Simple lithium ion battery physical dynamic modeling method for fast charging

Abstract

The invention provides a simple lithium ion battery physical dynamic modeling method for fast charging. The method comprises the following steps: S01, designing a characteristic test signal; S02, constructing an ohmic impedance response module; S03, constructing a diffusion dynamic voltage drop module; s04, an open-circuit voltage lookup table module is constructed; and S05, a lithium ion battery model is composed of three parts including an ohmic impedance dynamic response module, a diffusion dynamic voltage drop module and the open-circuit voltage lookup table module, and modeling is carried out on the terminal voltage, the positive electrode and the negative electrode of the whole battery. According to the method, ohmic impedance dynamic response, diffusion dynamic voltage drop and a full battery (OCV) are simulated based on a model, then the terminal voltage, the positive electrode and the negative electrode of the full battery are modeled, it is verified that the diffusion behavior of the negative electrode is a key influence factor of a low SOC error through a constant-current discharge experiment, and the dynamic response characteristic of the battery model is verified through simulation; and a feasible basis is provided for optimization of a fast charging strategy of the lithium ion battery.

Description

Technical Field

[0001] The present invention belongs to the technical field of fast charging optimization of lithium-ion batteries, and relates to a simple physical dynamic modeling method for lithium-ion batteries for fast charging. Background Art

[0002] Lithium-ion batteries have advantages such as high energy density and long cycle life, and are widely used in fields such as electric vehicles and portable devices. However, their performance is affected by the modeling accuracy of the battery management system.

[0003] Existing models have some limitations. For example, electrochemical models, although they have high accuracy, are computationally complex, have many parameters, require complex physical and chemical experiments to obtain, and are difficult to apply in real time; traditional equivalent circuit models, although they are computationally simple, ignore the diffusion process, resulting in large errors in the low SOC range. Summary of the Invention

[0004] 1. Technical problems to be solved:

[0005] Existing models have some limitations. Electrochemical models have high accuracy but are computationally complex, have many parameters, require complex physical and chemical experiments to obtain, and are difficult to apply in real time; traditional equivalent circuit models are computationally simple but ignore the diffusion process, resulting in large errors in the low SOC range.

[0006] 2. Technical solutions:

[0007] To solve the above problems, the present invention provides a simple physical dynamic modeling method for lithium-ion batteries for fast charging, including the following steps:

[0008] Step S01: Design a characteristic test signal: Design a multi-frequency sine signal as an odd-frequency random-phase multi-frequency sine signal and optimize the amplitude.

[0009] Step S02: Construct an ohmic impedance response module: Perform a characterization test on a three-electrode battery, and use the discrete Fourier transform to obtain a multi-frequency sine impedance spectrum based on the characterization test data, thereby establishing an impedance equation.

[0010] Step S03: Construct a diffusion dynamic voltage drop module: Perform constant current discharge experiments at different rates within the full SOC range, establish a diffusion equation, numerically solve it using the Chebyshev pseudospectral method, and use the simulated annealing algorithm to estimate the model parameters, and finally obtain the diffusion dynamic voltage drop.

[0011] Step S04: Construct an open-circuit voltage look-up table module: Use the incremental OCV method to calculate and obtain the OCV-SOC curve, directly measure the positive and negative electrode voltages using a three-electrode configuration, and construct the open-circuit voltage of the full battery.

[0012] Step S05: Based on the fact that the lithium-ion battery model consists of three parts, namely, an ohmic impedance dynamic response module, a diffusion dynamic voltage drop module, and an open-circuit voltage lookup table module, model the terminal voltage of the full battery and the positive and negative electrodes.

[0013] It further includes Step S06: Verify the dynamic response characteristics of the simplified lithium-ion battery model through simulation.

