A method for predicting capacity loss of lithium-ion batteries for full lifecycle utilization

Abstract

The present invention provides a method for predicting capacity loss of lithium-ion batteries over their entire lifecycle. This method establishes an LLI capacity loss mechanism model based on chemical reaction rate analysis and a LAM capacity loss mechanism model based on fatigue crack growth. The LLI and LAM capacity loss mechanism models are used to obtain a full-lifecycle capacity loss model for the battery. Undetermined parameters in the full-lifecycle capacity loss model are identified to obtain the battery capacity loss model, which is then used to predict lithium-ion battery capacity loss. The present invention can reliably predict battery capacity loss over its entire lifecycle.

Description

Technical Field

[0001] The present invention belongs to the technical field of power battery life prediction, and specifically relates to a method for predicting capacity loss of lithium-ion batteries for full life utilization. Background Art

[0002] Lithium-ion batteries inevitably experience a decline in both available capacity and power over time. To maximize the battery's full potential, it's necessary to predict performance changes at various stages of its lifecycle before it's deployed. This allows for effective macro-level planning of battery deployment and replacement times.

[0003] Research on battery capacity loss prediction models to address this issue can be broadly categorized into four categories: empirical / semi-empirical models, data-driven models, mechanistic models, and fusion models. First, empirical / semi-empirical models rely primarily on observations of experimental data or modifications to existing mechanistic models. While these models are easy to construct because they rely solely on experimental data or existing models, their predictions may deviate from the true values ​​when battery operating conditions change. Second, data-driven models are constructed using historical and real-time data using techniques such as deep learning, machine learning, and model transfer. Data-driven approaches ignore underlying aging mechanisms and are therefore difficult to effectively extend to untrained batteries. Third, mechanistic models aim to describe the specific physical and chemical changes that occur during battery operation. However, studies based solely on chemical reaction processes overlook particle damage caused by lithium insertion and extraction, and thus fail to explain the rapid capacity decline seen in batteries during late-stage aging. Finally, the fusion model is a comprehensive reflection of multiple prediction models, extracting as much aging information as possible from historical and real-time data. Compared with a single model, this type of model has higher prediction accuracy. However, the model prediction results will be distorted by the battery operating conditions, and because many factors need to be considered at the same time, the model establishment process is relatively complicated.

[0004] Although the above modeling methods have made varying degrees of contribution to battery life prediction, they are still unable to achieve the goal of predicting the capacity attenuation of energy storage batteries throughout their life cycle under their operating conditions. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the present invention provides a lithium-ion battery capacity loss prediction method for full life cycle utilization, which can achieve reliable prediction of battery capacity loss during the entire life cycle.

[0006] The present invention achieves the above technical objectives through the following technical means.

[0007] A method for predicting capacity loss of lithium-ion batteries for full lifecycle utilization is as follows:

[0008] Establish an LLI capacity loss mechanism model based on chemical reaction rate analysis and a LAM capacity loss mechanism model based on fatigue crack growth;

[0009] Adding the LLI capacity loss mechanism model and the LAM capacity loss mechanism model to obtain a battery full life capacity loss model;

[0010] Identifying undetermined parameters in the battery full-life capacity loss model to obtain a battery capacity loss model;

[0011] The battery capacity loss model is used to predict the capacity loss of a lithium-ion battery.

[0012] In a further technical solution, the LLI capacity loss mechanism model is:

[0013]

[0014] Where: C loss,LLI is the loss of active lithium, β1, β2, β3 and β4 are all undetermined model parameters, T is the temperature of the battery, I chg is the charging current, Q Σ,chg is the total charging capacity;

[0015] In a further technical solution, the LAM capacity loss mechanism model is:

[0016]

[0017] Where: C loss,LAM is the loss of active material, SOC ANE,max is the maximum lithium insertion rate of available active negative electrode materials, SOC ANE,min is the minimum lithium insertion rate among available active negative electrode materials, C NE,0 is the initial capacity of the negative electrode material, I dis is the battery discharge current, Q Σ,dis is the total discharge capacity, γ1 is an undetermined parameter, γ2 is the initial crack length, γ3 is the expected critical crack length, and γ4 is the standard deviation of the critical crack length.

