, so that more comprehensive model parameters can be obtained, thereby improving the adaptability of the model under different temperature conditions.

[0073] The present invention dynamically couples the second-order RC equivalent circuit model and the two-state thermal model to obtain an electro-thermal coupling model. First, the establishment of the electro-thermal coupling model can simultaneously consider the electrical and thermal characteristics of the battery, thereby realizing high-precision monitoring and evaluation of the battery performance. This comprehensive evaluation method is more accurate than considering the electrical or thermal characteristics alone, and can better reflect the actual working state of the battery. Secondly, the electro-thermal coupling model also considers the dynamic changes of the battery during the discharge process. Through cyclic iterative calculations, we can update the battery information in real time, including voltage, current, temperature and remaining capacity, so as to realize continuous monitoring of battery performance. Finally, the electro-thermal coupling model provides more accurate data support for the battery management system (BMS). By real-time monitoring of the electrical and thermal characteristics of the battery, the BMS can more accurately judge the key indicators such as the battery's health status, remaining life and safety; and based on the prediction results of the electro-thermal coupling model, a more reasonable charging and discharging strategy can be formulated to avoid the occurrence of dangerous situations such as overcharging, over-discharging or overheating of the battery, thereby extending the service life of the battery. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] In order to make the purpose, technical solution and advantages of the invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0075] Figure 1 The logical block diagram of the modeling method for the electrical-thermal coupling model of a single lithium battery.

[0076] Figure 2 It is the second-order RC model of lithium battery.

[0077] Figure 3 It is a simulation model for parameter identification of second-order RC model.

[0078] Figure 4 This is the flow chart of parameter identification of the second-order RC model.

[0079] Figure 5 Comparison between simulation and experimental results of the equivalent circuit model at 25℃.

[0080] Figure 6 This is the battery parameter identification result.

[0081] Figure 7 Experimental battery temperature curve for pulse discharge test.

[0082] Figure 8 It is a two-state thermal model of a single cell.

[0083] Fig. 9 It is the equivalent thermal model of a single battery.

[0084] Fig.10 This is the flow chart of single cell thermal model parameter identification.

[0085] Fig.11 It is the electric-thermal coupling model of a single cell.

[0086] Fig.12 Comparison between the simulation and experimental results of the electro-thermal coupling model.

[0087] Fig.13 Comparison between the simulation and experimental results of the electro-thermal coupling model. DETAILED DESCRIPTION

[0088] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but only represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0089] It should be noted that similar numbers and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings. In the description of the present invention, it should be noted that the orientation or position relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inside", "outside", etc. is based on the orientation or position relationship shown in the drawings, or the orientation or position relationship in which the invention product is usually placed when used, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation of the present invention. In addition, the terms "first", "second", "third", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance. In addition, the terms "horizontal", "vertical", etc. do not mean that the components are required to be absolutely horizontal or suspended, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted. In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "set", "install", "connect", and "connect" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0090] The following is a further detailed description through specific implementation methods:

[0091] Example:

[0092] This embodiment discloses a method for modeling an electric-thermal coupling model of a single lithium battery.

[0093] like Figure 1 As shown, a method for modeling an electric-thermal coupling model of a single lithium battery includes:

[0094] S1: Construct a second-order RC equivalent circuit model of a single lithium battery;

[0095] S2: The parameters of the second-order RC equivalent circuit model are identified by using the least squares method using the battery experimental data at different ambient temperatures to obtain the second-order RC model parameters at different temperatures;

[0096] S3: Construct a two-state thermal model of a single lithium battery;

[0097] S4: Parameter identification of the two-state thermal model using battery experimental data;

[0098] S5: Dynamically couple the second-order RC equivalent circuit model and the two-state thermal model to obtain an electro-thermal coupling model; the electro-thermal coupling model can be used to iteratively calculate battery information of a single lithium battery during the entire discharge process.