[0014] 3. Beneficial effects:

[0015] A simple physical dynamic modeling method for lithium-ion batteries for fast charging proposed by the present invention characterizes the linear ohmic impedance dynamic response of a three-electrode battery under test through a multi-frequency sine signal. Under such a very small current signal test, the SOC of the lithium battery hardly changes, so the influence of the diffusion process can be ignored. A new diffusion module is added. Through constant-current discharge testing, only voltage and current data are required, and the parameters of the diffusion module can be obtained without complex physical and chemical experiments. Through this method, the long-time kinetics related to the diffusion process and the short-time kinetics related to the ohmic dynamic response are separated, thereby improving the accuracy and calculation efficiency of the model.

[0016] The present invention simulates, based on the model, the ohmic impedance dynamic response, the diffusion dynamic voltage drop, and the full battery (OCV), then models the terminal voltage of the full battery and the positive and negative electrodes, verifies through constant-current discharge experiments that the diffusion behavior of the negative electrode is a key influencing factor for low SOC error, and verifies the dynamic response characteristics of the simplified lithium-ion battery model through simulation, providing a feasible basis for the optimization of the high-rate fast charging strategy of lithium-ion batteries. Description of the drawings

[0017] Figure 1 is a flowchart of a simple physical dynamic modeling method for lithium-ion batteries for fast charging.

[0018] Figure 2 is a schematic diagram of a design method for an odd-frequency random-phase multi-frequency sine signal.

[0019] Figure 3 is a physical diagram of a three-electrode battery and a schematic diagram of a three-electrode battery model.

[0020] Figure 4 is a schematic diagram of the structure of a simple physical dynamic model of a lithium-ion battery.

[0021] Figure 5 is a simulation result diagram of the terminal voltage of a simple physical dynamic model of a lithium-ion battery.

[0022] Figure 6 is a simulation result diagram of the terminal voltage and the positive / negative electrode potentials of a simple physical dynamic model of a lithium-ion battery. Detailed implementation manners

[0023] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0024] As Figure 1 shown, the present invention provides a simple physical dynamic modeling method for fast-charging lithium-ion batteries, including the following steps:

[0025] Step S01: Design a characteristic test signal: Design a multi-frequency sine signal as an odd-numbered frequency random-phase multi-frequency sine signal and optimize the amplitude.

[0026] Step S02: Construct an ohmic impedance response module: Characterize and test a three-electrode battery, and use the discrete Fourier transform on the characterization test data to obtain a multi-frequency sine impedance spectrum, thereby establishing an impedance equation.

[0027] Step S03: Construct a diffusion dynamic voltage drop module: Conduct constant current discharge experiments at different rates within the full SOC range, establish a diffusion equation, numerically solve it using the Chebyshev pseudospectral method, and use the simulated annealing algorithm to estimate the model parameters, and finally obtain the diffusion dynamic voltage drop.

[0028] Step S04: Construct an open-circuit voltage lookup table module: Calculate and obtain the OCV-SOC curve using the incremental OCV method, directly measure the positive and negative electrode voltages using a three-electrode configuration, and construct the open-circuit voltage of the full battery.

[0029] Step S05: Based on the lithium-ion battery model consisting of three parts, namely, an ohmic impedance dynamic response module, a diffusion dynamic voltage drop module, and an open-circuit voltage lookup table module, model the terminal voltage and positive and negative electrodes of the full battery.

[0030] The following will describe each step in detail.

[0031] Step S01: Design an odd-numbered random-phase multi-frequency sine current excitation signal and optimize the amplitude.

[0032] In an embodiment of the present invention, the multi-frequency sine signal is designed as an odd-numbered random-phase multi-frequency sine signal as the characteristic test signal of the present invention, and the expression is as follows:

[0033]

[0034] In the formula, K is the highest harmonic order, A k is the amplitude of the k-th harmonic, f s is the sampling frequency, N is the number of sampling points within a single period, the initial phase of the k-th harmonic, and n is the discrete time index.