[0018] In a further technical solution, the battery life capacity loss model is:

[0019]

[0020] A further technical solution is to identify the undetermined parameters in the battery life capacity loss model by performing least squares fitting on the battery life capacity loss model to obtain the values ​​of each undetermined parameter in the model.

[0021] In a further technical solution, the battery capacity loss model is:

[0022]

[0023] In a further technical solution, the active lithium loss amount satisfies:

[0024]

[0025] in: is the loss rate of battery LLI, t chg is the charging time, b1 is the parameter related to the electron and lithium ion concentrations in the SEI film formation reaction equation, and b2 is the parameter related to the solvent molecule concentration in the SEI film formation reaction equation.

[0026] In a further technical solution, the active lithium loss also satisfies:

[0027]

[0028] Where: E a,1 The apparent activation energy associated with the SEI formation reaction, E a,2 is the apparent activation energy associated with the diffusion of solvent molecules, and R is the gas constant.

[0029] In a further technical solution, the battery discharge current also satisfies:

[0030]

[0031] in: is the crack growth rate, a crc is the crack length, N Σ is the number of cycles, h1 and m are coefficients related to material composition and structure, ΔSOC ANE is the variation range of the available graphite electrode SOC, and ΔSOC is the variation range of the graphite electrode SOC.

[0032] In a further technical solution, the γ3 and γ4 also satisfy:

[0033]

[0034] Where: χ is the loss rate of particles in the electrode.

[0035] The beneficial effects of the present invention are as follows: the present invention first establishes an LLI capacity loss mechanism model based on chemical reaction rate analysis and a LAM capacity loss mechanism model based on fatigue crack extension, then obtains a battery full-life capacity loss model from the LLI capacity loss mechanism model and the LAM capacity loss mechanism model, identifies undetermined parameters in the battery full-life capacity loss model, obtains the battery capacity loss model, and uses the battery capacity loss model to predict the capacity loss of lithium-ion batteries, thereby achieving reliable prediction of the capacity loss of the battery throughout its life cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a flow chart of the method for predicting capacity loss of lithium-ion batteries for full lifecycle utilization according to the present invention;

[0037] Figure 2 This is a diagram showing the prediction effect of the battery capacity loss using the battery capacity loss model in Experiment D of the present invention;

[0038] Figure 3 This is a graph showing the prediction error of the battery capacity loss using the battery capacity loss model in Experiment D of the present invention;

[0039] Figure 4 This is a diagram showing the effect of predicting the battery capacity loss using the battery capacity loss model in Experiment E of the present invention;

[0040] Figure 5 This is a prediction error diagram of the battery capacity loss amount using the battery capacity loss model in Experiment E described in the present invention. DETAILED DESCRIPTION

[0041] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.

[0042] like Figure 1 As shown, the present invention provides a method for predicting capacity loss of lithium-ion batteries for full lifecycle utilization, which specifically includes the following steps:

[0043] Step 1: Establish an LLI capacity loss mechanism model based on chemical reaction rate analysis

[0044] The formation and thickening of the solid electrolyte interface film (SEI) on the surface of the negative electrode is the main cause of the loss of active lithium (LLI) in the battery. If it is approximately assumed that the thickness of the SEI is proportional to the amount of LLI loss caused by it, and the diffusion coefficient of the solvent molecules in the SEI does not change with the thickening of the SEI, then according to Fick's first law, the concentration of solvent molecules on the particle surface will be inversely proportional to the thickness of its SEI film, and then inversely proportional to the current LLI loss. The present invention combines the description of the correspondence between the reactant concentration and the reaction rate in the chemical reaction rate equation to obtain the relationship between the loss rate and the loss amount of the battery LLI, as shown in formula (1):

[0045]

[0046] Where, t chg is the charging time (h), I chg is the charging current (A), b1 is the parameter related to the electron and lithium ion concentrations in the SEI film formation reaction equation, b2 is the parameter related to the solvent molecule concentration in the SEI film formation reaction equation, C loss,LLI is the loss of active lithium.

