Super capacitor branch model branch quantity calculation method and model construction method

Abstract

This invention discloses a method for calculating the number of branches in a supercapacitor branch model and a method for modeling the model, specifically relating to the field of supercapacitor modeling. The method includes: determining the relationship between branch time constants and resistance / capacitance based on charge redistribution phenomena; determining the resistance and capacitance of the first branch based on supercapacitor cyclic charge-discharge tests, and determining the first branch time constant using the relationship between the branch time constant and resistance / capacitance; determining the number of branches in the supercapacitor based on the relationship between the time constants of each branch, the first branch time constant, and a preset model prediction time. This invention determines the relationship between branch time constants and resistance / capacitance through charge redistribution phenomena, and further determines the time constants of each branch through experimental testing. It determines the model prediction time based on operating conditions, and uses a preset multiple of the branch time constant as the prediction time to determine the number of branches, thus better predicting external characteristics under different operating conditions.

Description

Technical Field

[0001] This invention relates to the field of supercapacitor modeling, specifically to a method for calculating the number of branches in a supercapacitor branch model and a method for model construction. Background Technology

[0002] For supercapacitor energy storage systems, modeling is crucial for design prediction, condition monitoring, and control integration. Since models are tools for simulating and analyzing the actual system under certain operating conditions, their accuracy depends on the specific application conditions and requirements; therefore, modeling must be based on actual operating conditions. Numerous supercapacitor models exist, and many have been studied for different purposes, including electrochemical models, thermal models, self-discharge models, and aging models. Currently, the three most commonly used supercapacitor models are electrochemical models, circuit models, and neural network models. Generally, electrochemical models offer high accuracy but low computational efficiency because they capture the actual internal reaction processes of the supercapacitor, hindering their application in real-time energy management and control systems. In contrast, equivalent circuit models are derived from experience and experimental data under specific conditions, which may fail to represent the true external characteristics of the supercapacitor, leading to model mismatch problems. Furthermore, their parameters and states lack physical representation. However, their structural simplicity and good modeling accuracy make them widely accepted in applications such as real-time simulation and integrated energy management, where only the external characteristics of the supercapacitor need to be observed. In contrast, intelligent models perform better in predicting actual external outputs, but their interpretability is weak, failing to explain their internal relationships and generally making them inconvenient to incorporate into real-time simulations and other energy storage applications. Therefore, to date, equivalent circuit models are the most widely used in practical applications of energy storage systems, including distributed grid energy storage, electric vehicle energy storage, and urban rail transit energy storage systems.

[0003] Equivalent circuit models employ parametric RC (capacitor-resistance) networks to simulate the external characteristics of supercapacitors. These models are simple and easy to implement due to the use of ordinary differential equations in their formulas. Different models exhibit varying degrees of accuracy, depending on the circuit configuration and the number of components. Increasing circuit complexity generally improves model accuracy but also drastically increases model complexity and reduces simulation prediction efficiency. To simulate the distributed capacitance and electrolyte resistance determined by porous electrodes, transmission line models are introduced. Considering transient and long-term behavior, the model's complexity typically depends on the number of RC networks employed. Each RC network is specified to delineate the capacitance and resistance distribution in each pore of the electrode. Generally, increasing the number of RC networks tends to improve model fidelity but at the expense of computational efficiency. Currently, many circuit models exist for supercapacitors, many of which fit experimental data well but have relatively low practicality, predicting external characteristics only for a few fixed operating time periods. As the predicted time range expands, the practicality of some models decreases, and accuracy degrades. Typically, since the number of branches is uncertain, the time constant for each branch is usually set based on practical experience. Although the model fits well for specific experimental conditions, it does not fit well when the prediction time is extended. It may result in only the final value being correct, but there may be a large discrepancy in the process of external characteristic changes. Summary of the Invention

[0004] To address the problem in existing technologies where the number of branches cannot be determined and the model's practicality and accuracy decrease as the preset time range expands, this invention provides a method for calculating the number of branches in a supercapacitor branch model and a method for constructing the model.

[0005] To achieve the above-mentioned technical objectives, the first aspect of the present invention provides a method for calculating the number of branches in a supercapacitor branch model, which may include, but is not limited to, at least one of the following steps.

[0006] The relationship between branch time constant and resistance and capacitance is determined based on the charge redistribution phenomenon.

[0007] The resistance and capacitance of the first branch are determined based on the supercapacitor cyclic charge-discharge test, and the time constant of the first branch is determined by the relationship between the branch time constant and the resistance and capacitance.

[0008] The number of branches of the supercapacitor is determined based on the relationship between the time constants of each branch, the time constant of the first branch, and the preset model prediction time.

[0009] This invention determines the relationship between branch time constants and resistance and capacitance through charge redistribution phenomena, and further determines the time constants of each branch through experimental testing. The model prediction time is determined according to the working conditions, and the number of branches is determined by using a preset multiple of the branch time constant as the prediction time, thereby better predicting the external characteristics under different working conditions.

[0010] Optionally, determining the relationship between branch time constant and resistance / capacitance based on charge redistribution includes: determining the equivalent circuit diagram of constant voltage or constant current charge / discharge based on the resistance experienced by ions at different pore sizes, according to the charge redistribution phenomenon; and determining the relationship between branch time constant and resistance / capacitance based on the relationship between resistance and capacitance in the equivalent circuit diagram of constant voltage or constant current charge / discharge.

[0011] This invention analyzes the influence of external response through the phenomenon of charge redistribution. By performing circuit equivalence on constant voltage or constant current charging and discharging processes, the capacitance and resistance are determined, thereby obtaining the relationship between the branch time constant and the resistance and capacitance.

