Voltage prediction method of lithium battery in standing state after charging

Abstract

The invention discloses a method for predicting the voltage of a lithium battery in a standing state after charging, and the method comprises the following steps: (1) deducing a relational expression between the potential Uoc of a positive electrode and a negative electrode of the lithium battery and the proportion x (t) of lithium ions on the positive electrode and the proportion y (t) of lithium ions on the negative electrode based on a Nernst equation; (2) analyzing the change relation of the voltage of the lithium battery in the standing state after charging along with time, predicting the positive and negative electrode potentials Uoc of the lithium battery in the standing state after charging, and establishing a CVSP prediction model; and (3) through a parameter identification method, using the CVSP prediction model to predict the voltage change condition of the lithium battery in a standing state after charging. According to the method, the problem that the SOC estimation error of a common open-circuit voltage method is large is solved, and the maximum prediction error is controlled within 0.015 V.

Description

Technical Field

[0001] The present invention relates to the technical field of lithium battery voltage prediction, and in particular to a method for predicting the voltage of a lithium battery in a static state after being charged. Background Art

[0002] During use, lithium batteries are in an alternating state of discharge, charge and rest. Their voltage will be unstable under the action of polarization, especially the open circuit voltage in the rest state after charging will change with the rest time, which will lead to a large estimation error of the SOC estimation method based on the open circuit voltage. Therefore, how to improve the accuracy of charge estimation for the voltage of lithium batteries in the rest state after charging has become a difficult problem that needs to be solved urgently. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a voltage prediction method for a lithium battery in a static state after charging, which solves the problem of large SOC estimation error of the commonly used open circuit voltage method and controls the maximum prediction error within 0.015V.

[0004] In order to solve the above technical problems, the present invention adopts the following technical solution: A voltage prediction method of a lithium battery in a static state after charging of the present invention has the following innovative features:

[0005] (1) Based on the Nernst equation, the positive and negative electrode potentials U of lithium batteries are derived. oc The relationship between the proportion of lithium ions on the positive electrode x(t) and the proportion of lithium ions on the negative electrode y(t);

[0006] (2) Analyze the relationship between the voltage of the lithium battery in the static state after charging and time, which is used to predict the positive and negative electrode potentials U of the lithium battery in the static state after charging. oc , and establish a CVSP prediction model;

[0007] (3) Through the parameter identification method, the CVSP prediction model is used to predict the voltage change of the lithium battery in the static state after charging.

[0008] Preferably, in the above step (1), the specific process for deriving the relationship between the potential of the positive and negative electrodes of the lithium battery and the proportion of lithium ions on the positive electrode and the proportion of lithium ions on the negative electrode is:

[0009] (1.1) During the charging and discharging process, the lithium battery completes the conversion between electrical energy and chemical energy by embedding and de-embedding the lithium ions inside it at its positive and negative electrodes. Therefore, when the lithium battery is in a static state after charging, its battery terminal voltage is

[0010]

[0011] Where U ocIndicates the positive and negative electrode potential of lithium battery; Indicates the positive electrode potential of the lithium battery; Indicates the negative electrode potential of lithium battery;

[0012] (1.2) According to the positive electrode reaction during the charging and discharging process of lithium batteries, combined with the Nernst equation, the relationship between the positive electrode potential of lithium batteries and the activity of their component substances is determined as follows:

[0013]

[0014] In the formula, represents the standard redox potential of the positive electrode material LiFePO4; T represents the thermodynamic temperature; R represents the molar gas constant; n represents the number of electrons gained or lost in the battery reaction; F represents the Faraday constant; as well as are the activities of the positive electrode components;

[0015] According to the negative electrode reaction during the charge and discharge process of the lithium battery, combined with the Nernst equation, the relationship between the negative electrode potential of the lithium battery and the activity of its component substances is determined as follows:

[0016]

[0017] In the formula, Represents the standard redox potential of graphite, the negative electrode material; and a C Both represent the activity of negative electrode component materials;

