Modeling method of molten salt material migration in liquid metal batteries based on counter-electrode batteries

Abstract

The present invention discloses a method for modeling the migration of molten salt substances in a liquid metal battery based on a counter-electrode battery. The counter-electrode battery is charged and discharged at different rates at an optimal operating temperature, and a lumped expression form is determined according to the charge and discharge curves, and the expression is solved based on a model identification algorithm. By designing a counter-electrode battery in which both the upper and lower layers of liquid metal are pure lithium, complex information on the migration of substances in the molten salt layer is obtained, and a fractional-order formula is used to characterize the migration process of substances in the molten salt. This method can quickly characterize the migration process of molten salt substances, laying the foundation for high-precision modeling and efficient management of liquid metal batteries. The characterization of the migration process of molten salt substances is an important part of full-battery modeling, and the method provided by the present invention lays the foundation for liquid metal battery management and state estimation.

Description

Technical Field

[0001] The present invention belongs to the field of liquid metal batteries, and more specifically, relates to a method for modeling the migration of molten salt substances in liquid metal batteries based on counter-electrode batteries. Background Art

[0002] Currently, the development of clean energy, including renewable energy generation and novel energy storage technologies, has become a hot topic of research. However, due to the intermittent and fluctuating nature of renewable energy generation, such as solar and wind power, direct integration into the power grid can significantly impact its safe and stable operation. Energy storage technology is crucial for shaving peak loads, improving power quality, and further enhancing the safety and stability of power systems. Among various energy storage technologies, electrochemical energy storage, due to its high specific energy, high power, and flexible design, has become a key development area for large-scale energy storage.

[0003] Liquid metal batteries are a new electrochemical energy storage technology developed in recent years for large-scale energy storage applications in power systems. Compared to traditional battery technology, liquid metal batteries, composed of liquid metal electrodes and inorganic molten salts, offer advantages such as large storage capacity, long cycle life, and low energy storage costs. Their development is expected to meet the critical requirements of large-scale energy storage applications. However, because liquid metal batteries operate under high-temperature conditions, in-situ observation of internal reactions within the battery is difficult. Molten salts, due to their complex composition, are increasingly difficult to directly capture. Existing methods for modeling molten salt migration processes suffer from high computational complexity and the inability to accurately measure model parameters. Summary of the Invention

[0004] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a method for modeling the migration of molten salt materials in a liquid metal battery based on a counter-electrode battery, thereby solving the technical problems that the existing methods for modeling the migration process of molten salt materials have large computational complexity and the model parameters cannot be accurately measured.

[0005] To achieve the above objectives, according to a first aspect of the present invention, a method for modeling molten salt material migration in a liquid metal battery based on a counter electrode battery is provided, comprising:

[0006] S1, charging and discharging a vertically placed counter electrode battery having the same molten salt composition and structure as the liquid metal battery at different rates at a preset temperature for a preset time, and collecting the charge and discharge voltages;

[0007] S2, the voltage response expression of the electrode battery during charge and discharge Characterizing the molten salt material migration process of the liquid metal battery;

[0008] S3, according to the charge and discharge voltage, identify the parameters in the voltage response expression; wherein a is the initial charging voltage without polarization stage, R dis is the ratio of discharge voltage to discharge current; b, c, d, and m are identified using an intelligent algorithm based on the charging voltage, and s is a frequency domain variable.

[0009] Preferably, b, c, d, and m are identified using a genetic algorithm based on the charging voltage, specifically:

[0010] In the initial population generation stage, the initial values ​​are set to {b0, c0, d0, m0};

[0011] In the population evolution stage, the initial value is updated and iterated to obtain {b i , c i , d i , m i};

[0012] To {b i , c i , d i , m i The root mean square error between the voltage value obtained after substituting it into the voltage response expression and the actual voltage value is used as the individual evaluation index;

[0013] When the preset number of iterations is reached, the iteration is stopped and the individual with the smallest evaluation index in the last generation of population is regarded as the optimal solution identified;

[0014] Wherein, i is the number of iterations, and the population evolution stages include parent selection, gene crossover, gene mutation and introduction of foreign individuals.

[0015] Preferably, for a 20Ah counter electrode battery, when its charge and discharge current is 1A, 2A, 3A, 4A, 5A, and 6A, its voltage response H(s) satisfies the following relationship:

[0016]

[0017] Preferably, the preset temperature is the optimal operating temperature of the molten salt electrolyte.

[0018] Preferably, when the molten salt is a mixture of LiF, LiCl, and LiBr, the optimal operating temperature is set to 550°C.

[0019] Preferably, the size of the counter electrode battery is the same as that of the stainless steel housing and the nickel foam of the liquid metal battery.

[0020] Preferably, the upper portion of the counter-electrode battery is the negative electrode, and the lower portion is the positive electrode.