[0047] The temperature of the battery will directly affect the reaction rate of the battery and promote the diffusion of solvent molecules in the SEI film. The effect of temperature on the reaction rate of the battery and the diffusion of solvent molecules in the SEI film are consistent with the Arrhenius model. The formation rate of the SEI film, that is, the relationship between the loss rate of the battery LLI and the temperature can be obtained as shown in formula (2):

[0048]

[0049] Where, T is the temperature of the battery (°C), E a,1 is the apparent activation energy related to the SEI formation reaction (J / mol), E a,2 is the apparent activation energy associated with the diffusion of solvent molecules (J / mol), and R is the gas constant (8.314 J / (mol·K)).

[0050] Combining equations (1) and (2), we can obtain the loss rate equation of LLI as shown in equation (3):

[0051]

[0052] Where b3 and b4 are material-related coefficients, and b4 = E a,1 / R+b2(E a,2 / R).

[0053] For equation (3), the initial condition is t chg =0 and C loss,LLI= 0, and the expression of battery capacity loss changing with charging time is obtained as shown in formula (4):

[0054]

[0055] Because t chg =Q Σ,chg / I chg , so the expression for battery capacity loss caused by LLI can be obtained as shown in formula (5):

[0056]

[0057] Where Q Σ,chg is the total charging capacity (Ah), which is equal to 1 / 2 of the total capacity throughput; β1, β2, β3 and β4 are all unknown model parameters, where

[0058] Step 2: Establish a LAM capacity loss mechanism model based on fatigue crack growth

[0059] Loss of active material (LAM) in the negative electrode is another important cause of battery capacity loss. The present invention describes the growth of particle cracks in lithium-ion batteries using the Paris law, a general rule for fatigue crack growth. The relationship between the crack growth rate and the stress it experiences can be expressed as follows:

[0060]

[0061] Where a crc is the crack length (m), N Σ is the number of cycles, h1 and m are coefficients related to material composition and structure, ΔK is the intensity factor amplitude, and K is the stress intensity factor. The relationship between it and the tensile stress of the opening crack satisfies formula (7):

[0062]

[0063] Where σ θ is the tangential tensile stress on the crack (Mpa), and f is the geometric correction factor.

[0064] Since the cracks on the surface of the negative electrode material are subjected to compression and tension stresses respectively when the negative electrode material is lithium-intercalated or lithium-deintercalated, and the ratio of compression to tension stress is negative, the value of the stress intensity factor amplitude of the crack during the charge and discharge process depends only on the maximum tangential tensile stress of the negative electrode material during lithium-deintercalation (discharge), that is, formula (7) can be rewritten as formula (8):

[0065]

[0066] Where σ θ,max is the maximum tangential tensile stress (Mpa) experienced by the crack.

[0067] The tangential stress on the particle surface crack under given SOC conditions is proportional to the working rate of the current, that is:

[0068] σ θ,max ∝I bat (9)

[0069] Where, I bat is the battery operating current value (A).

[0070] The tangential stress on the particles is proportional to the range of the molar concentration of lithium in the particles. For graphite particles, since the range of the molar concentration of lithium in the graphite particles is proportional to the range of the SOC of the particle electrode (i.e., ΔSOC ANE ), so we can get:

[0071] σ θ,max ∝ΔSOC ANE (10)

[0072] Since the charge and discharge process of the battery is the result of the joint action of a large number of particles in the electrode, the volume change of the particles in the electrode depends not only on the expansion and contraction of the particles themselves, but also on the interaction force between the particles, that is, the volume change of the entire electrode. Therefore, Equation (10) should be corrected to:

[0073]

[0074] Substituting equations (8), (9) and (10) into equation (6), we can obtain the differential equation between the crack growth rate and its stress influencing factors as shown in equation (12):

[0075]

[0076] Where, I dis is the battery discharge current value (A), ΔSOC ANE is the variation range of the available graphite electrode SOC, and ΔSOC is the variation range of the graphite electrode SOC.

[0077] For graphite negative electrode, its m value can be approximately taken as 2, then formula (12) can be sorted as follows:

[0078]

[0079] At the same time, due to:

[0080]

[0081] Where C bat,0is the capacity of the new battery (Ah), Q Σ is the total power throughput (Ah).