[0018] (1.3) Considering that the above activities are difficult to quantify, according to the principle of lithium batteries, when the structural morphology changes of the positive and negative electrode oxides and the reduced products are not considered, the proportion of lithium ions on the positive electrode x(t) and the proportion of lithium ions on the negative electrode y(t) are used to replace the activities of the corresponding substances respectively. Then, the relationship between the positive and negative electrode potentials of lithium batteries and the proportion of lithium ions on the positive electrode and the proportion of lithium ions on the negative electrode is:

[0019]

[0020] Preferably, in the above step (2), according to the electrochemical principle, the changes in the lithium ion ratio x(t) on the positive electrode and the lithium ion ratio y(t) on the negative electrode are related to the lithium ion diffusion rate near the electrodes, that is, when the lithium battery is in a static state after charging, due to the concentration difference between the reactants formed by charging and the solution body, the lithium ions attached to the surfaces of the positive and negative electrodes will diffuse, thereby reducing the lithium ion ratio y(t) on the negative electrode and increasing the lithium ion ratio x(t) on the positive electrode; therefore, the voltage of the lithium battery in the static state after charging will decrease.

[0021] Preferably, in the above step (2), the specific process of establishing the CVSP prediction model is:

[0022] (2.1) According to Fick’s law, the lithium ion ratio x(t) on the positive electrode and the lithium ion ratio y(t) on the negative electrode are both related to the diffusion degree of lithium ions near their surfaces along the concentration gradient direction, and the diffusion degree is expressed by the diffusion flux J, that is,

[0023]

[0024] Where D is the diffusion coefficient; C is the lithium ion concentration; l represents the distance between the position where the lithium ion concentration is C and the electrode; Represents the gradient of lithium ion concentration along the diffusion direction;

[0025] (2.2) Assume that the rate of change of the amount of lithium ion substance passing through the diffusion cross section per unit time is Then formula (5) can be written as

[0026]

[0027] In the formula, A represents the cross-sectional area in the diffusion direction; M represents the molar mass of lithium ions;

[0028] (2.3) Due to the gradient of lithium ion concentration along the diffusion direction It changes slowly over time, so is approximately a constant, then under charging conditions, the relationship between the change in the proportion of lithium ions x(t) on the positive electrode and the proportion of lithium ions y(t) on the negative electrode with respect to time is:

[0029]

[0030] In the formula, x0 represents the initial value of the lithium ion ratio on the positive electrode after charging; y0 represents the initial value of the lithium ion ratio on the negative electrode after charging; Represents the rate of change of positive electrode lithium ions with respect to time; Indicates the rate of change of negative electrode lithium ions with respect to time;

[0031] (2.4) Since the changes of x(t) and y(t) are very small, the above formula (7) is substituted into formula (4), and the CVSP prediction model can be obtained as follows:

[0032]

[0033] In the formula, U0 represents the terminal voltage after charging without considering the concentration polarization factor; It represents the coefficient of change of positive electrode potential caused by lithium ion diffusion; It indicates the coefficient of change of negative electrode potential caused by lithium ion diffusion.

[0034] Preferably, in the above step (3), according to the positive and negative electrode potentials U of the lithium battery under different charging test conditionsoc The experimental observation value is used to obtain the model parameter θ that minimizes the sum of squares of the cumulative errors between the experimental observation value and the estimated value of the CVSP prediction model by using the criterion of the minimum residual square of the least square method, and its expression is

[0035]

[0036] In the formula, Yes i The estimated value of the CVSP prediction model for the static voltage after charging at the moment; U oc (t i ) is t i is the experimental observation value of the static voltage after charging at time; k refers to the number of voltage data obtained from the static experiment after charging;

[0037] The above model parameters θ include U0, x0, y0, and Then, by substituting the identified parameter θ into the above formula (8), the relationship between the static voltage of the lithium battery after charging and time can be predicted, and then the static voltage of the lithium battery after charging can be predicted.

[0038] Beneficial effects of the present invention: The present invention solves the problem of large SOC estimation error of the commonly used open circuit voltage method, and controls the maximum prediction error within 0.015V. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0040] Figure 1 This is a schematic diagram of a voltage prediction method for a lithium battery in a static state after being charged according to the present invention. DETAILED DESCRIPTION

[0041] The technical solution of the present invention will be clearly and completely described below through specific implementation methods.

