Method for constructing equivalent circuit model of lithium titanate battery based on electrode ion solid-phase diffusion process

Abstract

The invention discloses a construction method of a lithium titanate battery equivalent circuit model based on an electrode ion solid phase diffusion process, and relates to the technical field of new energy lithium ion batteries. Determining the corresponding relation between the balance potential of the positive and negative electrodes and the OCV of the whole battery by fitting the actually measured open-circuit voltage and the synthesized OCV of the whole battery, and obtaining the initial average lithiation state of the positive and negative electrodes; establishing a positive and negative electrode ion solid-phase diffusion model based on the positive and negative electrode voltage and the total battery end voltage under different-rate constant-current charging and discharging; dynamic performance parameters of the lithium titanate battery equivalent circuit model are decoupled and identified through a pulse current experiment, and finally the lithium titanate battery equivalent circuit model based on the electrode ion solid phase diffusion process is formed. According to the lithium titanate battery equivalent circuit model based on the electrode ion solid phase diffusion process provided by the invention, the accurate simulation of the full-interval voltage of the lithium titanate battery under a large current rate is realized, and a model support is provided for the power prediction of the lithium titanate battery under a short time scale.

Description

Technical Field

[0001] This invention relates to the field of new energy lithium-ion battery technology, specifically a method for constructing an equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process. Background Technology

[0002] Lithium titanate (LTi) batteries, due to their excellent rate performance, long cycle life, and wide temperature range operation, have become crucial energy storage components in key fields such as rail transportation, military, and aerospace. However, the voltage response of LTi batteries is complex and variable, significantly affected by factors such as temperature and current rate, and closely coupled with electrode OCP, temperature, and polarization processes. This places higher demands on the battery models and state estimation of existing battery management systems. Traditional equivalent circuit models, such as multi-order RC equivalent circuit models, have significant limitations in simulating the voltage dynamic characteristics of LTi batteries under actual operating conditions, especially at high current rates and wide temperature ranges. They struggle to fully capture the internal dynamic processes of the battery, posing a serious challenge to the development of high-precision algorithms and low-cost model calculations for LTi batteries. Therefore, there is an urgent need to construct an equivalent circuit model that balances model accuracy and computational efficiency, capable of simulating the high-rate and wide-temperature conditions of LTi batteries under actual operating conditions. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for constructing an equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process, which aims to balance computational efficiency and model accuracy, and solve the technical problems of low voltage accuracy of existing RC equivalent circuit models at high current rates and in high and low SOC ranges.

[0004] To address the aforementioned technical problems, embodiments of the present invention provide the following technical solution: an equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process, comprising the following steps:

[0005] Obtain basic data for lithium titanate batteries;

[0006] By fitting the measured OCV and the synthesized OCV of the full cell, the correspondence between the positive and negative electrode OCP and the full cell OCV is determined, and the initial average SOL of the positive and negative electrodes is obtained.

[0007] Based on the positive and negative electrode OCP and the full cell terminal voltage under constant current charge and discharge at different rates, a solid-phase diffusion model of positive and negative electrode ions is established.

[0008] By decoupling and identifying the dynamic performance parameters in the solid-phase diffusion process model of positive and negative electrode ions, an equivalent circuit model of lithium titanate battery based on the solid-phase diffusion process of electrode ions is formed, enabling accurate simulation of the full voltage range of lithium titanate battery under high current rate.

[0009] Preferably, the basic data of the lithium titanate battery includes the positive electrode OCP-SOL curve, the negative electrode OCP-SOL curve, and the measured OCV-SOC (State of Charge, SOC) curve of the entire cell;

[0010] Preferably, obtaining the full-cell synthesized OCV includes: converting the positive and negative electrode OCP-SOL curves to the full-cell SOC scale, and then subtracting the negative electrode OCP curve from the converted positive electrode OCP curve.

[0011] Preferably, obtaining the initial average SOL of the positive and negative electrodes includes: based on the matching relationship between the positive and negative electrode OCP-SOL curves obtained by fitting the measured OCV and synthesized OCV of the full cell and the full cell OCV-SOC curve, obtaining the corresponding SOL at the positive and negative electrode OCP corresponding to the current full cell OCV, denoted as and .