[0021] According to a second aspect of the present invention, there is provided a system for modeling molten salt material migration in a liquid metal battery based on a counter electrode battery, comprising: a computer-readable storage medium and a processor;

[0022] The computer-readable storage medium is used to store executable instructions;

[0023] The processor is configured to read the executable instructions stored in the computer-readable storage medium and execute the method according to the first aspect.

[0024] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0025] The present invention provides a method for modeling the migration of molten salt substances in a liquid metal battery based on a counter-electrode battery. By designing a counter-electrode battery in which both the upper and lower layers of the liquid metal are pure lithium, complex information on the migration of substances in the molten salt layer is obtained, and a fractional-order formula is used to characterize the migration process of substances in the molten salt. This avoids the process of solving parameters such as the electrical migration and diffusion coefficient of each ion in the molten salt, and can quickly characterize the migration of molten salt substances in terms of external characteristics. The model parameters can be identified quickly, the calculation amount is small, and the accuracy is high. The characterization of the migration process of molten salt substances is an important part of full-battery modeling. The method provided by the present invention lays the foundation for the management and state estimation of liquid metal batteries. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 A structural diagram of the counter electrode battery provided by the present invention;

[0027] Figure 2 A schematic diagram of a counter electrode battery placed in a furnace provided by the present invention;

[0028] Figure 3 A charge and discharge curve diagram of the counter electrode battery provided by the present invention;

[0029] Figure 4 The charging curve of the electrode battery provided by the invention (taking I=6A as an example);

[0030] Figure 5 Schematic diagram of the model parameter identification results and fitting results provided by the present invention;

[0031] Figure 6 This is the verification result of the battery fractional-order model provided by the present invention. DETAILED DESCRIPTION

[0032] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0033] The reaction mechanism of molten salt in liquid metal batteries is unclear, and the material migration process is relatively complex, making it difficult to describe the dynamic process of molten salt. The existing methods for modeling the material migration process of molten salt are as follows:

[0034] The molten salt composition of liquid metal batteries is generally Li + Halides (such as LiF, LiCl, LiBr, LiI, etc.). The mass transfer in molten salt mainly occurs in three forms: diffusion, electromigration, and convection. The diffusion rate is proportional to the concentration gradient, the electromigration rate is related to the electric field strength in the molten salt, and the convection rate is determined by the product of the flow rate and concentration. The flux N of substance i in the molten salt is i It can be described by the Nernst-Planck equation:

[0035] N i =-D i ▽c i -z i μ i Fc i ▽φ el +μc i (1)

[0036] Where D i 、c i 、z i and μ i They represent the diffusion coefficient, concentration, charge and electromigration of ion i in the molten salt respectively; φ el represents the potential difference of the molten salt, and μ represents the convection rate. The electrical mobility is expressed by the Nernst-Einstein equation:

[0037]

[0038] Where R is the gas constant and T is the temperature. All ions must satisfy the law of conservation of mass, and there is no local charge accumulation in the molten salt. Therefore, the sum of the rate of change of any ion concentration and its divergence in the molten salt is always zero, and the molten salt is electrically neutral everywhere:

[0039]

[0040]

[0041] According to formulas (1)-(4), the molten salt electrolyte current density J el It can be obtained as shown in formula (5):

[0042]

[0043] However, the parameters such as the ion diffusion coefficient, concentration, and electrical mobility in formula (5) are difficult to solve. To this end, an embodiment of the present invention provides a method for modeling the migration of molten salt substances in a liquid metal battery based on a counter-electrode battery. The counter-electrode battery is charged and discharged at different rates at an optimal operating temperature, and the lumped expression form is determined based on the charge and discharge curves. The expression is then solved based on a model identification algorithm, specifically including:

[0044] S1, charging and discharging a vertically placed counter electrode battery having the same molten salt composition and structure as the liquid metal battery at different rates at a preset temperature for a preset time, and collecting the charge and discharge voltages thereof.

[0045] Preferably, the preset temperature is the optimal operating temperature of the molten salt electrolyte.

[0046] Preferably, when the molten salt is a mixture of LiF, LiCl, and LiBr, the optimal operating temperature is set to 550°C.

[0047] Preferably, the size of the counter electrode battery is the same as that of the stainless steel housing and the nickel foam of the liquid metal battery.

[0048] Preferably, the upper portion of the counter-electrode battery is the negative electrode, and the lower portion is the positive electrode.

[0049] Liquid metal batteries of different capacities require the design of counter-electrode cells of specific sizes. To ensure that the reaction in the molten salt is consistent with that in the full battery, the same size stainless steel casing, the same size nickel foam, and the same distance from the molten salt should be used.