[0099] The present invention constructs a second-order RC equivalent circuit model and a two-state thermal model for a single lithium battery. First, by constructing a second-order RC equivalent circuit model, the voltage response characteristics of the battery during the charging and discharging process can be accurately captured, including key electrical parameters such as ohmic internal resistance, polarization internal resistance and polarization capacitance, which can effectively reflect the changes in the internal state of the battery. Secondly, the influence of temperature changes on battery performance is further considered in combination with the two-state thermal model. Further, by identifying the model parameters, the influence of temperature on the electrical characteristics of the battery can be quantified, including changes in internal resistance, enhancement or weakening of polarization effects, etc. Among them, the least squares method is used to identify the model parameters, which can make full use of the information in the experimental data and improve the accuracy of the model parameters. Finally, the second-order RC model parameters at different temperatures are obtained by experimental identification at different ambient temperatures, so that more comprehensive model parameters can be obtained, thereby improving the adaptability of the model under different temperature conditions.

[0100] The present invention dynamically couples the second-order RC equivalent circuit model and the two-state thermal model to obtain an electro-thermal coupling model. First, the establishment of the electro-thermal coupling model can simultaneously consider the electrical and thermal characteristics of the battery, thereby realizing high-precision monitoring and evaluation of the battery performance. This comprehensive evaluation method is more accurate than considering the electrical or thermal characteristics alone, and can better reflect the actual working state of the battery. Secondly, the electro-thermal coupling model also considers the dynamic changes of the battery during the discharge process. Through cyclic iterative calculations, we can update the battery information in real time, including voltage, current, temperature and remaining capacity, so as to realize continuous monitoring of battery performance. Finally, the electro-thermal coupling model provides more accurate data support for the battery management system (BMS). By real-time monitoring of the electrical and thermal characteristics of the battery, the BMS can more accurately judge the key indicators such as the battery's health status, remaining life and safety; and based on the prediction results of the electro-thermal coupling model, a more reasonable charging and discharging strategy can be formulated to avoid the occurrence of dangerous situations such as overcharging, over-discharging or overheating of the battery, thereby extending the service life of the battery.

[0101] In order to better introduce the technical solution of the present invention, this embodiment is described through the following parts.

[0102] First and second order RC equivalent circuit model

[0103] In this embodiment, a second-order RC equivalent circuit model is used as the electrical model of the lithium battery, which has higher accuracy and moderate computational complexity than the first-order RC model. The key parameters of the electrical model (such as ohmic resistance, polarization resistance and polarization capacitance) are identified by the least squares method, and a three-dimensional mapping relationship between the model parameters and the state of charge (SOC) and temperature is established to ensure that the model can dynamically reflect the changes in the electrical characteristics of the lithium battery.

[0104] The second-order RC equivalent circuit model is as follows Figure 2 As shown, the left part of the model C b Indicates the capacity of the battery (Ah), the current source I b The right side of the model is the controlled voltage source U ocv , ohmic resistor R0 and two RC polarization loops are connected in series, U ocv Represents the open circuit voltage of the battery; R0 is used to simulate the response characteristics of the terminal voltage when the instantaneous current excitation changes suddenly; R p and R s is the polarization resistance, C p and C s For polarized capacitors, two RC polarization loops are used to simulate the electrochemical polarization and concentration polarization of the battery. t Indicates the battery terminal voltage.

[0105] Specifically, we need to find the continuous state space expression of the second-order RC equivalent circuit model, with the current I b is the input variable of the model, terminal voltage U t is the model output variable, [x(t),U p (t),U s (t)] T is the system state variable, the expression can be obtained as follows:

[0106]

[0107] Where: x(t) represents the battery SOC at time t; U p and U s They represent the polarization voltage of the two RC parallel circuits of the battery; η is the coulomb efficiency; C b Indicates battery capacity; I b Indicates the battery current; U ocv represents the open circuit voltage of the battery; R0 represents the ohmic resistance; R p and R s Represents polarization resistance; C p and C s represents polarized capacitance; T represents ambient temperature;

[0108] Discretize the continuous state space expression of the second-order RC equivalent circuit model, and obtain the state space expression of the second-order RC equivalent circuit model in discrete time domain:

[0109]

[0110] Where: Δt represents the sampling period; k represents the sampling time point.