[0012] Optionally, the resistance and capacitance of the first branch are determined based on the supercapacitor cyclic charge-discharge test, and the time constant of the first branch is determined by using the relationship between the branch time constant and the resistance and capacitance. This includes: obtaining the instantaneous voltage and charging current of the supercapacitor under preset charging current based on the supercapacitor fast charge-discharge experiment, and determining the resistance of the first branch; obtaining the time, external voltage difference of the supercapacitor, and charging current obtained from the supercapacitor cyclic charge-discharge test based on the supercapacitor fast charge-discharge experiment, and determining the capacitance of the first branch; and substituting the resistance and capacitance of the first branch into the relationship between the branch time constant and the resistance and capacitance to obtain the time constant of the first branch.

[0013] This invention obtains experimental data through rapid charging and discharging experiments of supercapacitors, and uses the experimental data obtained from the tests as the basis for calculating the resistance and capacitance parameters of the first branch. The data is then substituted into the relationship between resistance and capacitance to obtain the time constant of the first branch.

[0014] Optionally, the number of branches of the supercapacitor is determined based on the relationship between the time constants of each branch, the time constant of the first branch, and the preset model prediction time. This includes: determining the prediction time of the supercapacitor branch model; determining the time constant of the next branch sequentially based on the relationship between the time constants of each branch and the time constant of the first branch; stopping the calculation of the time constant of the next branch when the preset multiple of the determined branch time constant is equal to the time, and determining the number of branches of the supercapacitor based on the number of branches at this time.

[0015] This invention determines the time constant of the next branch by calculating the relationship between the time constant of the first branch and the time constant of the next RC branch being charged to its steady state after the previous RC branch reaches a steady state. The calculation continues until the time constant of the obtained branch is a preset fixed multiple of the predicted time, at which point the calculation stops, thus determining the number of branches of the supercapacitor.

[0016] Based on the above process, a second aspect of the present invention provides a supercapacitor branch model branch number calculation device, which may include, but is not limited to, a branch time constant determination unit, a first branch time constant determination unit, and a branch number determination unit.

[0017] The branch time constant determination unit is used to determine the relationship between the branch time constant and the resistance and capacitance based on the charge redistribution phenomenon.

[0018] The first branch time constant determination unit is used to determine the resistance and capacitance of the first branch based on the supercapacitor cyclic charge and discharge test, and to determine the first branch time constant by using the relationship between the branch time constant and the resistance and capacitance.

[0019] The branch number determination unit is used to determine the number of branches of the supercapacitor based on the relationship between the time constants of each branch, the time constant of the first branch, and the preset model prediction time.

[0020] A third aspect of this invention provides a method for constructing a multi-branch model of a supercapacitor, comprising: determining initial values ​​of the resistance and capacitance of each branch based on the relationship between the time constants of each branch, the relationship between the branch time constants and the resistance and capacitance, and the first branch time constant determined by the method for calculating the number of branches of the supercapacitor branch model in the first aspect and any embodiment of the first aspect of this invention; optimizing the initial values ​​of the resistance and capacitance of each branch using a genetic algorithm based on the error between the supercapacitor charging and resting test and the initial values ​​of the resistance and capacitance of each branch to obtain the resistance and capacitance parameters of each branch; and constructing a multi-branch model of the supercapacitor based on the number of branches of the supercapacitor and the resistance and capacitance parameters of each branch.

[0021] This invention determines the number of branches by calculation, and then uses a static experiment of a supercapacitor to calculate the initial values ​​of the resistance and capacitance of each branch with a fixed time constant. Combined with the initial values ​​of a given set of circuit parameters, the relative error of the external characteristics of the supercapacitor in the time domain is obtained, and the supercapacitor branch circuit parameters are obtained by optimization through an optimization algorithm.

[0022] Optionally, based on the error between the supercapacitor charging and static testing and the initial values ​​of the resistors and capacitors of each branch, a genetic algorithm is used to optimize the initial values ​​of the resistors and capacitors of each branch to obtain the parameters of the resistors and capacitors of each branch. This includes: applying the initial values ​​of the resistors and capacitors of each branch to the state transition system to obtain the voltage simulation curve across the supercapacitor, comparing it with the voltage experimental curve measured in the supercapacitor charging and static testing to obtain the error value; and using the genetic algorithm to optimize the initial values ​​of the resistors and capacitors of each branch to minimize the error value, thereby obtaining the optimized parameters of the resistors and capacitors of each branch.

[0023] This invention combines initial value calculation and optimization algorithm with actual experimental data. The initial value calculation determines the approximate range of each model parameter, and then the optimization algorithm of curve fitting is used to finally obtain the model parameters. This avoids the influence of ripple and other errors during data acquisition in the experiment, and obtains more accurate supercapacitor branch model parameters.

[0024] The fourth aspect of the present invention provides a supercapacitor multi-branch model construction device, which may include, but is not limited to, a branch resistance and capacitance initial value determination unit, a branch resistance and capacitance acquisition unit, and a supercapacitor multi-branch model construction unit.

[0025] The branch resistance and capacitance initial value determination unit is used to determine the initial values ​​of each branch resistance and capacitance based on the relationship between the time constants of each branch, the relationship between the branch time constant and the resistance and capacitance, and the first branch time constant determined by the method for calculating the number of branches of the supercapacitor branch model in the first aspect and any embodiment of the present invention.

[0026] The branch resistance and capacitance unit is used to optimize the initial values ​​of each branch resistance and capacitance based on the error between the supercapacitor charging and static testing and the initial values ​​of each branch resistance and capacitance, thereby obtaining the parameters of each branch resistance and capacitance.

[0027] The supercapacitor multi-branch model building unit is used to construct a supercapacitor multi-branch model based on the number of branches of the supercapacitor and the resistance and capacitance parameters of each branch.

[0028] To achieve the above-mentioned technical objectives, a fifth aspect of the present invention provides an electronic device, which may include a memory and a processor. The memory stores computer-readable instructions. When the computer-readable instructions are executed by the processor, the processor performs the steps of the method for calculating the number of branches in the supercapacitor branch model in the first aspect and any embodiment of the first aspect of the present invention, and the steps of the method for constructing a multi-branch supercapacitor model in the third aspect of the present invention.