[0050] In order to ensure that the direction of material movement in the molten salt is consistent with that of the entire battery, the upper part of the electrode battery is defined as the negative electrode and the lower part as the positive electrode.

[0051] The counter-electrode cell is placed vertically in a heating furnace, and the furnace temperature is set to the optimal operating temperature of the corresponding molten salt electrolyte. For example, the molten salt is a LiF|LiCl|LiBr mixture, and the optimal operating temperature is set to 550°C.

[0052] S2, the voltage response expression of the electrode battery during charge and discharge Characterizing the molten salt material migration process of the liquid metal battery;

[0053] S3, according to the charge and discharge voltage, identify the parameters in the voltage response expression; wherein a is the initial charging voltage without polarization stage, Rdis is the ratio of discharge voltage to discharge current; b, c, d, and m are identified using an intelligent algorithm based on the charging voltage, and s is a frequency domain variable.

[0054] Preferably, b, c, d, and m are identified using a genetic algorithm based on the charging voltage, specifically:

[0055] In the initial population generation stage, the initial values ​​are set to {b0, c0, d0, m0};

[0056] In the population evolution stage, the initial value is updated and iterated to obtain {b i , c i , d i , m i};

[0057] To {b i , c i , d i , m i The root mean square error between the voltage value after substituting it into the voltage response expression and the actual voltage value is used as the individual evaluation index;

[0058] When the preset number of iterations is reached, the iteration is stopped and the individual with the smallest evaluation index in the last generation of population is regarded as the optimal solution identified;

[0059] Wherein, i is the number of iterations, and the population evolution stages include parent selection, gene crossover, gene mutation and introduction of foreign individuals.

[0060] Preferably, for a 20Ah counter electrode battery, when its charge and discharge current is 1A, 2A, 3A, 4A, 5A, and 6A, its voltage response H(s) satisfies the following relationship:

[0061]

[0062] Taking the 20AH capacity liquid metal battery as an example, in order to ensure that the molten salt reaction is consistent with the full battery, Figure 1 As shown, take a stainless steel casing (70mm high, 64mm diameter) of the same size as a full 20Ah battery. Take two 40mm nickel foams and soak them with lithium. First, seal and secure the bottoms. Then, pour in a sufficient amount of molten salt and secure the tops. It's important to note that the distance between the upper and lower nickel foams in the counter electrode cell is consistent with the distance between the positive and negative electrodes in a 20Ah liquid metal battery (12.5mm).

[0063] like Figure 2 As shown, the counter electrode battery is fixed vertically on the base, placed in the furnace, and the leads are extended out of the furnace for battery testing.

[0064] The counter electrode battery is charged and discharged. Preferably, a 20Ah liquid metal battery is taken as an example with a charge and discharge rate of 0.1C-0.3C. Therefore, in this embodiment, the charge and discharge current is set to 1A-6A. It should be noted that, compared with a full battery, the counter electrode battery has no alloy positive electrode, and its capacity cannot be accurately defined. Therefore, the charge and discharge in the counter electrode battery is set with the true value of the current, not with the rate. Figure 3 The graph shows the charge and discharge curve of the electrode battery. From left to right, the voltage curves are from 1A to 6A. Figure 3 As can be seen in the figure, at the same current, the charging voltage suddenly increases, while the discharge voltage varies proportionally with the current. This indicates that polarization occurs during charging, but not during discharge. This is because low-density lithium tends to migrate upward, so the lithium in the molten salt is more likely to form a concentration difference during charging, thus causing polarization.

[0065] Figure 4 This is the charging curve of the electrode battery when I=6A, as shown in Figure 4 As shown in the figure, the charging voltage change can be divided into three stages. The voltage is relatively stable in the first stage, while the voltage suddenly rises in the second stage and stabilizes in the third stage. This shows that the internal material concentration is relatively stable in the first stage, polarization occurs in the second stage, and the material concentration stabilizes in the third stage. Similarly, the charging curves at other currents can be as follows Figure 4 It is divided into three stages.

[0066] In order to describe the charge and discharge response of the electrode molten salt, a fractional order function is used to characterize the charging process, and a constant internal resistance R is used. dis Characterizes the battery discharge internal resistance. Figure 4 The charging curve shown in the figure shows that the first stage response is represented by a, and the second and third stages are represented by the fractional order formula b / (s c +d) and delay link e m The final voltage response expression of the electrode battery is:

[0067]

[0068] Among them, R dis It can be obtained by dividing the discharge voltage by the discharge current. Parameter a is the initial polarization stage (corresponding to Figure 4 The charging voltage of the first stage (for example, the average charging voltage of the first stage) is used, while other parameters are obtained using intelligent algorithms, such as genetic algorithms. Genetic algorithms are search algorithms used to find the optimal solution to optimization problems. They obtain the optimal solution through iterative processes such as initial value selection, crossover, and mutation.