[0082] Therefore, formula (13) can be rewritten as:

[0083]

[0084] Where h1' is a coefficient related to material composition and structure and h1' = h1 / C bat,0 , SOC ANE,max is the maximum lithium insertion rate of available active negative electrode materials, SOC ANE,min It is the minimum lithium insertion rate among available active negative electrode materials.

[0085] Here, SOC ANE,max With SOC ANE,min The value will depend on the charge and discharge cut-off voltage of the cycle. Σ,dis =0, a crc =a crc,0 (Here a crc,0 When is the initial length of the crack (m), solving equation (15) we can obtain:

[0086]

[0087] Let a crc,0 =γ2,γ1=2h1', then:

[0088]

[0089] Where γ1 is the unknown parameter (A -3 h -1 ), γ2 is the initial crack length (m), Q Σ,dis is the total discharge capacity (Ah), which is equal to 1 / 2 of the total capacity throughput.

[0090] For all particles, the crack length corresponding to their separation from the electron transport network, i.e., the critical length, will show a good normal distribution law. Therefore, the function of the overall loss rate of the negative electrode material at a certain crack length can be obtained as shown in formula (18):

[0091]

[0092] Where χ is the particle loss rate in the electrode (%), γ3 is the expected critical crack length (m), and γ4 is the standard deviation of the critical crack length (m).

[0093] For a single particle, the probability of its fracture occurring during the entire cycle is equal. The lithium content in the isolated region can be considered to be the same as the average lithium content of the active negative electrode material during the cycle, and the resulting battery capacity loss can be obtained as shown in formula (19):

[0094]

[0095] Where C loss,LAM is the loss of active material, C NE,0 is the initial capacity of the negative electrode material (Ah).

[0096] Substituting equations (17) and (18) into equation (19), we can obtain a comprehensive expression for the battery capacity loss caused by LAM, as shown in equation (20):

[0097]

[0098] Step 3: Establish a battery life capacity loss model under multi-stress coupling conditions

[0099] At this point, by combining equations (5) and (20), we can get the battery life capacity loss model as shown in equation (21). In the constant current cycle condition, I chg =–I dis =|I bat |, Q Σ,chg =Q Σ,dis =Q Σ / 2, while SOC ANE,max With SOC ANE,min Depends on the battery's charge and discharge limit voltage U bat,max with U bat,min Therefore, the input phasor of the battery life capacity loss model can be recorded as [T,I bat ,U bat,max ,U bat,min ,Q Σ ], record the battery life capacity loss output as C loss .

[0100]

[0101] Step 4: Parameter identification of the battery life capacity loss model to obtain a complete battery capacity loss model

[0102] This study used LFP / graphite batteries as the research object, with the selected samples all being 32650 lithium-ion batteries with a nominal capacity of 5Ah. Five sets of experiments were designed: Experiments A, B, and C served as training experiments for model parameter identification, while Experiments D and E were used to verify the model's prediction accuracy.

[0103] To shorten the total duration of the experiment and obtain sufficient experimental data, the intervals between the capacity test experiments will be selected from three cycle intervals: 50, 100, or 200 cycles, depending on the different capacity loss rates under various aging conditions. The operating conditions of the five battery cycle aging experiments A, B, C, D, and E are (1C, 60℃, 3.65V-2.5V), (2C, 25℃, 3.65V-2.5V), (1C, 25℃, 3.65V-3.2V), (1C, 25℃, 3.65V-2.5V), and (1.5C, 40℃, 3.65V-2.9V).

[0104] Using the stress conditions corresponding to the experimental AC and the data obtained, the battery life capacity loss model (i.e., Equation (21)) was fitted with the least squares method to obtain the values ​​of the parameters to be determined in the model, specifically: β1 = 7.98 × 10 -1 , β2=8.90×10 -1 , β3=1.68×10, β4=3.51×10 3 ,γ1=2.95×10 -5 ,γ2=3.97×10 -9 ,γ3=6.44×10 -8 ,γ4=2.47×10 -8 ; Then the obtained parameters and the stress conditions corresponding to each experiment are brought back to the battery full life capacity loss model to obtain a complete battery capacity loss model, see formula (22).