[0029] To achieve the above-mentioned technical objectives, a sixth aspect of the present invention provides a storage medium storing computer-readable instructions. When the memory-readable instructions are executed by one or more processors, the one or more processors perform the steps of the method for calculating the number of branches in a supercapacitor branch model in the first aspect and any embodiment of the first aspect of the present invention, and the steps of the method for constructing a multi-branch supercapacitor model in the third aspect of the present invention.

[0030] The beneficial effects of this invention are as follows:

[0031] This invention obtains the relationship between branch time constants and resistance / capacitance through charge redistribution phenomena, and obtains experimental data through supercapacitor cyclic charge-discharge tests to determine the resistance and capacitance of the first branch. The time constant of the first branch is determined by the relationship between the branch time constant and the resistance / capacitance. The time range is predicted based on the operating conditions, and the number of branches is determined by using a preset multiple of the obtained branch time constant as the prediction time. This allows for better prediction of the external characteristics of actual supercapacitors under different operating conditions, solving the problem in existing technologies where the practicality and accuracy of the model decrease when the number of branches cannot be determined and the preset time range is expanded. Attached Figure Description

[0032] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0033] Figure 1 A flowchart illustrating a specific example of the method for calculating the number of branches in a supercapacitor branch model according to an embodiment of the present invention;

[0034] Figure 2 This is a schematic diagram of the pore classification of the porous carbon electrode of the supercapacitor in an embodiment of the present invention;

[0035] Figure 3 This is a schematic diagram of pore ion movement during the complete discharge process of a supercapacitor in an embodiment of the present invention.

[0036] Figure 4 This is a schematic diagram of pore ion movement during the high-current charging process of a supercapacitor in an embodiment of the present invention.

[0037] Figure 5 This is a schematic diagram of positive ion aggregation at the pore opening of the large-pore electrolyte in a supercapacitor, as shown in an embodiment of the present invention.

[0038] Figure 6This is a schematic diagram of ion movement during the continuous constant voltage charging process after high current charging of the supercapacitor in an embodiment of the present invention.

[0039] Figure 7 This is a schematic diagram of ion movement during the static setting process after high-current charging of the supercapacitor in an embodiment of the present invention.

[0040] Figure 8 This is a schematic diagram of ideal pore constant voltage charging of a supercapacitor in an embodiment of the present invention;

[0041] Figure 9 This is a schematic diagram of the equivalent circuit for ideal pore constant voltage charging of a supercapacitor in an embodiment of the present invention;

[0042] Figure 10 This is a diagram showing the response state changes of a supercapacitor at different depths of the pores to a step input in an embodiment of the present invention.

[0043] Figure 11 This is a schematic diagram illustrating a specific example of a supercapacitor branch model branch number calculation device in an embodiment of the present invention.

[0044] Figure 12 This is a schematic diagram of a supercapacitor branch model in an embodiment of the present invention;

[0045] Figure 13 This is a schematic diagram illustrating a specific example of a supercapacitor multi-branch model construction device in an embodiment of the present invention.

[0046] Figure 14 This is a specific example diagram of an electronic device in an embodiment of the present invention. Detailed Implementation

[0047] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] like Figure 1 As shown, this embodiment of the invention provides a method for calculating the number of branches in a supercapacitor branch model, which includes, but is not limited to, steps S100 to S300.

[0049] Step S100: Determine the relationship between the branch time constant and the resistance and capacitance based on the charge redistribution phenomenon.

[0050] For example, by classifying the pore sites of charge redistribution phenomena, the current or voltage changes of the supercapacitor at different pore depths can be obtained, thereby determining the relationship between the branch time constant and the resistance and capacitance.

[0051] Step S200: Determine the resistance and capacitance of the first branch based on the supercapacitor cyclic charge-discharge test, and determine the time constant of the first branch by using the relationship between the branch time constant and the resistance and capacitance.

[0052] For example, the capacitance and resistance of the first branch are calculated using experimental data obtained from the supercapacitor cyclic charge-discharge test, and the time constant of the first branch is determined using the relationship between the branch time constant and the capacitance and resistance.

[0053] Step S300: Determine the number of branches of the supercapacitor based on the relationship between the time constants of each branch, the time constant of the first branch, and the preset model prediction time.

[0054] For example, after determining the time constant of the first branch, the time for charging the next RC branch to 63.2% of its steady state after the previous RC branch reaches steady state is the branch time constant. The iteration terminates when the predicted operating time is 3-5 times the branch time constant. The number of branches at this time is the number of branches of the supercapacitor.

[0055] This invention determines the relationship between branch time constants and resistance and capacitance through charge redistribution phenomena, and further determines the time constants of each branch through experimental testing. The model prediction time is determined according to the working conditions, and the number of branches is determined by using a preset multiple of the branch time constant as the prediction time, thereby better predicting the external characteristics under different working conditions.

[0056] As an optional embodiment of the present invention, determining the relationship between branch time constant and resistance and capacitance based on charge redistribution phenomenon includes: determining the equivalent circuit diagram of constant voltage or constant current charge and discharge based on the resistance encountered by ions under different aperture sizes according to charge redistribution phenomenon; and determining the relationship between branch time constant and electronic capacitance based on the relationship between resistance and capacitance in the equivalent circuit diagram of constant voltage or constant current charge and discharge.

[0057] For example, in the fabrication of porous carbon electrodes for supercapacitors, chemical solvents are often used to wash the carbon electrodes to increase their contact area with the electrolyte and thus improve the supercapacitor's capacity, making them porous. However, this washing process cannot control the size of the carbon electrode pores, nor can it control the degree of washing at different locations on the electrode, resulting in pores of varying sizes, shapes, and depths. Figure 2 As shown, the pores can be divided into three types: large, medium, and small.