[0111] 2. Parameter identification of the second-order RC equivalent circuit model

[0112] 1. Battery test data

[0113] 1) Battery experimental data includes data obtained through battery capacity test experiments;

[0114] The experimental steps of the battery capacity test experiment include:

[0115] S201: Place the experimental target battery in an incubator, adjust the incubator temperature to 25°C, and leave for 3 hours;

[0116] S202: Set the charging program to constant current-constant voltage charging, the charging voltage is 4.2V, the charging current is a standard charging current rate of 0.5C; define the stop condition when full (cut-off voltage is 4.2V, cut-off current is 0.05C), and leave it for 3 hours after full charge;

[0117] Among them, the current rate C of the single lithium battery charge and discharge rate The calculation formula is:

[0118]

[0119] Where: i b Indicates the battery charging and discharging current; C b Indicates the battery capacity.

[0120] S203: adjusting the temperature of the incubator to the experimental target temperature and leaving it for 6 hours;

[0121] The experimental target temperatures include 35°C, 25°C (room temperature), 15°C, 5°C, and -5°C;

[0122] S204: setting the discharge program to constant current discharge, the current rate to 0.5C, and defining the stop condition at the end of discharge (the cut-off voltage is 2.5V);

[0123] S205: Repeat steps S201 to S204 several times (three times), and calculate an average value of the battery capacities measured several times.

[0124] 2) Battery experimental data includes data obtained through intermittent pulse discharge test experiments;

[0125] The experimental steps of the intermittent pulse discharge test experiment include:

[0126] S211: Place the experimental target battery in an incubator, adjust the incubator temperature to 25°C, and leave for 3 hours;

[0127] S212: The charging program is set to constant current-constant voltage charging. The charging and cut-off conditions are consistent with those in the capacity test experiment. After being fully charged, the charging is left for 3 hours.

[0128] S213: adjusting the temperature of the incubator to the experimental target temperature and leaving it for 6 hours;

[0129] The experimental target temperatures include 35℃, 25℃, 15℃, 5℃ and -5℃;

[0130] S214: Set the discharge program to constant current discharge, the current rate to 1C, the discharge time to 6 minutes, and the protection condition to the cut-off voltage to 2.5V. This step reduces the battery SOC by 10%;

[0131] S215: leaving the single lithium battery for 1 hour;

[0132] S216: Steps S214 to S215 are cycled ten times, at which point the total discharge capacity of the experimental target battery is (just about) 100% capacity.

[0133] 2. Least Squares Method

[0134] The least squares method is an algorithm widely used for parameter identification, and the battery model is a nonlinear system, and its parameter identification also widely uses the least squares method. Therefore, the parameter identification method used in this embodiment is the least squares method. Figure 3 As shown, a single cell battery parameter identification simulation model is built based on the Matlab / Simulink simulation platform. Figure 3 In the figure, the I_discharge module imports the data information of the discharge current changing with time as the battery discharge current source; Li-ion battery represents the lithium-ion second-order equivalent battery model; V_bat represents the terminal voltage signal of the battery, which is output to the oscilloscope and output port 1.

[0135] The parameter identification flow chart is as follows: Figure 4 As shown in the figure, the mapping relationship between the model parameters and SOC at the corresponding temperature is established by looking up the table and interpolation method. According to the results of the battery intermittent discharge test, there are 11 SOC breakpoints with an interval of 0.1. Before running, the battery discharge current and terminal voltage data files are imported into the model, and then the model parameters are identified by the least squares fitting tool.

[0136] like Figure 5As shown in the figure, it is a comparison between the experimental value of the battery terminal voltage and the model simulation value in the 25℃ intermittent pulse discharge test experiment. The fitting effect of the simulation curve in the figure is good, the absolute value of the maximum error voltage is less than 0.2V, and the accuracy is high, which meets the use requirements of the battery system.