[0035] First, to obtain a current signal with zero - mean constraint, the fundamental frequency of the 0 - th harmonic is suppressed to ensure the stable state of the battery. Then, in the zero - mean odd - frequency random - phase multi - frequency sine signal, all even - numbered harmonics within the considered bandwidth are suppressed, and any one of each group of three consecutive odd - numbered harmonics (e.g., 1, 3, 5 or 7, 9, 11) is randomly selected and suppressed. Compared with the traditional multi - frequency sine signal, by suppressing even - numbered harmonics and some odd - numbered harmonics, linear response, odd - numbered / even - numbered non - linear distortion can be distinguished, which is especially suitable for analyzing the diffusion process of the battery. The design of random phase can reduce the instantaneous current amplitude, avoid hardware overload, and also weaken the influence of noise to improve the estimation accuracy.

[0036] A larger excitation current amplitude will cause non - linear distortion of the lithium - ion battery. Therefore, the present invention selects to optimize the signal amplitude and scale it to an appropriate value. The specific expression is as follows:

[0037]

[0038] M is the target amplitude, is the scaled discrete - time signal, and u is the original signal vector. Thus, the odd - frequency random - phase multi - frequency sine signal with optimized amplitude is used as the characteristic test signal of the present invention.

[0039] Step S02: Based on the designed multi - frequency sine signal, perform characterization tests on the three - electrode battery. Transform the time - domain information data to the frequency domain through discrete Fourier transform (DFT) to obtain the multi - frequency sine impedance spectrum, and then estimate the dynamic response of the linear ohmic impedance. In the embodiment of the present invention, as Figure 2 shown, the process is as follows:

[0040] First, based on the measured current and voltage data sets, in order to make the estimation result more accurate, discard the first three cycles and calculate the average data of the remaining cycles:

[0041]

[0042] Secondly, use the multi - frequency sine signal to perform characterization tests on a 11.5 mA·h three - electrode battery. Since the current signal is small, the change in the SOC of the lithium - ion battery during the test is small, and the thermodynamics is described by the OCV section. Therefore, the diffusion process has no influence on the test results.

[0043] To further improve the accuracy of the ohmic impedance dynamic response estimation, remove the DC component to obtain the over - potential:

[0044]

[0045] Finally, the discrete Fourier transform transforms the time-domain information data obtained from the test into the frequency domain to obtain the multi-frequency sinusoidal impedance spectrum Z(K), and the relationship between the ohmic impedance dynamic response V(K) and the current I(K) and the impedance Z(K) is:

[0046] V(K) = Z(K) × I(K) + E(K)

[0047] E(K) represents the sum of the errors from any actual environment and the distortions from the non-linear battery behavior, and thus the ohmic impedance dynamic voltage response is obtained.

[0048] Step S03: Perform constant current discharge experiments at different rates within the full SOC range, establish the diffusion equation, numerically solve it using the Chebyshev pseudospectral method, and use the simulated annealing algorithm to estimate the model parameters. Finally, calculate the diffusion dynamic voltage drop. In the embodiment of the present invention, the process is as follows:

[0049] First step, construct a partial differential equation that explains the average and surface SOC changes caused by the diffusion process, and its expression is as follows:

[0050]

[0051] where τ d is the time constant related to the diffusion coefficient determined by the battery chemical materials and manufacturing process.

[0052] Secondly, set the boundary conditions, convert the continuous lithium-ion concentration distribution into the concentration at several discrete points (0 - 1) on the electrode particles, simplify the calculation while retaining the accuracy, and set the boundary conditions as:

[0053]

[0054] where Q is the parameter corresponding to the battery capacity.

[0055] Second step, use the Chebyshev pseudospectral method to convert the continuous diffusion partial differential equation into a discrete algebraic equation system, and the solution of the SOC variable z(t, 0 ≤ x ≤ 1) at the grid points x j =(1 + cos(jπ / N) / 2, j = 0, …, N can be found, and these grid points are distributed from the center to the surface of the battery particle and satisfy the equation:

[0056]

[0057] where, D 2 = D × D = (b jk )0 ≤ j ≤ N, 0 ≤ k ≤ N is the square of the derivative matrix D (here N is arbitrarily selected as 6 in this study).