[0058] For example, in the electrochemical model, when ions adsorb onto the electrode, they are divided into two layers: a compact layer and a diffuse layer. When ions are in the compact layer, their volume and diameter are not negligible. When ions are in the diffuse layer, they can be considered as point charges. That is, when the diameter of the ions in the electrolyte is not negligible relative to the diameter of the porous carbon electrode, the ions cannot be considered as point charges, and the interactions of particles within the compact layer must be considered. In other words, in pores with smaller pore sizes, the volume of ions needs to be considered, while in pores with larger pore sizes, the volume of ions in the diffuse layer is almost negligible. Figure 2 As shown in ① and ②, the diffusion layer is relatively large at this point, resulting in good ion flow and easier movement within the pores. When the ion diameter in the electrolyte cannot be ignored relative to the pore diameter in the porous carbon electrode, as... Figure 2 As shown in ③ and ④, ions cannot be considered as point charges; the volume and interactions of ions within the compact layer must be taken into account. Under extreme conditions, when the pore size is almost the same as the diameter of the counterion, a requirement for ion adsorption by the electrode in the pore is that, as the ion further enters the pore, the solvent and counterions trapped in front of the adsorbed ion must be able to move out of the pore so that the adsorbed ion can eventually be evenly distributed on the electrode. In other words, a given ion can only continue to move by displacing the counterion or solvent molecules in front of it, such as... Figure 2 As shown in ④.

[0059] For example, when a supercapacitor is in equilibrium, the positive and negative ions in the electrolyte solution are uniformly distributed in the pores. When a given ion enters a pore during charging, there must be a net movement of a counterion or solvent molecule to create space for the given ion to enter. Unless the pore is open at only one end, the counterion or solvent molecule can initially move in the same or opposite direction as the given ion. Therefore, the given ion can still move, albeit more slowly, even if it must lose some water or solvent molecules dissolved in the ion. It can continue to move unless the pore is close to the size of a bare ion. However, as charging continues, the ion will eventually begin to enter both ends of the pore, and then there may be a net movement of solvent molecules or counterions in one direction, i.e., outward over the given ion. In a narrow pore that is closed at one end or has ions entering at both ends, the given ion can only continue to move by displacing the counterion or solvent molecule in front of it. This becomes an increasingly difficult process as the pore size approaches the size of the given ion, so the movement of ions into the depths of the pore is also a slow process.

[0060] For example, such as Figure 3 As shown, under complete discharge, positive and negative ions are evenly distributed. Figure 4As shown, with the commencement of high-current charging, electrons move to the electrode surface and attract positive ions from the pores. Negative ions still present in the pores are repelled due to the potential difference and move towards the pore openings. As charging continues, a large number of positive ions from the electrolyte are also attracted, while negative ions in the pores move further away. Due to the high-current charging and short charging time, some positive ions that haven't had time to adsorb deep into the pores are already charged to the supercapacitor's rated voltage. These positive ions that haven't reached the depths of the pores accumulate at the pore openings, causing charge redistribution over a subsequent period. Figure 5 The image shows the accumulation of positive ions from macroporous electrolytes at the pore opening.

[0061] For example, Figure 6 and Figure 7 Both schematically illustrate the charge redistribution under two conditions: continuous constant voltage charging and resting, following a short period of high-current charging. Both originate from... Figure 5 This is the situation that begins. If constant voltage charging continues (current decreases), such as... Figure 6 As shown, because the charge accumulated at the pore opening moves deeper into the pore, it attracts free electrons in the carbon electrode to move to the electrode surface, forming a more stable and tightly adsorbed structure. Therefore, the charge at the pore opening decreases, but as constant voltage charging proceeds, more charge enters the pore. Simultaneously, ions move further within the pore, becoming very uniformly distributed; if charging is stopped immediately after rapid charging, such as... Figure 7 As shown, positive ions and free electrons will also be evenly distributed after a period of time. However, during this charge redistribution process, some of the unstable positive ions that have been adsorbed on the electrode move away from the electrode due to the concentration gradient, while others penetrate deeper into the electrode and are more tightly adsorbed with the free electrons in the electrode. Because the total number of ions adsorbed on the electrode decreases, the external voltage of the supercapacitor drops. This simple pore model can only qualitatively explain the voltage drop phenomenon during charge redistribution. However, in reality, the surface of a supercapacitor is not composed of pores with uniform diameter, but rather of branched pores with different, non-constant diameters. Different pore sizes result in varying degrees of difficulty for ions to penetrate into the pores, thus leading to different times for charge redistribution to reach stability. These differences represent the influence of different pore sizes on the response speed to external inputs.

[0062] For example, different locations with the same aperture exhibit varying response speeds to external inputs, quantifying the response time of different pore sizes and depths to external inputs. For instance... Figure 8 As shown, a step signal is applied to a semi-infinite cylindrical pore with a constant diameter, and the pore is charged by constant voltage. Figure 9 yes Figure 8The equivalent circuit diagram is shown. Since the electrode resistance is much smaller than the electrolyte resistance R, the electrode resistance is ignored in the equivalent circuit. z represents the direction along the pores. Counterions adsorb onto the electrodes to form a capacitor C. The migration rate and difficulty of ions in smaller and larger pores are not the same. Ions near larger pores can more easily penetrate to the depth of the pore, while ions near smaller pores, when drifting to the depth of the smaller pore due to the potential difference, experience greater resistance due to the concentration difference and drift effect compared to ions near larger pores. Therefore, the electrolyte resistance R of a smaller pore is greater than that of a larger pore.

[0063] On a cross-section dz with an infinitesimally small aperture, the resistance Rdz is in the z-direction, and the capacitance Cdz is perpendicular to the z-direction. Then:

[0064]

[0065]

[0066] Differentiating Equations 1 and 2 with respect to time t and distance z respectively, and combining them, we obtain Equation 3:

[0067]

[0068] The initial conditions of the circuit are:

[0069]

[0070] e(0,t)=E (5)

[0071] Perform a Laplace transform on Equation 3:

[0072]

[0073]

[0074]

[0075] We can solve this using equation 6-8:

[0076]

[0077] The solution in the time domain is:

[0078]

[0079] like Figure 10As shown, the potential at different locations changes with time as z changes. Even for apertures of the same size, the response time to applied current / voltage varies at different depths. Within the same time frame, the potential at different locations within the same aperture decreases with increasing depth. The response speed of the electrode voltage to external input is related to both the aperture size and the aperture depth.