[0042] A method for predicting the voltage of a lithium battery in a static state after charging of the present invention is as follows: Figure 1 As shown, the following steps are included:

[0043] (1) Based on the Nernst equation, the positive and negative electrode potentials U of lithium batteries are derived. oc The relationship between the proportion of lithium ions on the positive electrode x(t) and the proportion of lithium ions on the negative electrode y(t).

[0044] In the above steps, the specific process of deriving the relationship between the positive and negative electrode potentials of the lithium battery and the proportion of lithium ions on the positive electrode and the proportion of lithium ions on the negative electrode is:

[0045] (1.1) During the charging and discharging process, the lithium battery completes the conversion between electrical energy and chemical energy by embedding and de-embedding the lithium ions inside it at its positive and negative electrodes. Therefore, when the lithium battery is in a static state after charging, its battery terminal voltage is

[0046]

[0047] Where U oc Indicates the positive and negative electrode potential of lithium battery; Indicates the positive electrode potential of the lithium battery; Indicates the negative electrode potential of lithium battery;

[0048] (1.2) According to the positive electrode reaction during the charging and discharging process of lithium batteries, combined with the Nernst equation, the relationship between the positive electrode potential of lithium batteries and the activity of their component substances is determined as follows:

[0049]

[0050] In the formula, represents the standard redox potential of the positive electrode material LiFePO4; T represents the thermodynamic temperature; R represents the molar gas constant; n represents the number of electrons gained or lost in the battery reaction; F represents the Faraday constant; as well as are the activities of the positive electrode components;

[0051] According to the negative electrode reaction during the charge and discharge process of the lithium battery, combined with the Nernst equation, the relationship between the negative electrode potential of the lithium battery and the activity of its component substances is determined as follows:

[0052]

[0053] In the formula, Represents the standard redox potential of graphite, the negative electrode material; and a C Both represent the activity of negative electrode component materials;

[0054] (1.3) Considering that the above activities are difficult to quantify, according to the principle of lithium batteries, when the structural morphology changes of the positive and negative electrode oxides and the reduced products are not considered, the proportion of lithium ions on the positive electrode x(t) and the proportion of lithium ions on the negative electrode y(t) are used to replace the activities of the corresponding substances respectively. Then, the relationship between the positive and negative electrode potentials of lithium batteries and the proportion of lithium ions on the positive electrode and the proportion of lithium ions on the negative electrode is:

[0055]

[0056] (2) Analyze the relationship between the voltage of the lithium battery in the static state after charging and time, which is used to predict the positive and negative electrode potentials U of the lithium battery in the static state after charging. oc , and establish a CVSP prediction model.

[0057] In the above steps, according to the electrochemical principles, the changes in the lithium ion ratio x(t) on the positive electrode and the lithium ion ratio y(t) on the negative electrode are related to the lithium ion diffusion rate near the electrodes, that is, when the lithium battery is in a static state after charging, due to the concentration difference between the reactants formed by charging and the solution body, the lithium ions attached to the surfaces of the positive and negative electrodes will diffuse, thereby reducing the lithium ion ratio y(t) on the negative electrode and increasing the lithium ion ratio x(t) on the positive electrode; therefore, the voltage of the lithium battery in the static state after charging will decrease.

[0058] In the above steps, the specific process of establishing the CVSP prediction model is as follows:

[0059] (2.1) According to Fick’s law, the lithium ion ratio x(t) on the positive electrode and the lithium ion ratio y(t) on the negative electrode are both related to the diffusion degree of lithium ions near their surfaces along the concentration gradient, and the diffusion degree is expressed by the diffusion flux J, that is,

[0060]

[0061] Where D is the diffusion coefficient; C is the lithium ion concentration; l represents the distance between the position where the lithium ion concentration is C and the electrode; Represents the gradient of lithium ion concentration along the diffusion direction;

[0062] (2.2) Assume that the rate of change of the amount of lithium ion substance passing through the diffusion cross section per unit time is Then formula (5) can be written as

[0063]

[0064] In the formula, A represents the cross-sectional area in the diffusion direction; M represents the molar mass of lithium ions;

[0065] (2.3) Due to the gradient of lithium ion concentration along the diffusion direction It changes slowly over time, so is approximately a constant, then under charging conditions, the relationship between the change in the proportion of lithium ions x(t) on the positive electrode and the proportion of lithium ions y(t) on the negative electrode with respect to time is:

[0066]

[0067] In the formula, x0 represents the initial value of the lithium ion ratio on the positive electrode after charging; y0 represents the initial value of the lithium ion ratio on the negative electrode after charging; Represents the rate of change of positive electrode lithium ions with respect to time; Indicates the rate of change of negative electrode lithium ions with respect to time;

[0068] (2.4) Since the changes of x(t) and y(t) are very small, the above formula (7) is substituted into formula (4), and the CVSP prediction model can be obtained as follows:

[0069]

[0070] In the formula, U0 represents the terminal voltage after charging without considering the concentration polarization factor; It represents the coefficient of change of positive electrode potential caused by lithium ion diffusion; It indicates the coefficient of change of negative electrode potential caused by lithium ion diffusion.

[0071] (3) Through the parameter identification method, the CVSP prediction model is used to predict the voltage change of the lithium battery in the static state after charging.

[0072] In the above steps, according to the positive and negative electrode potentials U of the lithium battery under different charging experimental conditions oc The experimental observation value is used to obtain the model parameter θ that minimizes the sum of squares of the cumulative errors between the experimental observation value and the estimated value of the CVSP prediction model by using the criterion of the minimum residual square of the least square method, and its expression is

[0073]

[0074] In the formula, Yes i The estimated value of the CVSP prediction model for the static voltage after charging at the moment; U oc (t i ) is t i is the experimental observation value of the static voltage after charging at time; k refers to the number of voltage data obtained from the static experiment after charging;

[0075] The above model parameters θ include U0, x0, y0, and Then, by substituting the identified parameter θ into the above formula (8), the relationship between the static voltage of the lithium battery after charging and time can be predicted, and then the static voltage of the lithium battery after charging can be predicted.

[0076] Beneficial effects of the present invention: The present invention solves the problem of large SOC estimation error of the commonly used open circuit voltage method, and controls the maximum prediction error within 0.015V.

[0077] The embodiments described above are merely descriptions of preferred implementation modes of the present invention, and are not intended to limit the concept and scope of the present invention. Without departing from the design concept of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary engineering technicians in the field should fall within the protection scope of the present invention. The technical contents for which protection is sought in the present invention have been fully recorded in the technical requirements.

Claims

1. A method for predicting the voltage of a lithium battery in a static state after charging, characterized in that The following steps are involved: (1) Based on the Nernst equation, the positive and negative electrode potentials U of lithium batteries are derived. oc The relationship between the proportion of lithium ions on the positive electrode x(t) and the proportion of lithium ions on the negative electrode y(t); (2) Analyze the relationship between the voltage of the lithium battery in the static state after charging and time, which is used to predict the positive and negative electrode potentials U of the lithium battery in the static state after charging. oc , and establish a CVSP prediction model; (3) Through the parameter identification method, the CVSP prediction model is used to predict the voltage change of the lithium battery in the static state after charging.

2. The method for predicting voltage of a lithium battery in a static state after charging according to claim 1, characterized in that: In the above step (1), the specific process of deriving the relationship between the potential of the positive and negative electrodes of the lithium battery and the proportion of lithium ions on the positive electrode and the proportion of lithium ions on the negative electrode is: (1.1) During the charging and discharging process, the lithium battery completes the conversion between electrical energy and chemical energy by embedding and de-embedding the lithium ions inside it at its positive and negative electrodes. Therefore, when the lithium battery is in a static state after charging, its battery terminal voltage is Where U oc Indicates the positive and negative electrode potential of lithium battery; Indicates the positive electrode potential of the lithium battery; Indicates the negative electrode potential of lithium battery; (1.2) According to the positive electrode reaction during the charging and discharging process of lithium batteries, combined with the Nernst equation, the relationship between the positive electrode potential of lithium batteries and the activity of their component substances is determined as follows: In the formula, represents the standard redox potential of the positive electrode material LiFePO4; T represents the thermodynamic temperature; R represents the molar gas constant; n represents the number of electrons gained or lost in the battery reaction; F represents the Faraday constant; as well as are the activities of the positive electrode components; According to the negative electrode reaction during the charge and discharge process of the lithium battery, combined with the Nernst equation, the relationship between the negative electrode potential of the lithium battery and the activity of its component substances is determined as follows: In the formula, Represents the standard redox potential of graphite, the negative electrode material; and a C Both represent the activity of negative electrode component materials; (1.3) Considering that the above activities are difficult to quantify, according to the principle of lithium batteries, when the structural morphology changes of the positive and negative electrode oxides and the reduced products are not considered, the proportion of lithium ions on the positive electrode x(t) and the proportion of lithium ions on the negative electrode y(t) are used to replace the activities of the corresponding substances respectively. Then, the relationship between the positive and negative electrode potentials of lithium batteries and the proportion of lithium ions on the positive electrode and the proportion of lithium ions on the negative electrode is:

3. The method for predicting the voltage of a lithium battery in a static state after charging according to claim 2, characterized in that: In the above step (2), according to the electrochemical principle, the changes in the lithium ion ratio x(t) on the positive electrode and the lithium ion ratio y(t) on the negative electrode are related to the lithium ion diffusion rate near the electrodes, that is, when the lithium battery is in a static state after charging, due to the concentration difference between the reactants formed by charging and the solution body, the lithium ions attached to the positive and negative electrode surfaces will diffuse, thereby reducing the lithium ion ratio y(t) on the negative electrode and increasing the lithium ion ratio x(t) on the positive electrode; therefore, the voltage of the lithium battery in the static state after charging will decrease.

4. The method for predicting the voltage of a lithium battery in a static state after charging according to claim 3, characterized in that: In the above step (2), the specific process of establishing the CVSP prediction model is as follows: (2.1) According to Fick’s law, the lithium ion ratio x(t) on the positive electrode and the lithium ion ratio y(t) on the negative electrode are both related to the diffusion degree of lithium ions near their surfaces along the concentration gradient, and the diffusion degree is expressed by the diffusion flux J, that is, Where D is the diffusion coefficient; C is the lithium ion concentration; l represents the distance between the position where the lithium ion concentration is C and the electrode; Represents the gradient of lithium ion concentration along the diffusion direction; (2.2) Assume that the rate of change of the amount of lithium ion substance passing through the diffusion cross section per unit time is Then formula (5) can be written as In the formula, A represents the cross-sectional area in the diffusion direction; M represents the molar mass of lithium ions; (2.3) Due to the gradient of lithium ion concentration along the diffusion direction It changes slowly over time, so is approximately a constant, then under charging conditions, the relationship between the change in the proportion of lithium ions x(t) on the positive electrode and the proportion of lithium ions y(t) on the negative electrode with respect to time is: In the formula, x0 represents the initial value of the lithium ion ratio on the positive electrode after charging; y0 represents the initial value of the lithium ion ratio on the negative electrode after charging; Indicates the rate of change of positive electrode lithium ions with respect to time; Indicates the rate of change of negative electrode lithium ions with respect to time; (2.4) Since the changes of x(t) and y(t) are very small, the above formula (7) is substituted into formula (4), and the CVSP prediction model can be obtained as follows: In the formula, U0 represents the terminal voltage after charging without considering the concentration polarization factor; It represents the coefficient of change of positive electrode potential caused by lithium ion diffusion; It indicates the coefficient of change of negative electrode potential caused by lithium ion diffusion.

5. The method for predicting voltage of a lithium battery in a static state after charging according to claim 4, characterized in that: In the above step (3), according to the positive and negative electrode potentials U of the lithium battery under different charging test conditions oc The experimental observation value is used to obtain the model parameter θ that minimizes the sum of squares of the cumulative errors between the experimental observation value and the estimated value of the CVSP prediction model by using the criterion of the minimum residual square of the least square method, and its expression is In the formula, Yes i The estimated value of the CVSP prediction model for the static voltage after charging at the moment; U oc (t i ) is t i is the experimental observation value of the static voltage after charging at time; k refers to the number of voltage data obtained from the static experiment after charging; The above model parameters θ include U0, x0, y0, and Then, by substituting the identified parameter θ into the above formula (8), the relationship between the static voltage of the lithium battery after charging and time can be predicted, and then the static voltage of the lithium battery after charging can be predicted.

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