[0058] In the third step, during the parameter identification process, to avoid falling into local optima and improve the voltage prediction accuracy of the model in the low SOC region, the simulated annealing algorithm is selected to estimate the parameters Q and τ of the diffusion block d , and the optimization objective of this algorithm is to minimize the cost function J, which is defined as the sum of the weighted squared errors between the measured voltage and the model output voltage:

[0059]

[0060] v(t) represents the measured voltage value, and v m (t) is the voltage calculated by the model, and σ v(t) represents the standard deviation of the voltage measurement.

[0061] In the fourth step, the diffusion dynamic voltage drop is obtained. When the battery is working, due to the diffusion process, the distribution of lithium-ion concentration in the particles is uneven. The open-circuit voltage can be represented by the lithium-ion concentration on the positive and negative electrode surfaces. Among them, the potential difference is denoted as the lithium-ion concentration. And to better suit the model proposed in the present invention, the relationship between the potential difference and the lithium concentration on the particle surface is as follows:

[0062] ΔU surf = U c (c c,surf ) - U a (c a,surf ) = U OCV (z surf ).

[0063] In addition, during the solid-phase diffusion process, the diffusion voltage loss related to the difference between the average lithium-ion concentration and the surface lithium-ion concentration can be written as an equation:

[0064]

[0065] From this, the diffusion dynamic voltage drop η D caused by the diffusion process can be obtained.

[0066] Step S04: Use the incremental OCV method to calculate and obtain the OCV-SOC curve, and directly measure the positive and negative electrode voltages using a three-electrode configuration, so as to more accurately construct the open-circuit voltage (OCV) of the full battery. In the embodiment of the present invention, the process is as follows:

[0067] First, for modeling purposes, it is assumed that the sizes and kinetics of the electrode particles in the electrode are the same. Therefore, the cathode and anode can be regarded as two electrode particles. Therefore, the battery SOC expression can be defined as:

[0068]

[0069] and Correspond to the lithium-ion concentrations at full battery charge (100% SOC) and empty battery (0% SOC), respectively.

[0070] Secondly, the incremental OCV method is used to calculate and obtain the OCV-SOC curve.

[0071] Finally, as Figure 3 shown, the three-electrode configuration used in the present invention can directly measure the OCV of the positive and negative electrodes, thereby more accurately constructing the OCV of the full battery. According to the electrochemical principle, the OCV of the battery is determined by the equilibrium potential difference between the positive and negative electrodes, and its expression is as follows:

[0072]

[0073] U c and U a are the equilibrium potentials of the positive and negative electrodes, respectively, and are the average concentrations of lithium ions in the electrode particles. Thus, the OCV of the full battery can be obtained, as Figure 4 shown.

[0074] Step S05: Based on the fact that the model consists of three parts, namely, the ohmic impedance dynamic response module, the diffusion dynamic voltage drop module, and the open circuit voltage OCV look-up table module, and model the full battery terminal voltage and the positive and negative electrodes, revealing the key influence of the negative electrode diffusion behavior on the low SOC error. In the embodiment of the present invention, the process is as follows:

[0075] By integrating the identified linear ohmic impedance module and the SOC-related diffusion module, the battery model proposed by the present invention is constructed. This battery model simulates the key dynamic characteristics of lithium-ion batteries, including ohmic response, diffusion process, and full battery OCV, and its expression is as follows:

[0076]

[0077] Thus, the simplified battery model is obtained.

[0078] Use a three-electrode battery to measure the potential dynamic responses of the positive and negative electrodes respectively. This design allows the behavior of each electrode to be analyzed separately. Therefore, the present invention models the full battery terminal voltage and the positive and negative electrodes, and calculates the difference between the surface SOC and the average SOC through a constant current discharge experiment in combination with the proposed model. It is found that at low SOC, the difference between the surface SOC and the average SOC of the negative electrode increases significantly, thereby increasing the voltage estimation error of the model. Thus, it is obtained that the negative electrode diffusion behavior is the key influencing factor for the low SOC error.