[0012] Preferably, the solid-state diffusion process model of positive and negative electrode ions describes the correspondence between current and electrode SOL offset and the lumped DC internal resistance. The model parameters can be obtained based on the positive and negative electrode OCP and the full battery terminal voltage under different constant current charging and discharging rates, according to the first preset formula.

[0013] Preferably, the first preset formula is as follows:

[0014]

[0015]

[0016] In the formula, k and b are the parameters of the ion solid-phase diffusion equation to be fitted based on constant current charge-discharge experiments at different rates, and I is the current. This indicates the offset of the electrode lithiation state at the corresponding current rate. The shift in the lithiation state of an electrode under quasi-equilibrium conditions, where the electrode is fully lithium-intercalated (positive electrode) or delithiated (negative electrode), relative to the electrode's lithiation state at SOC=0 in the full cell, is measured on a full cell scale. R represents the shift in the lithiation state of the electrode at the corresponding current rate, where the electrode is fully lithium-intercalated (positive electrode) or delithiated (negative electrode), relative to the lithiation state of the electrode at SOC=0 in the full cell at the full cell scale. sum V is the lumped DC internal resistance, and V is the measured terminal voltage of the full cell at the corresponding current rate. OCV was synthesized for full cells.

[0017] Preferably, the dynamic performance parameters in the equivalent circuit model of the lithium titanate battery include: ohmic polarization on a short time scale, activation polarization on a medium time scale, and diffusion polarization on a long time scale. These parameters can be identified by pulse current experiments, based on the second preset formula and parameters of the model, and decoupled identification of the target function.

[0018] Preferably, the second preset formula of the model is as follows:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] In the formula, R sum R0 and R1 are the lumped DC internal resistance, ohmic polarization internal resistance and activation polarization internal resistance, respectively; V(t) and I(t) are the functions of the full cell terminal voltage and current as a function of time, respectively, t0 is the initial no-current state time, and t1 is the pulse current excitation time; and SOL PE (t) represents the time-varying functions of the average lithiation state of the cathode solid phase and the surface lithiation state, respectively. and SOL NE (t) represent the time-dependent functions of the average lithiation state of the solid phase and the surface lithiation state, respectively; Q PE and Q NE The maximum usable capacity of the positive and negative electrodes, τ, are respectively. PE and τ NE These are the diffusion polarization time constants for the positive and negative electrodes, respectively. and points Do not use SOL as the lithiation state. PE (t), SOL NE The positive and negative electrode OCP corresponding to time (t), k p and b p To fit the parameters of the positive electrode diffusion equation, k n and b n The parameters of the fitted negative electrode diffusion equation are given, and C1 is the activation polarization capacitor.

[0027] Preferably, the parameter identification objective function is as follows:

[0028]

[0029] In the formula, V is the measured terminal voltage of the full cell at the corresponding current rate. To simulate the full battery terminal voltage in the model, θ is the dynamic performance parameter to be identified, the subscript j is the index of the sampling data point, and n represents the total number of sampling data points.

[0030] The beneficial effects of the above-described technical solution of the present invention are as follows:

[0031] By utilizing constant current charge-discharge experiments at different rates and pulse current experiments, a solid-phase diffusion model of positive and negative electrode ions was established. By decoupling and identifying the dynamic performance parameters of the equivalent circuit model of lithium titanate battery, an equivalent circuit model of lithium titanate battery based on the solid-phase diffusion process of electrode ions was formed. This enabled accurate simulation of the full voltage range of lithium titanate battery under high current rate, providing model support for power prediction of lithium titanate battery on a short time scale, and is of great significance for the development of state estimation algorithms for battery management systems. Attached Figure Description

[0032] Figure 1 This diagram illustrates the steps involved in constructing the equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process of the present invention.

[0033] Figure 2 This is a schematic diagram of the equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process of the present invention.

[0034] Figure 3 This is a diagram showing the correspondence between the positive and negative electrodes OCP-SOL and the full cell OCV-SOC according to an embodiment of the present invention;

[0035] Figure 4 This is a diagram showing the relationship between current and SOL offset of positive and negative electrodes according to an embodiment of the present invention;

[0036] Figure 5 This is a diagram showing the verification results of the model voltage accuracy under constant current and DST conditions in an embodiment of the present invention.