[0080] In Equation 10, the product of the branch resistance and the branch capacitance is the branch time constant, i.e., τ = RC.

[0081] As an optional embodiment of the present invention, the resistance and capacitance of the first branch are determined based on the supercapacitor cyclic charge-discharge test, and the time constant of the first branch is determined by using the relationship between the branch time constant and the resistance and capacitance. This includes: obtaining the instantaneous voltage and charging current of the supercapacitor under preset charging current based on the supercapacitor fast charge-discharge experiment, and determining the resistance of the first branch; obtaining the time, external voltage difference of the supercapacitor, and charging current obtained from the supercapacitor cyclic charge-discharge test based on the supercapacitor fast charge-discharge experiment, and determining the capacitance of the first branch; and substituting the resistance and capacitance of the first branch into the relationship between the branch time constant and the resistance and capacitance to obtain the time constant of the first branch.

[0082] For example, in apertures of the same diameter, the deeper the aperture, the slower the response speed to external voltage, meaning the charge rearrangement process takes longer. In apertures of different diameters, the larger aperture responds to external signals faster than the smaller aperture. Therefore, there must exist a point at a certain depth in the larger aperture that has the same response rate to changes in external signals as a point at a shallower depth in the smaller aperture; that is, the charge rearrangement process takes the same amount of time. Therefore, this invention treats points with consistent response speeds to external signals as uniform, regardless of whether they are near a small or large aperture, or whether they are located at a deep or shallow aperture. As long as they have the same response speed to external signals, they are considered to have the same time constant in the charging / discharging and charge rearrangement processes. When establishing the supercapacitor model, points with the same response speed are considered to have the same time constant and are grouped into the same branch.

[0083] For example, a rapid charge-discharge experiment of a supercapacitor was conducted at 25℃. The experimental equipment included a Ningbo New Energy 3000F supercapacitor cell, an Arbin tester, a high and low temperature test chamber, and a host computer. The external voltage characteristics of the supercapacitor were recorded. The data acquisition time interval was 10 milliseconds, and the minimum voltage measurement accuracy was 1 millivolt. The experimental steps are as follows: ① Constant voltage charging: The supercapacitor cell was charged to 1.35V and held at a constant voltage for 30 minutes to ensure that the first branch and other branches with shorter time constants were fully charged. ② Constant current charging: Simulating actual operating conditions, the supercapacitor was charged at a constant current of 250A until the cell voltage reached 2.7V. ③ Constant current discharging: Simulating actual operating conditions, the supercapacitor was discharged at a constant current of 250A until the cell voltage reached 1.35V. ④ Repeat steps ② and ③ 50 times to conduct a cyclic charge-discharge experiment of the supercapacitor. The table below shows the parameters of the Ningbo New Energy 3000F supercapacitor cell, the Arbin tester, and the high and low temperature test chamber.

[0084] Table 1. Main parameters of Ningbo New Energy's 3000F supercapacitor cell

[0085]

[0086] Table 2 Main parameters of the Arbin tester

[0087]

[0088] Table 3 Main parameters of the high and low temperature test chamber

[0089] Test temperature range -40-150℃ Temperature fluctuations ±0.5℃ heating rate 3℃ / min Security alarm system Safety

[0090] For example, in a supercapacitor fast charge / discharge experiment, the voltmeter is actually measuring the capacitance effect of the flat external electrode surface and large pores. Small and medium-sized pores, or deep within the pores, cannot follow the changes in potential or current so quickly. Therefore, during the measurement process, the capacitance that closely follows the input and can be measured is considered to be the capacitance formed by the electrode surface and large pores with counterions. However, the voltage change of the supercapacitor during the resting phase after charge / discharge is affected by small and medium-sized pores or deep within the pores.

[0091] For example, the fast charge and discharge experimental data are used as the basis for calculating the parameters of the first branch resistor and capacitor. The instantaneous voltage, charging current, time difference, external voltage difference of the supercapacitor, voltage across the supercapacitor, and total charging time of the supercapacitor are obtained through experimental measurement.

[0092] The formula for calculating the resistance of the first branch is:

[0093]

[0094] Where V1 is the instantaneous voltage rise when the supercapacitor is just being charged with a large current, and I ch This is the charging current.

[0095] The capacitor of the first branch is

[0096] C1 = C0 + K p *V

[0097] Where C0 is the initial capacitance of the supercapacitor at low voltage. K p This is the coefficient of capacitance as a function of voltage. V is the voltage across the supercapacitor; where Δt is the time difference obtained from the supercapacitor's cyclic charge-discharge test, and ΔV is the external voltage difference of the supercapacitor during this time period. rated The rated voltage across the supercapacitor is 2.7V, Q. tot The total charge that can be charged into a supercapacitor, after the capacitor voltage has been charged to its rated voltage, can be calculated as Q. tot =I ch ×t ch =C1×V rated , t ch Total charging time for the supercapacitor.

[0098] For example, the branch time constant refers to the product of a certain RC branch in the branch circuit model, that is, the time constant of the first-order circuit, and the first branch time constant τ1 = R1*C1.

[0099] As an optional embodiment of the present invention, the number of branches of the supercapacitor is determined based on the relationship between the time constants of each branch, the time constant of the first branch, and a preset model prediction time, including: determining the prediction time of the supercapacitor branch model; determining the time constant of the next branch sequentially based on the relationship between the time constants of each branch and the time constant of the first branch; stopping the calculation of the time constant of the next branch when the preset multiple of the determined branch time constant is equal to the time, and determining the number of branches of the supercapacitor based on the number of branches at this time.