[0137] like Figure 6 As shown, it is a three-dimensional relationship image of each model parameter changing with temperature and SOC. After identifying the second-order RC model parameters at different temperatures, the three-dimensional relationship of each second-order RC model parameter changing with temperature and SOC is established according to the fitting method and interpolation method, so that the second-order RC model parameters at the corresponding temperature can be directly obtained according to the current temperature and SOC of the single lithium battery.

[0138] It should be emphasized that this embodiment is an intermittent pulse discharge test experiment under different ambient temperatures, and each discharge capacity is 10% of the battery SOC. Since the discharge process is short and the current is not large, the temperature rise of the battery during the discharge stage is small. Figure 7 The figure shows the temperature change curve of the battery in the intermittent pulse discharge test experiment. It can be seen that the temperature rise is about 1-2°C during each 10% SOC discharge process of the battery. Therefore, the influence of the temperature rise in this process on the battery model parameters will be ignored in this embodiment.

[0139] 3. Two-state thermal model

[0140] like Figure 8 As shown in the figure, the two-state thermal model divides the battery into two parts: the core and the surface. Assuming that the temperature distribution on the battery surface is uniform and the heat is only generated by the chemical reaction inside the battery without external heat source, the two-state thermal model can be expressed as:

[0141]

[0142] Where: and Respectively represent the rate of change of battery surface temperature and core temperature; R c and R u Respectively represent the equivalent internal thermal resistance and the equivalent external thermal resistance; C s and C c They represent the surface concentrated heat capacity and the core concentrated heat capacity respectively; Q represents the heat generated inside the battery; T amb In order to facilitate understanding, the above thermal model can be constructed as a second-order RC equivalent circuit model similar to that of electricity, such as Fig. 9 shown.

[0143] Since the heat generated by lithium batteries is mainly Joule heat generated by the internal resistance of the battery, this embodiment only considers the heat generated by the Joule heat of the battery, and the reversible heat can be ignored because of its low proportion. The value of Q can be calculated according to the BERNARDI formula:

[0144] Q=I×(U ocv -U t ).

[0145] 4. Parameter Identification of Two-State Thermal Model

[0146] 1. Battery test data

[0147] 1) Before obtaining battery experimental data, conduct a battery drilling preparatory experiment;

[0148] The experimental steps of the battery drilling preparation experiment include:

[0149] S401: Completely drain the battery of the experimental target to avoid short circuit during drilling;

[0150] S402: In a protective operating box, drill a hole from the center of the anode or cathode of the battery (if there is an air pressure valve, do not drill from this pole). During the drilling process, keep it perpendicular to the plane where this pole of the battery is located to avoid drilling crookedly and damaging the internal structure of the battery;

[0151] S403: Select a thermocouple that fits the battery size and place it in the hole. The length of the thermocouple placed inside the battery should be half the height of the battery and should be placed perpendicular to the plane where the electrodes are located.

[0152] S404: Use insulating silicone with good thermal conductivity to seal the gap between the thermocouple and the drilled hole to ensure the normal operation of the battery;

[0153] S405: Compare the battery charging and discharging test with the external characteristics before drilling to ensure that the whole process has no significant impact on the battery characteristics before conducting subsequent scheduled experiments.

[0154] 2) Battery experimental data includes data obtained from battery temperature rise test experiments;

[0155] The experimental steps of the battery temperature rise test experiment include:

[0156] S411: placing the experimental target battery in an incubator, adjusting the incubator temperature to 25° C., and leaving it for 3 hours;

[0157] S412: Set the charging program to constant current-constant voltage charging, the charging voltage is 4.2V, the charging current is a standard charging current rate of 0.5C, the stop condition when full is defined (the cut-off voltage is 4.2V, the cut-off current is 0.05C), and leave it for 3 hours after full charge;

[0158] S413: Set the discharge program to constant current discharge with a current rate of 1C, define the stop condition at the end of discharge (cut-off voltage is 2.5V), and record the middle surface temperature and internal core temperature of the battery during the entire discharge process.