[0037] Figure 6 This is a comparison chart of the relative voltage errors of two models under constant current (4C) and DST conditions, according to an embodiment of the present invention. Detailed Implementation

[0038] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0039] The relevant parameter terms in this invention include OCV, SOC, OCP, and SOL, which respectively represent the open-circuit voltage of the full cell, the state of charge of the full cell, the electrode equilibrium potential, and the state of lithiation of the electrode; OCP-SOL and OCV-SOC are the corresponding curves of the electrode equilibrium potential and the state of lithiation of the electrode, and the corresponding curves of the open-circuit voltage of the full cell and the state of charge.

[0040] Reference Figure 1 An equivalent circuit model of a lithium titanate battery based on the solid-phase diffusion process of electrode ions is proposed. This model is established using constant current charge-discharge experiments at different rates and pulse current experiments to model the solid-phase diffusion process of positive and negative electrode ions. The dynamic performance parameters of the equivalent circuit model are identified through decoupling, thus forming an equivalent circuit model of a lithium titanate battery based on the solid-phase diffusion process of electrode ions. The model includes the following steps:

[0041] S1. Obtain basic data for lithium titanate batteries;

[0042] S2. By fitting the measured OCV and the synthesized OCV of the full cell, the correspondence between the positive and negative electrode OCP and the full cell OCV is determined, and the initial average SOL of the positive and negative electrodes is obtained.

[0043] S3. Based on the positive and negative electrode OCP and the full cell terminal voltage under constant current charge and discharge at different rates, establish a solid-phase diffusion model of positive and negative electrode ions;

[0044] S4. Decoupling and identifying dynamic performance parameters in the equivalent circuit model of lithium titanate battery based on the electrode ion solid-phase diffusion process, forming an equivalent circuit model of lithium titanate battery based on the electrode ion solid-phase diffusion process.

[0045] In step S1 above, the basic data of the lithium titanate battery obtained include the positive electrode OCP-SOL curve, the negative electrode OCP-SOL curve, and the measured OCV-SOC (State Of Charge, SOC) curve of the whole cell.

[0046] In step S2 above, obtaining the full-cell synthesis OCV includes converting the positive and negative electrode OCP-SOL curves to the full-cell SOC scale, and then subtracting the negative electrode OCP curve from the converted positive electrode OCP curve.

[0047] In step S2 above, obtaining the initial average SOL of the positive and negative electrodes includes matching the positive and negative electrode OCP-SOL curves with the full-cell OCV-SOC curve obtained by fitting the measured OCV and synthesized OCV of the full cell, and obtaining the corresponding SOL at the positive and negative electrode OCP corresponding to the current full-cell OCV, denoted as and .

[0048] In step S3 above, the correspondence between the current and the electrode SOL offset described by the solid-state diffusion model of positive and negative electrodes, as well as the lumped DC internal resistance, can be obtained based on the positive and negative electrode OCP and the full battery terminal voltage under different constant current charge and discharge rates, according to the following formula:

[0049]

[0050]

[0051] In the formula, k and b are the parameters of the ion solid-phase diffusion equation to be fitted based on constant current charge-discharge experiments at different rates, and I is the current. This indicates the offset of the electrode lithiation state at the corresponding current rate. The shift in the lithiation state of an electrode under quasi-equilibrium conditions, where the electrode is fully lithium-intercalated (positive electrode) or delithiated (negative electrode), relative to the electrode's lithiation state at SOC=0 in the full cell, is measured on a full cell scale. R represents the shift in the lithiation state of the electrode at the corresponding current rate, where the electrode is fully lithium-intercalated (positive electrode) or delithiated (negative electrode), relative to the lithiation state of the electrode at SOC=0 in the full cell at the full cell scale. sum V is the lumped DC internal resistance, and V is the measured terminal voltage of the full cell at the corresponding current rate. OCV was synthesized for full cells.