[0105]

[0106] Step 5: Capacity loss prediction

[0107] In order to verify the capacity loss prediction ability of the battery capacity loss model under any given working conditions, experiments D and E were designed. The battery capacity loss was predicted using formula (22) under the working conditions of experiments D and E. In experiment D, the battery capacity loss caused by LLI and LAM under different power throughput conditions and the overall capacity loss of the battery were obtained as follows: Figure 2 As shown in Figure 2, it can be seen that good prediction results are shown throughout the battery life; Figure 3 As shown in Figure 2, the prediction error is well controlled within 5%. In Experiment E, the battery capacity loss caused by LLI and LAM under different power throughput conditions and the overall battery capacity loss are shown in Figure 2. Figure 4 As shown in , it can be seen that the prediction effect is good under different power throughputs; Figure 5 As shown, the prediction error is controlled within 5%.

[0108] The embodiments described are preferred implementations of the present invention, but the present invention is not limited to the above implementations. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention are within the scope of protection of the present invention.

Claims

1. A method for predicting capacity loss of lithium-ion batteries for full lifecycle utilization, characterized by: Establish an LLI capacity loss mechanism model based on chemical reaction rate analysis and a LAM capacity loss mechanism model based on fatigue crack growth; Adding the LLI capacity loss mechanism model and the LAM capacity loss mechanism model to obtain a battery full life capacity loss model; Identifying undetermined parameters in the battery full-life capacity loss model to obtain a battery capacity loss model; Predicting the capacity loss of a lithium-ion battery using the battery capacity loss model; The LLI capacity loss mechanism model is: Where: C loss,LLI is the loss of active lithium, β1, β2, β3 and β4 are all undetermined model parameters, T is the temperature of the battery, I chg is the charging current, Q Σ,chg is the total charging capacity.

2. The method for predicting capacity loss of a lithium-ion battery according to claim 1, wherein: The LAM capacity loss mechanism model is: Where: C loss,LAM is the loss of active material, SOC ANE,max is the maximum lithium insertion rate of available active negative electrode materials, SOC ANE,min is the minimum lithium insertion rate among available active negative electrode materials, C NE,0 is the initial capacity of the negative electrode material, I dis is the battery discharge current, Q Σ,dis is the total discharge capacity, γ1 is an undetermined parameter, γ2 is the initial crack length, γ3 is the expected critical crack length, and γ4 is the standard deviation of the critical crack length.

3. The method for predicting capacity loss of a lithium-ion battery according to claim 2, wherein: The battery life capacity loss model is:

4. The method for predicting capacity loss of a lithium-ion battery according to claim 1, wherein: Identifying the undetermined parameters in the battery life capacity loss model is to perform least squares fitting on the battery life capacity loss model to obtain the values ​​of each undetermined parameter in the model.

5. The method for predicting capacity loss of a lithium-ion battery according to claim 4, wherein: The battery capacity loss model is:

6. The method for predicting capacity loss of a lithium-ion battery according to claim 1, wherein: The active lithium loss amount satisfies: in: is the loss rate of battery LLI, t chg is the charging time, b1 is the parameter related to the electron and lithium ion concentrations in the SEI film formation reaction equation, and b2 is the parameter related to the solvent molecule concentration in the SEI film formation reaction equation.

7. The method for predicting capacity loss of a lithium-ion battery according to claim 1, wherein: The active lithium loss also satisfies: Where: E a,1 The apparent activation energy associated with the SEI formation reaction, E a,2 is the apparent activation energy related to the diffusion of solvent molecules, R is the gas constant, and b2 is the parameter related to the solvent molecule concentration in the SEI film formation reaction equation.

8. The method for predicting capacity loss of a lithium-ion battery according to claim 2, wherein: The battery discharge current also satisfies: in: is the crack growth rate, a crc is the crack length, N Σ is the number of cycles, h1 and m are coefficients related to material composition and structure, ΔSOC ANE is the variation range of the available graphite electrode SOC, and ΔSOC is the variation range of the graphite electrode SOC.

9. The method for predicting capacity loss of a lithium-ion battery according to claim 8, wherein: The γ3 and γ4 also satisfy: Where: χ is the loss rate of particles in the electrode.

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