[0159] 2. Least Squares Method

[0160] The least square method is still used for the parameter identification method of the single battery thermal model. A program for identifying the battery thermal model parameters is written based on the software Matlab. The identification flow chart of the program is as follows: Fig.10 The main idea of ​​the identification process is to compare the temperature simulation value calculated by the model with the temperature value obtained by the experiment. If the two do not match, the thermal model parameters will be corrected by the least square method until the error between the two is reduced to the required range. In this case, the thermal model parameters R can be identified. c , R u , C s and C c .

[0161] 5. Electrical-thermal coupling model

[0162] During the operation of the battery, the heat generated by the electrochemical reaction inside the battery will cause the battery temperature to change. The change in battery temperature will cause the battery model parameters to change. The change in battery model parameters will cause the polarization voltage inside the battery to change, thereby affecting the heat generated by the electrochemical reaction inside the battery. This embodiment analyzes this mutual coupling relationship through an electric-thermal coupling model. Fig.11 Shown is a schematic diagram of the calculation process of the electrical-thermal coupling model of a single battery.

[0163] Combination Fig.11 As shown in the figure, the working logic of the electric-thermal coupling model includes:

[0164] S501: The single lithium battery is left for a long enough time (internal polarization effect basically disappears) so that the internal polarization voltage can be regarded as 0, the battery terminal voltage is approximately equal to the internal open circuit voltage, and the battery core temperature and surface temperature are also regarded as being consistent with the ambient temperature. The initial values ​​of various variables at this time are brought into the electric-thermal coupling model;

[0165] S502: Inputting current information of a single lithium battery;

[0166] S503: Calculate each voltage value of the second-order RC equivalent circuit model when discharging starts, and update the SOC information;

[0167] S504: Calculate the heat generated Q at this time; substitute Q into the two-state thermal model to calculate the core temperature and surface temperature of the single lithium battery at the next moment;

[0168] The formula is:

[0169] Q=I×(U ocv -U t );

[0170] Where: I represents current; U t Indicates the terminal voltage of the battery; U ocv Indicates open circuit voltage;

[0171] S505: Calculate the average temperature T by core temperature and surface temperature a ; The average temperature T a Substitute into the second-order RC equivalent circuit model;

[0172] The formula is:

[0173]

[0174] S506: According to the average temperature T a The second-order RC model parameters at the next moment are obtained by looking up the table with SOC information;

[0175] S507: updating the second-order RC equivalent circuit model by using the second-order RC model parameters at the next moment, and calculating various voltage values ​​and SOC information at the next moment;

[0176] S508: Execute S504 to S507 in a loop to calculate the battery information of the single lithium battery during the entire discharge process, including SOC, various voltage values, core temperature and surface temperature.

[0177] This embodiment verifies the validity of the single-cell electric-thermal coupling model based on a constant current discharge experiment, and verifies it by comparing the external characteristics of the terminal voltage changing with time during the discharge experiment. The constant current discharge experiment steps are similar to the capacity test experiment steps, and only the experimental temperature and discharge current rate need to be modified, so the experimental steps are not repeated. This embodiment conducted a constant current discharge experiment at 1C at an ambient temperature of 25°C. Fig.12 and Fig.13 The following are the curves showing the variation of the experimental and simulated values ​​of the battery terminal voltage over time for the electrical model and the electrical-thermal coupling model, respectively. The percentage error E in the figure is defined as:

[0178]

[0179] It can be seen that the electro-thermal model has a good simulation effect and can simulate the external characteristics of the battery within the error range. Compared with the electrical model, the electro-thermal coupling model has improved the simulation effect of the external characteristics of the battery, especially at low SOC. The electro-thermal coupling model can better simulate the external characteristic behavior of the single lithium battery. The estimated battery temperature has a good tracking characteristic with the actual battery temperature, which meets the accuracy requirements of the estimation, making this method particularly suitable for the development of module-level battery pack models and battery management systems.