[0079] Step S06: Verify the dynamic response characteristics of the simplified lithium-ion battery model through simulation. In the embodiment of the present invention, the simulation results are as Figure 5 andFigure 6 As shown, it provides a theoretical basis and feasibility verification for the optimization of the high-rate fast charging strategy of lithium-ion batteries.

Claims

1. A simple physical dynamic modeling method for fast-charging lithium-ion batteries, characterized in that: It includes the following steps: Step S01: Design characteristic test signal: Design the multi-frequency sine signal as an odd-frequency random-phase multi-frequency sine signal and optimize the amplitude; Step S02: Construct the ohmic impedance response module: Characterize and test the three-electrode battery, and use the discrete Fourier transform based on the characterization test data to obtain the multi-frequency sine impedance spectrum, thereby establishing an impedance equation; Step S03: Construct the diffusion dynamic voltage drop module: Conduct constant current discharge experiments at different rates within the full SOC range, establish a diffusion equation, numerically solve it using the Chebyshev pseudospectral method, and use the simulated annealing algorithm to estimate the model parameters, and finally obtain the diffusion dynamic voltage drop; Step S04: Construct the open-circuit voltage look-up table module: Use the incremental OCV method to calculate and obtain the OCV-SOC curve, directly measure the positive and negative electrode voltages using the three-electrode configuration, and construct the open-circuit voltage of the full battery; Step S05: Based on the lithium-ion battery model which consists of three parts, namely the ohmic impedance dynamic response module, the diffusion dynamic voltage drop module, and the open-circuit voltage look-up table module, model the terminal voltage and the positive and negative electrodes of the full battery.

2. The simple physical dynamic modeling method for fast-charging-oriented lithium-ion batteries according to claim 1, wherein: The specific method of Step S01 is: First, suppress the fundamental frequency of the 0th harmonic; then, in the zero-mean odd-frequency random-phase multi-frequency sine signal, suppress all even harmonics within the considered bandwidth, and randomly select one odd harmonic from any one of each group of three consecutive odd harmonics and suppress it.

3. The simplified physical dynamic modeling method for fast-charging-oriented lithium-ion batteries according to claim 1, characterized in that: The expression of the multi-frequency sine signal in Step S01 is as follows: where K is the highest harmonic order, A k is the amplitude of the k-th harmonic, f s is the sampling frequency, N is the number of sampling points within a single period, is the initial phase of the k-th harmonic, and n is the discrete-time index.

4. The simple physical dynamic modeling method for fast-charging-oriented lithium-ion batteries according to claim 1, wherein: In Step S01, the specific expression for optimizing the amplitude is as follows: M is the target amplitude, is the scaled discrete-time signal, and u is the original signal vector. Thus, the odd-numbered random-phase multi-frequency sine signal with optimized amplitude is used as the characteristic test signal of the present invention.

5. The simplified physical dynamic modeling method for fast-charging-oriented lithium-ion batteries according to claim 1, characterized in that: The specific method of Step S02 is: First, based on the measured current and voltage data sets, discard the first three cycles and obtain the average data of the remaining cycles: Secondly, use the multi-frequency sine signal to conduct characterization tests on the three-electrode battery of 11.5 mAh; Remove the DC component to obtain the overpotential: Finally, transform the test-obtained time-domain information data to the frequency domain through the discrete Fourier transform to obtain the multi-frequency sine impedance spectrum Z(K), and the relationship between the ohmic impedance dynamic response V(K), the current I(K), and the impedance Z(K) is: V(K) = Z(K) × I(K) + E(K), E(K) represents the sum of the errors from any actual environment and the distortion from the non-linear battery behavior, and thus the ohmic impedance dynamic voltage response is obtained.