[0100] For example, the formula is obtained by inputting point pairs of different pore depths when charging and discharging a cylindrical pore with a constant diameter under constant current or constant voltage conditions.

[0101] Where i or e is the magnitude of the current or voltage at time t when the input is constant current or constant voltage at depth z.

[0102] Even pores of the same size will exhibit different response speeds due to variations in depth, and the relationship between instantaneous current i (instantaneous voltage), pore depth z, and time t is quantitatively described. In the formula, R is related to the pore size; the larger the pore diameter, the less resistance there is for counterions to move to deeper pores, the shorter the charge rearrangement process, and the smaller R.

[0103] For example, Defined as a time constant T, the relationship between the current (or voltage) at a certain point on the electrode and time when the supercapacitor is charging, discharging, or resting is as follows: The constant T is used to characterize the response time of a point to an external input, and it is related to the size and depth of the pore, the type of attracted charge, and the electrolyte concentration. Each point on the supercapacitor electrode has a corresponding response time T, regardless of the size or depth of the pore. The response time to an external input can be characterized by the time constant T. Corresponding to the multi-branch model used in this paper, each branch has a corresponding time constant τ, which, from a circuit perspective, characterizes the response speed of each branch to an external input. In the branch model, since the time constants of adjacent branches differ by more than 20 times, it is assumed that the next branch is charged and discharged only after the previous branch reaches a steady state. Reflected in the pore, this means that the potential or current of a set of capacitors with a response time constant of T1 reaches a steady state before charging the next set of capacitors with a response time constant of T2. As is well known, the RC response at time τ is 63.2% of the steady state (rising phase). Since adjacent branches in the branch model of this invention are connected in parallel, the steady-state values ​​of the capacitances of the two branches are the same. Similarly, in the electrochemical model, the potentials of two adjacent sets of capacitors with different response time constants are also the same when they reach steady state. Assuming that after the previous RC branch reaches steady state, the time it takes to charge the next RC branch to 63.2% of its steady-state potential is this branch's time constant τ2, in the electrochemical model, the time it takes to reach 63.2% of the steady-state potential after the capacitor with time constant T1 finishes charging is the time constant T2.

[0104] For example, to ensure that the electrochemical model and the branch model are on the same time scale and that the ratio of time constant to response time is in the same dimension, the time constant τ1 of the previous branch can be calculated to determine the time constant τ2 of the next branch. In the fast charge-discharge experiment of a supercapacitor, the external characteristics of branches with short response times are actually being measured. Therefore, in a short-duration charge-discharge experiment, the parameters of the first branch in the branch model can be initially calculated from experimental data. In other words, the time constant of the first branch is known, and the time constants of subsequent branches in the branch model are calculated from experimental data. get.

[0105] For example, the time constant of the first branch can be obtained by calculation, which can be achieved through... The time constant of each branch is calculated sequentially. The iteration terminates when the time constant of a branch is approximately 3-5 times the predicted time of the model. The predicted time range refers to the range of time the supercapacitor model needs to predict based on the operating conditions. For example, in a distributed power grid, the time difference between charging and discharging is large, typically one day or even longer. Therefore, when the calculated time constant of the last branch is one-third of a day, the number of branches obtained is the supercapacitor model under this operating condition. In urban rail transit ground-based energy storage, the supercapacitor's cyclic charging and discharging interval is approximately 2 minutes, with longer intervals during off-peak periods. Therefore, the number of branches in the supercapacitor model under this operating condition will be significantly less than the number of branches in the distributed power grid model. When the response time of a first-order RC branch to the input reaches 3-5 times the time constant, the circuit is considered to have finished responding to the external input. The number of branches at this point is the final number of supercapacitor branches.

[0106] like Figure 11 The present invention provides a supercapacitor branch model branch number calculation device, which may include, but is not limited to, a branch time constant determination unit, a first branch time constant determination unit, and a branch number determination unit, as detailed below.

[0107] The branch time constant determination unit is used to determine the relationship between the branch time constant and the resistance and capacitance based on the charge redistribution phenomenon.

[0108] The first branch time constant determination unit is used to determine the resistance and capacitance of the first branch based on the supercapacitor cyclic charge and discharge test, and to determine the first branch time constant by using the relationship between the branch time constant and the resistance and capacitance.

[0109] The branch number determination unit is used to determine the number of branches of the supercapacitor based on the relationship between the time constants of each branch, the time constant of the first branch, and the preset model prediction time.

[0110] This invention determines the relationship between branch time constant and resistance / capacitance through charge redistribution phenomenon, and further determines the time constant of the first branch through experimental testing. The model prediction time is determined according to the working conditions, and the number of branches is determined according to the preset multiple of the branch time constant, so as to better predict the external characteristics under different working conditions.

[0111] Based on a method for calculating the number of branches in a supercapacitor branch model, one or more embodiments of the present invention can also provide a method for constructing a multi-branch supercapacitor model. This method includes determining initial values ​​for the resistance and capacitance of each branch based on the relationship between the time constants of each branch, the relationship between the branch time constants and the resistance and capacitance, and the first branch time constant determined by the method for calculating the number of branches in any embodiment of the supercapacitor branch model; optimizing the initial values ​​for the resistance and capacitance of each branch using a genetic algorithm based on the error between the supercapacitor charging and resting test and the initial values ​​for the resistance and capacitance of each branch, thereby obtaining the resistance and capacitance parameters of each branch; and constructing a multi-branch supercapacitor model based on the number of branches in the supercapacitor and the resistance and capacitance parameters of each branch.

[0112] For example, the supercapacitor was tested at 25°C. After charging, it was allowed to stand for 7 days before the experiment to ensure complete discharge. The external voltage characteristics of the supercapacitor were recorded during the experiment, with a sampling interval of 1 second. ① Constant current charging: The supercapacitor was charged at a constant current of 250A until the individual cell voltage reached 2.7V. ② After standing for 30 minutes, the voltage across the supercapacitor was observed and recorded.