[0069] The value of parameter a is fixed. In the initial population generation stage, a vector consisting of coefficients to be identified is randomly generated according to the initial value setting range. In this example, the initial value of the vector is {b0, c0, d0, m0}. The population evolution stage is divided into four parts: parent selection, gene crossover, gene mutation and introduction of foreign individuals. The initial value is updated and iterated. The iterative vector value is {b i , c i , d i , m i}, where i represents the number of iterations.

[0070] Substitute the iterated parameters into the voltage value V obtained in formula (6) sim (t) and the actual voltage value V exp The root mean square error of (t) is used as the evaluation index, as shown in formula (7). Wherein, t represents the sampling time, preferably, sampling is performed every 1 second in this example.

[0071]

[0072] When the number of iterations is greater than 1000, the iteration is stopped, and the individual with the smallest evaluation index in the last generation of population is regarded as the optimal coefficient solution identified.

[0073] Analyze the results of all parameter values ​​under different currents. In this example, parameters c and d do not change with current, and the values ​​of parameters a, b, and m under different currents are as follows: Figure 5 As shown. Use linear fitting to interpolate the parameters a, b, and m, as shown Figure 5 As shown in the straight line, the relationship between parameters a, b, m and current can be obtained. The relationship between each parameter and current is as follows Figure 5 As shown, the voltage H(s) expression of the molten salt material migration is obtained as follows:

[0074]

[0075] by Figure 3 Take I=2A, 4A, 6A as an example, Figure 6 The actual verification results of the fractional-order response obtained using the above method are shown. The solid line shows the actual voltage response of the counter-electrode battery, and the dotted line shows the simulation result using the method provided by the present invention. As can be seen from the figure, the fractional-order formula proposed in this invention well fits the response process of the counter-electrode battery, providing a new method for revealing the migration of molten salt substances in liquid metal batteries, and providing new ideas for high-precision modeling and efficient management of liquid metal batteries.

[0076] An embodiment of the present invention provides a liquid metal battery molten salt material migration modeling system based on a counter electrode battery, comprising: a computer-readable storage medium and a processor;

[0077] The computer-readable storage medium is used to store executable instructions;

[0078] The processor is configured to read the executable instructions stored in the computer-readable storage medium and execute the method described in any one of the above embodiments.

[0079] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for modeling the migration of molten salt substances in a liquid metal battery based on a counter electrode battery, characterized in that: include: S1, charging and discharging a vertically placed counter electrode battery having the same molten salt composition and structure as the liquid metal battery at different rates at a preset temperature for a preset time, and collecting the charge and discharge voltages; S2, the voltage response expression of the electrode battery during charge and discharge Characterizing the molten salt material migration process of the liquid metal battery; S3, according to the charge and discharge voltage, identify the parameters in the voltage response expression; wherein a is the initial charging voltage without polarization stage, R dis is the ratio of discharge voltage to discharge current; b, c, d, and m are identified using an intelligent algorithm based on the charging voltage, and s is a frequency domain variable.

2. The method according to claim 1, wherein According to the charging voltage, b, c, d, and m are identified using a genetic algorithm, specifically: In the initial population generation stage, the initial values ​​are set to {b0, c0, d0, m0}; In the population evolution stage, the initial value is updated and iterated to obtain {b i , c i , d i , m i }; To {b i , c i , d i , m i The root mean square error between the voltage value obtained after substituting it into the voltage response expression and the actual voltage value is used as the individual evaluation index; When the preset number of iterations is reached, the iteration is stopped and the individual with the smallest evaluation index in the last generation of population is regarded as the optimal solution identified; Wherein, i is the number of iterations, and the population evolution stages include parent selection, gene crossover, gene mutation and introduction of foreign individuals.

3. The method according to claim 2, wherein For a 20Ah counter electrode battery, when its charge and discharge current is 1A, 2A, 3A, 4A, 5A, and 6A, its voltage response H(s) satisfies the following relationship:

4. The method according to claim 1, wherein The preset temperature is the optimal operating temperature of the molten salt electrolyte.

5. The method according to claim 4, wherein When the molten salt is a mixture of LiF, LiCl, and LiBr, the optimal operating temperature is set to 550°C.

6. The method according to claim 1, wherein The size of the counter electrode battery is the same as that of the stainless steel shell and the nickel foam of the liquid metal battery.

7. The method according to claim 1, wherein The upper portion of the counter electrode battery is the negative electrode, and the lower portion is the positive electrode.

8. A liquid metal battery molten salt material migration modeling system based on a counter electrode battery, characterized in that: include: Computer-readable storage medium and processor; The computer-readable storage medium is used to store executable instructions; The processor is configured to read the executable instructions stored in the computer-readable storage medium and execute the method according to any one of claims 1 to 7.

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