6. The simplified physical dynamic modeling method for a fast-charging oriented lithium-ion battery according to claim 1, wherein: The specific method of Step S03 is: The first step is to construct a partial differential equation that explains the average and surface SOC changes caused by the diffusion process, and its expression is as follows: where τ d is the time constant related to the diffusion coefficient determined by the battery chemical materials and manufacturing process, Set the boundary conditions, convert the continuous lithium-ion concentration distribution into the concentration at several discrete points on the electrode particles (0 - 1), simplify the calculation while retaining the accuracy, and set the boundary conditions as: where Q is a parameter corresponding to the battery capacity; In the second step, the Chebyshev pseudospectral method is used to transform the continuous diffusion partial differential equation into a discrete algebraic equation system, and the solution of the SOC variable z(t, 0 ≤ x ≤ 1) at the grid points x j = (1 + cos(jπ / N) / 2, j = 0, …, N is found. These grid points are distributed from the center to the surface of the battery particle and satisfy the equation: z0(t) = 0 Among them, D 2 = D×D = (b jk ) 0 ≤ j ≤ N, 0 ≤ k ≤ N is the square of the derivative matrix D; In the third step, the simulated annealing algorithm is used to estimate the parameters Q and τ of the diffusion plate d , and the optimization objective of this algorithm is to minimize the cost function J, which is defined as the sum of the weighted squared errors between the measured voltage and the model output voltage: v(t) represents the measured voltage value, and v m (t) is the voltage calculated by the model, and σ v(t) represents the standard deviation of the voltage measurement; The fourth step is to obtain the diffusion dynamic voltage drop. The open-circuit voltage is represented by the lithium-ion concentration on the positive and negative electrode surfaces. Among them, the potential difference is denoted as the lithium-ion concentration, and the relationship between the potential difference and the lithium concentration on the particle surface is as follows: ΔU surf = U c (c c,surf ) - U a (c a,surf ) = U OCV (z surf ), During the solid-phase diffusion process, the diffusion voltage loss related to the difference between the average lithium-ion concentration and the surface lithium-ion concentration is written as an equation: Thus, the diffusion dynamic pressure drop η caused by the diffusion process is obtained. D .

7. The simplified physical dynamic modeling method for fast charging-oriented lithium-ion batteries according to claim 1, characterized in that: The specific method of Step S04 is: First, for modeling purposes, it is assumed that the size and kinetics of the electrode particles within the electrodes are the same. Therefore, the cathode and anode are regarded as two electrode particles, and thus the battery SOC expression is defined as: and correspond to the lithium-ion concentrations at full battery charge (100% SOC) and empty battery (0% SOC), respectively; Secondly, the incremental OCV method is used to calculate and obtain the OCV-SOC curve; Finally, the three-electrode configuration used directly measures the OCV of the positive and negative electrodes to construct the full-cell OCV. According to the electrochemical principle, the OCV of the battery is determined by the equilibrium potential difference between the positive and negative electrodes, and its expression is as follows: U c and U a are the equilibrium potentials of the positive and negative electrodes, respectively, and is the average concentration of lithium ions in the electrode particles, from which the open-circuit voltage of the full cell is obtained.

8. The simplified physical dynamic modeling method for fast charging-oriented lithium-ion batteries according to claim 1, characterized in that: The specific method of step S05 is: by integrating the identified linear Ohmic impedance module and the SOC-related diffusion module, a battery model is constructed. The battery model simulates the key dynamic characteristics of the lithium-ion battery, including Ohmic response, diffusion process, and full-cell open-circuit voltage, and its expression is as follows: Thus, a simple battery model is obtained.

9. The simplified physical dynamic modeling method for fast-charging-oriented lithium-ion batteries according to claim 8, wherein: The potential dynamic responses of the positive and negative electrodes are measured separately using a three-electrode battery, the full-cell terminal voltage and the positive and negative electrodes are modeled, and the difference between the surface SOC and the average SOC is calculated through a constant-current discharge experiment in combination with the model.

10. The simplified physical dynamic modeling method for fast-charging-oriented lithium-ion batteries according to claim 1, characterized in that: It also includes step S06: verifying the dynamic response characteristics of the simplified lithium-ion battery model through simulation.

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