[0113] For example, the supercapacitor was tested at 25°C, followed by a static discharge experiment. To ensure complete discharge, the supercapacitor was charged at a constant voltage for 30 minutes before the experiment. The external voltage characteristics of the supercapacitor were recorded during the experiment, with a sampling interval of 1 second. ① Constant current charging: The supercapacitor was discharged at a constant current of 250A until the individual cell voltage reached 0V. ② Static discharge for 30 minutes: The voltage across the supercapacitor was observed and recorded.

[0114] For example, after determining the number of branches, a supercapacitor static experiment is conducted. During the charging phase, the amount of charge remains constant. Assuming that the next branch is charged only after the previous branch has finished charging, and given a fixed time constant for each branch, the initial values ​​of the resistance and capacitance of each branch can be calculated. Based on the branch model obtained in the previous step, the data from the rapid charge / discharge experiment, and the long-term static experiment, the parameters of the supercapacitor are obtained using initial value calculations and optimization algorithms to fit the experimental data.

[0115] This invention combines initial value calculation and optimization algorithm based on actual experimental data. The initial value calculation determines the approximate range of each model parameter, and then the optimization algorithm of curve fitting is used to finally obtain the model parameters. This avoids the influence of ripple and other errors during data acquisition in the experiment, and obtains more accurate supercapacitor branch model parameters.

[0116] As an optional embodiment of the present invention, based on the error between the supercapacitor charging and static testing and the initial values ​​of the resistors and capacitors of each branch, a genetic algorithm is used to optimize the initial values ​​of the resistors and capacitors of each branch to obtain the parameters of the resistors and capacitors of each branch. This includes: applying the initial values ​​of the resistors and capacitors of each branch to the state transition system to obtain the voltage simulation curve across the supercapacitor, comparing it with the voltage experimental curve measured in the supercapacitor charging and static testing to obtain the error value; and using the genetic algorithm to optimize the initial values ​​of the resistors and capacitors of each branch to minimize the error value, thereby obtaining the optimized parameters of the resistors and capacitors of each branch.

[0117] For example, when calculating initial parameter values ​​using circuit analysis, it is assumed that the next branch is charged and discharged only after the previous branch is fully charged (discharged). However, in actual circuit analysis, each branch starts charging and discharging simultaneously, only at different rates. This results in the parameters obtained from circuit analysis being directly applied to the model, leading to discrepancies between simulation and experimental data. Therefore, given the model parameters, the voltage curve across the supercapacitor is inferred under given experimental input conditions and compared with the experimentally measured voltage curve. An optimization algorithm is then used to optimize the model parameters (the capacitance and resistance values ​​of the branches) to minimize the error between the algorithm-derived voltage curve and the experimentally measured voltage curve. The optimized model parameters are then the final parameters of the supercapacitor model.

[0118] For example, based on the calculated number of branches, such as Figure 12 As shown, taking a three-branch supercapacitor model as an example, but not limited to a three-branch supercapacitor, the voltages of the three branch capacitors are taken as the system's state variables UC1, UC2, and UC3. Figure 9 The state transition expression for this circuit is:

[0119]

[0120] Where M = R1×R2 + R1×R3 + R2×R3, the solution for the capacitor voltage of each branch in the time domain is...

[0121] For example, the variable capacitor C1 changes with the external voltage of the cell, and the state matrix changes continuously, requiring recalculation each time the external voltage is obtained. When calculating the zero-state response, the upper limit of integration t is defined as the step size, similar to a memory in Simulink. A new state matrix A is obtained, the integration step time t is incremented, and the input response to the zero-state response at time t is calculated. Given an initial set of circuit parameters, these are input into the state transition to obtain the simulation curves. This allows us to obtain the external characteristics of the supercapacitor in the time domain, and the relative error can be obtained by comparing them with the external characteristics of the experimental curves measured in a static supercapacitor experiment. At this point, a genetic algorithm is used to optimize the circuit parameters, ultimately yielding the parameters for the three branches of the supercapacitor circuit.

[0122] like Figure 13 As shown, the present invention provides a supercapacitor multi-branch model construction device, which may include, but is not limited to, a branch resistance and capacitance initial value determination unit, a branch resistance and capacitance acquisition unit, and a supercapacitor multi-branch model construction unit, as detailed below.

[0123] The branch resistance and capacitance initial value determination unit is used to determine the initial values ​​of each branch resistance and capacitance based on the relationship between the time constants of each branch, the relationship between the branch time constant and the resistance and capacitance, and the first branch time constant determined by the method for calculating the number of branches of the supercapacitor branch model in the first aspect and any embodiment of the present invention.

[0124] The branch resistance and capacitance unit is used to optimize the initial values ​​of each branch resistance and capacitance based on the error between the supercapacitor charging and static testing and the initial values ​​of each branch resistance and capacitance, thereby obtaining the parameters of each branch resistance and capacitance.

[0125] The supercapacitor multi-branch model building unit is used to construct a supercapacitor multi-branch model based on the number of branches of the supercapacitor and the resistance and capacitance parameters of each branch.

[0126] This invention determines the number of branches by calculation, and then uses a static experiment of a supercapacitor to calculate the initial values ​​of the resistance and capacitance of each branch with a fixed time constant. Combined with the initial values ​​of a given set of circuit parameters, the relative error of the external characteristics of the supercapacitor in the time domain is obtained, and the supercapacitor branch circuit parameters are obtained by optimization through an optimization algorithm.

[0127] like Figure 14As shown, based on the same inventive concept as the method for calculating the number of branches in a supercapacitor branch model, one or more embodiments of the present invention can also provide an electronic device, including a memory and a processor. The memory stores computer-readable instructions. When the computer-readable instructions are executed by the processor, the processor performs the steps of the method for calculating the number of branches in a supercapacitor branch model in any embodiment of the present invention and the steps of the method for constructing a multi-branch supercapacitor model in any embodiment of the present invention.