[0180] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the technical solution. Those skilled in the art should understand that those modifications or equivalent substitutions of the technical solution of the present invention that do not depart from the purpose and scope of the technical solution should be included in the scope of the claims of the present invention.

Claims

1. A method for modeling an electric-thermal coupling model of a single lithium battery, characterized in that: include: S1: Construct a second-order RC equivalent circuit model of a single lithium battery; S2: The parameters of the second-order RC equivalent circuit model are identified by using the least squares method using the battery experimental data at different ambient temperatures to obtain the second-order RC model parameters at different temperatures; S3: Construct a two-state thermal model of a single lithium battery; S4: Parameter identification of the two-state thermal model using battery experimental data; S5: Dynamically couple the second-order RC equivalent circuit model and the two-state thermal model to obtain an electro-thermal coupling model; the electro-thermal coupling model can be used to iteratively calculate battery information of a single lithium battery during the entire discharge process.

2. The method for modeling the electric-thermal coupling model of a single lithium battery according to claim 1, characterized in that: In step S1, the formula of the second-order RC equivalent circuit model is expressed as: Where: x(t) represents the battery SOC at time t; U p and U s They represent the polarization voltage of the two RC parallel circuits of the battery; η is the coulomb efficiency; C b Indicates battery capacity; I b Indicates the battery current; U ocv represents the open circuit voltage of the battery; R0 represents the ohmic resistance; R p and R s Represents polarization resistance; C p and C s represents polarized capacitance; T represents ambient temperature; Discretize the continuous state space expression of the second-order RC equivalent circuit model, and obtain the state space expression of the second-order RC equivalent circuit model in discrete time domain: Where: Δt represents the sampling period; k represents the sampling time point.

3. The method for modeling the electric-thermal coupling model of a single lithium battery as claimed in claim 2, characterized in that: In step S2, after the second-order RC model parameters at different temperatures are identified, a three-dimensional relationship between the second-order RC model parameters and the temperature and SOC is established according to the fitting method and the interpolation method, so that the second-order RC model parameters at the corresponding temperature can be directly obtained by looking up the table according to the current temperature and SOC of the single lithium battery.

4. The method for modeling an electric-thermal coupling model of a single lithium battery as claimed in claim 1, characterized in that: In step S2, in step S2, the battery test data includes data obtained through a battery capacity test experiment; The experimental steps of the battery capacity test experiment include: S201: Place the experimental target battery in an incubator, adjust the incubator temperature to 25°C, and leave for 3 hours; S202: Set the charging program to constant current-constant voltage charging, the charging voltage is 4.2V, the charging current is a standard charging current rate of 0.5C; define the stop condition when full, and leave it for 3 hours after full; S203: adjusting the temperature of the incubator to the experimental target temperature and leaving it for 6 hours; The experimental target temperatures include 35℃, 25℃, 15℃, 5℃ and -5℃; S204: setting the discharge program to constant current discharge, with a current ratio of 0.5C, and defining a stop condition at the end of the discharge; S205: Repeat steps S201 to S204 several times, and calculate an average value of the battery capacities measured several times.

5. The method for modeling an electric-thermal coupling model of a single lithium battery as claimed in claim 4, characterized in that: In step S2, in step S2, the battery experimental data includes data obtained through an intermittent pulse discharge test experiment; The experimental steps of the intermittent pulse discharge test experiment include: S211: Place the experimental target battery in an incubator, adjust the incubator temperature to 25°C, and leave for 3 hours; S212: The charging program is set to constant current-constant voltage charging, the charging and cut-off conditions are consistent with the capacity test experiment, and the charging is left for 3 hours after being fully charged; S213: adjusting the temperature of the incubator to the experimental target temperature and leaving it for 6 hours; The experimental target temperatures include 35℃, 25℃, 15℃, 5℃ and -5℃; S214: Set the discharge program to constant current discharge, the current rate to 1C, the discharge time to 6 minutes, and the protection condition to the cut-off voltage to 2.5V. This step reduces the battery SOC by 10%; S215: leaving the single lithium battery for 1 hour; S216: Steps S214 to S215 are cycled ten times, at which point the total discharge capacity of the experimental target battery is 100% capacity.