[0052] In step S4 above, the dynamic performance parameters of the equivalent circuit model of the lithium titanate battery include ohmic polarization on a short timescale, activation polarization on a medium timescale, and diffusion polarization on a long timescale. These parameters are obtained through pulse current experiments based on parameter identification of the objective function and the following decoupling identification:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] In the formula, R sum R0 and R1 are the lumped DC internal resistance, ohmic polarization internal resistance and activation polarization internal resistance, respectively; V(t) and I(t) are the functions of the full cell terminal voltage and current as a function of time, respectively, t0 is the initial no-current state time, and t1 is the pulse current excitation time; and SOL PE (t) represents the time-varying functions of the average lithiation state of the cathode solid phase and the surface lithiation state, respectively. and SOL NE (t) represent the time-dependent functions of the average lithiation state of the solid phase and the surface lithiation state, respectively; Q PE and Q NE The maximum usable capacity of the positive and negative electrodes, τ, are respectively. PE and τ NE These are the diffusion polarization time constants for the positive and negative electrodes, respectively. and The lithiation state is SOL. PE (t), SOL NE The positive and negative electrode OCP corresponding to time (t), k p and b p To fit the parameters of the positive electrode diffusion equation, k n and b n The parameters of the fitted negative electrode diffusion equation are given, where C1 is the activation polarization capacitor. The objective function for parameter identification is shown in the following equation:

[0061]

[0062] In the formula, V is the measured terminal voltage of the full cell at the corresponding current rate. To simulate the full battery terminal voltage in the model, θ is the dynamic performance parameter to be identified, the subscript j is the index of the sampling data point, and n represents the total number of sampling data points.

[0063] In this embodiment, a schematic diagram of the equivalent circuit model of a lithium titanate battery based on the diffusion equations of the positive and negative electrodes is shown below. Figure 2 As shown; using a commercially available 25Ah lithium titanate battery as a reference, the basic data of the lithium titanate battery, including the positive electrode OCP-SOL curve, the negative electrode OCP-SOL curve, and the measured OCV-SOC curve of the whole cell, were first obtained. By fitting the measured OCV of the whole cell with the synthesized OCV, the correspondence between the positive and negative electrode OCP and the whole cell OCV was obtained (e.g., Figure 3 (As shown). Next, based on the positive and negative electrode OCP and the full battery terminal voltage under constant current charge and discharge rates at different rates, the lumped DC internal resistance is determined, and a diffusion equation model for charging and discharging of the positive and negative electrodes is established. The electrode diffusion equation parameter k is obtained through the correspondence between the current and the SOL offset of the positive and negative electrodes. p b p k n and b n (like Figure 4 As shown, where Figure 4 In the middle (a), the results of the charging parameter fitting are shown. Figure 4(b) shows the discharge fitting parameter results. Then, the dynamic performance parameters in the equivalent circuit model of the lithium titanate battery are divided into ohmic polarization on a short time scale, activation polarization on a medium time scale, and diffusion polarization on a long time scale. Using pulse current, decoupling identification is performed according to the model's preset formula and objective function, and finally, an equivalent circuit model of the lithium titanate battery based on the diffusion equations of the positive and negative electrodes is formed.

[0064] In this embodiment, the traditional second-order RC equivalent circuit model and the invented lithium titanate battery equivalent circuit model based on the electrode ion solid-phase diffusion process are compared through a 4C constant current experiment. Figure 5 (a) and DST conditions ( Figure 5 (b) The model voltage accuracy was verified. The error results were compared with those of the traditional second-order RC equivalent circuit model (as shown in Figures 1-2). Figure 6 (a) Figure 6 As shown in (b), the relative estimation error of the equivalent circuit model of lithium titanate battery based on the electrode ion solid-phase diffusion process does not exceed ±3%, which is smaller than that of the traditional second-order RC equivalent circuit model. It realizes accurate simulation of the full range voltage of lithium titanate battery under high current rate.

[0065] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0066] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0067] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0068] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0069] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for constructing an equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process, characterized in that, Includes the following steps: Obtain basic data for lithium titanate batteries, including positive electrode OCP-SOL curves, negative electrode OCP-SOL curves, and measured OCV-SOC curves for the entire cell; By fitting the measured OCV of the full cell with the synthesized OCV of the full cell, the correspondence between the positive and negative electrode OCP and the full cell OCV is determined, and the initial average SOL of the positive and negative electrodes is obtained. Based on the positive and negative electrode OCP and the full cell terminal voltage under constant current charge and discharge at different rates, a solid-phase diffusion process model of positive and negative electrode ions is established. The dynamic performance parameters of the positive and negative electrode ions during solid-phase diffusion are decoupled and identified, forming an equivalent circuit model of lithium titanate battery based on the electrode ion solid-phase diffusion equation.