[0128] like Figure 14 As shown, based on the same inventive concept as the method for calculating the number of branches in a supercapacitor branch model, one or more embodiments of the present invention can also provide a storage medium storing computer-readable instructions. When the computer-readable instructions are executed by one or more processors, the one or more processors cause the one or more processors to perform the steps of the method for calculating the number of branches in a supercapacitor branch model and the steps of the method for constructing a multi-branch supercapacitor model in any embodiment of the present invention.

[0129] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable storage medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable storage medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable storage media include: electrical connections (electronic devices) having one or more wires, portable computer disks (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM, or flash memory), fiber optic devices, and compact disc read-only memory (CDROM). Furthermore, computer-readable storage media can even be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0130] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0131] In the description of this specification, the references to terms such as "this embodiment," "an embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0132] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0133] 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 simple improvements made on the substantive content of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for constructing a multi-branch model of a supercapacitor, characterized in that, include: Determining the relationship between branch time constant and resistance / capacitance based on charge redistribution phenomenon; The resistance and capacitance of the first branch are determined based on the supercapacitor cyclic charge-discharge test, and the time constant of the first branch is determined by the relationship between the branch time constant and the resistance and capacitance. Determine the prediction time for the supercapacitor branch model; The time constant of the next branch is determined sequentially based on the relationship between the time constants of each branch and the time constant of the first branch. When the preset multiple of the determined branch time constant is equal to the time, the calculation of the next branch time constant is stopped, and the number of branches of the supercapacitor is determined according to the number of branches at this time. The initial values ​​of the resistance and capacitance of each branch are determined based on the relationship between the time constants of each branch, the relationship between the time constants of the branches and the resistance and capacitance, and the time constant of the first branch. Based on the error between the supercapacitor charging static test and the initial values ​​of the resistors and capacitors of each branch, a genetic algorithm is used to optimize the initial values ​​of the resistors and capacitors of each branch to obtain the resistor and capacitor parameters of each branch. A multi-branch model of a supercapacitor is constructed based on the number of branches and the resistance and capacitance parameters of each branch.

2. The method for constructing a multi-branch model of a supercapacitor according to claim 1, characterized in that, The determination of the relationship between branch time constant and resistance / capacitance based on charge redistribution includes: Based on the charge redistribution phenomenon, the equivalent circuit diagram of constant voltage or constant current charge and discharge is determined according to the resistance encountered by ions under different pore sizes. The relationship between the branch time constant and the resistance and capacitance is determined based on the relationship between the resistor and capacitance in the equivalent circuit diagram of constant voltage or constant current charging and discharging.

3. The method for constructing a multi-branch model of a supercapacitor according to claim 1, characterized in that, The method for determining the resistance and capacitance of the first branch based on supercapacitor cyclic charge-discharge testing, and determining the time constant of the first branch using the relationship between the branch time constant and the resistance and capacitance, includes: Based on the fast charge and discharge experiment of the supercapacitor, the instantaneous voltage and charging current of the supercapacitor under preset charging current are obtained, and the resistance of the first branch is determined. Based on the fast charge and discharge experiment of the supercapacitor, the time obtained from the cyclic charge and discharge test of the supercapacitor, the external voltage difference of the supercapacitor and the charging current are obtained, and the capacitance of the first branch is determined. Substituting the resistance and capacitance of the first branch into the relationship between the branch time constant and the resistance and capacitance, we obtain the time constant of the first branch.

4. The method for constructing a multi-branch model of a supercapacitor according to claim 1, characterized in that, The error between the supercapacitor charging and static testing and the initial values ​​of the resistors and capacitors of each branch is used to optimize the initial values ​​of the resistors and capacitors of each branch using a genetic algorithm, resulting in the following parameters for each branch: The initial values ​​of the resistors and capacitors of each branch are applied to the state transition system to obtain the voltage simulation curve across the supercapacitor. The voltage experimental curve is then compared with the voltage experimental curve measured during the supercapacitor charging and resting experiment to obtain the error value. The initial values ​​of the resistors and capacitors of each branch are optimized using a genetic algorithm to minimize the error value, resulting in optimized resistor and capacitor parameters for each branch.

5. A device for constructing a multi-branch model of a supercapacitor, characterized in that, include: Branch time constant determination unit, used to determine the relationship between branch time constant and resistance and capacitance based on charge redistribution phenomenon; The first branch time constant determination unit is used to determine the resistance and capacitance of the first branch based on the supercapacitor cyclic charge and discharge test, and to determine the first branch time constant by using the relationship between the branch time constant and the resistance and capacitance. The branch number determination unit is used to determine the prediction time of the supercapacitor branch model; based on the relationship between the time constants of each branch and the time constant of the first branch, the time constant of the next branch is determined in sequence; when the preset multiple of the determined branch time constant is equal to the time, the calculation of the time constant of the next branch is stopped, and the number of branches of the supercapacitor is determined according to the number of branches at this time. The branch resistance and capacitance initial value determination unit is used to determine the initial values ​​of each branch resistance and capacitance based on the relationship between the time constants of each branch, the relationship between the branch time constants and the resistance and capacitance, and the time constant of the first branch. The branch resistance and capacitance are obtained by using a genetic algorithm to optimize the initial values ​​of each branch resistance and capacitance based on the error between the supercapacitor charging and static testing and the initial values ​​of each branch resistance and capacitance, thereby obtaining the parameters of each branch resistance and capacitance. The supercapacitor multi-branch model building unit is used to construct a supercapacitor multi-branch model based on the number of branches of the supercapacitor and the resistance and capacitance parameters of each branch.

6. An electronic device, characterized in that, The device includes a memory and a processor, wherein the memory stores computer-readable instructions that, when executed by the processor, cause the processor to perform the steps of the supercapacitor multi-branch model construction method as described in any one of claims 1-4.

7. A storage medium storing computer-readable instructions, characterized in that, When the memory-readable instructions are executed by one or more processors, the one or more processors cause the processors to perform the steps of the supercapacitor multi-branch model construction method as described in any one of claims 1-4.

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