6. The method for modeling an electric-thermal coupling model of a single lithium battery as claimed in claim 4, characterized in that: In step S2, the current rate C of the single lithium battery charge and discharge rate The calculation formula is: Where: i b Indicates the battery charging and discharging current; C b Indicates the battery capacity.

7. The method for modeling an electric-thermal coupling model of a single lithium battery as claimed in claim 2, characterized in that: In step S3, the formula of the two-state thermal model is expressed as: Where: and Respectively represent the rate of change of battery surface temperature and core temperature; R c and R u Respectively represent the equivalent internal thermal resistance and the equivalent external thermal resistance; C s and C c They represent the surface concentrated heat capacity and the core concentrated heat capacity respectively; Q represents the heat generated inside the battery; T amb Indicates the ambient temperature.

8. The method for modeling an electric-thermal coupling model of a single lithium battery as claimed in claim 1, characterized in that: In step S4, before obtaining the battery experimental data, a battery drilling preparation experiment is performed; The experimental steps of the battery drilling preparation experiment include: S401: Completely drain the battery of the experimental target to avoid short circuit during drilling; S402: In an operating box with protective measures, drilling is performed from the center of the anode or cathode of the battery; S403: Select a thermocouple that fits the battery size and place it in the hole. The length of the thermocouple placed inside the battery should be half the height of the battery and should be placed perpendicular to the plane where the electrodes are located. S404: Use insulating silicone with good thermal conductivity to seal the gap between the thermocouple and the drilled hole to ensure the normal operation of the battery; S405: Perform a charge and discharge test on the battery and compare the external characteristics before drilling to ensure that the whole process has no impact on the battery characteristics.

9. The method for modeling an electric-thermal coupling model of a single lithium battery as claimed in claim 8, characterized in that: In step S4, the battery experimental data includes data obtained from a battery temperature rise test experiment; The experimental steps of the battery temperature rise test experiment include: S411: placing the experimental target battery in an incubator, adjusting the incubator temperature to 25° C., and leaving it for 3 hours; S412: Set the charging program to constant current-constant voltage charging, the charging voltage is 4.2V, the charging current is a standard charging current rate of 0.5C, the stop condition when full is defined, and leave it for 3 hours after full; S413: Set the discharge program to constant current discharge with a current rate of 1C, define the stop condition at the end of discharge, and record the middle surface temperature and internal core temperature of the battery during the entire discharge process.

10. The method for modeling an electric-thermal coupling model of a single lithium battery as claimed in claim 7, characterized in that: In step S5, the working logic of the electrical-thermal coupling model includes: S501: Bringing the initial values ​​of various variables into the electrical-thermal coupling model; S502: Inputting current information of a single lithium battery; S503: Calculate each voltage value of the second-order RC equivalent circuit model when discharging starts, and update the SOC information; S504: Calculate the heat generated Q at this time; substitute Q into the two-state thermal model to calculate the core temperature and surface temperature of the single lithium battery at the next moment; The formula is: Q=I×(U ocv -U t ); Where: I represents current; U t Indicates the terminal voltage of the battery; U ocv Indicates open circuit voltage; S505: Calculate the average temperature T by core temperature and surface temperature a ; The average temperature T a Substitute into the second-order RC equivalent circuit model; The formula is: S506: According to the average temperature T a The second-order RC model parameters at the next moment are obtained by looking up the table with SOC information; S507: updating the second-order RC equivalent circuit model by using the second-order RC model parameters at the next moment, and calculating various voltage values ​​and SOC information at the next moment; S508: Execute S504 to S507 in a loop to calculate the battery information of the single lithium battery during the entire discharge process, including SOC, various voltage values, core temperature and surface temperature.

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