2. The method for constructing the equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process according to claim 1, characterized in that, The method for obtaining the full-cell synthesized OCV is as follows: convert the positive electrode OCP-SOL curve and the negative electrode OCP-SOL curve to the full-cell SOC scale, and subtract the converted negative electrode OCP-SOL curve from the converted positive electrode OCP-SOL curve to obtain the full-cell synthesized OCV.

3. The method for constructing the equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process according to claim 1, characterized in that, The initial average SOL of the positive and negative electrodes is the corresponding SOL at the positive and negative electrodes OCP corresponding to the current full cell OCV, denoted as and .

4. The method for constructing the equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process according to claim 1, characterized in that, The solid-state diffusion process model of positive and negative electrode ions describes the correspondence between current and electrode SOL offset and the lumped DC internal resistance. The model parameters are based on the positive and negative electrode OCP and the full battery terminal voltage under different constant current charging and discharging rates, and are obtained according to the first preset formula.

5. The method for constructing the equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process according to claim 4, characterized in that, The first preset formula is: ； ； In the formula, k and b are the parameters of the ion solid-phase diffusion equation to be fitted based on constant current charge-discharge experiments at different rates, and I is the current. This indicates the offset of the electrode lithiation state at the corresponding current rate; The shift of the lithiation state of the electrode under quasi-equilibrium conditions, where the electrode is fully lithium-intercalated or delithilated, relative to the electrode lithiation state at SOC=0 in the full cell at the full cell scale. R represents the shift in the lithiation state of the electrode at the corresponding current rate (when lithium is fully inserted or delithiated) relative to the lithiation state of the electrode at SOC=0 in the full cell on a full cell scale. sum V is the lumped DC internal resistance, and V is the measured terminal voltage of the full cell at the corresponding current rate. OCV was synthesized for full cells.

6. The method for constructing the equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process according to claim 1, characterized in that, The dynamic performance parameters in the equivalent circuit model of the lithium titanate battery include: ohmic polarization on a short time scale, activation polarization on a medium time scale, and diffusion polarization on a long time scale. The objective function is decoupled and identified using pulse current experiments based on the second preset formula and parameters of the model.

7. The method for constructing the equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process according to claim 6, characterized in that, The second preset formula is: ； ； ； ； ； ； ； In the formula, R sum R0 and R1 are the lumped DC internal resistance, ohmic polarization internal resistance and activation polarization internal resistance, respectively; V(t) and I(t) are the functions of the full cell terminal voltage and current as a function of time, respectively, t0 is the initial no-current state time, and t1 is the pulse current excitation time; and SOL PE (t) represents the time-varying functions of the average lithiation state of the cathode solid phase and the surface lithiation state, respectively. and SOL NE (t) represent the time-dependent functions of the average lithiation state of the solid phase and the surface lithiation state, respectively; Q PE and Q NE The maximum usable capacity of the positive and negative electrodes, τ, are respectively. PE and τ NE These are the diffusion polarization time constants for the positive and negative electrodes, respectively. and The lithiation state is SOL. PE (t), SOL NE The positive and negative electrode OCP corresponding to time (t), k p and b p To fit the parameters of the positive electrode diffusion equation, k n and b n The parameters of the fitted negative electrode diffusion equation are given, and C1 is the activation polarization capacitor.

8. The method for constructing the equivalent circuit model of a lithium titanate battery based on the electrode ion solid-phase diffusion process according to claim 6, characterized in that, The formula for the objective function of parameter identification is as follows: ； In the formula, V is the measured terminal voltage of the full cell at the corresponding current rate. To simulate the full battery terminal voltage in the model, the subscript j is the index of the sampling data point, n represents the total number of sampling data points, θ is the dynamic performance parameter to be identified, and τ PE and τ NE C1 represents the diffusion polarization time constants of the positive and negative electrodes, respectively, and C2 represents the activation polarization capacitor.

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