A modeling simulation method and system of a hybrid sodium-ion capacitor model

Abstract

The application discloses a modeling simulation method of a mixed sodium-ion capacitor model, and comprises the following steps: establishing a Langmuir adsorption and desorption law model of a mixed sodium-ion capacitor and an electrochemical model of the mixed sodium-ion capacitor; the Langmuir adsorption and desorption law model is a model for describing a solid-phase mass transfer process of the mixed sodium-ion capacitor based on the Langmuir adsorption and desorption law; the Langmuir adsorption and desorption law model and the electrochemical model are mixed to obtain the mixed sodium-ion capacitor model; the parameters of the mixed sodium-ion capacitor in the mixed sodium-ion capacitor model are calibrated and verified to obtain a verified mixed sodium-ion capacitor model; and the output response of the mixed sodium-ion capacitor under different input conditions is obtained by simulating the verified mixed sodium-ion capacitor model.

Description

Technical Field

[0001] This invention relates to the field of mixed sodium ion capacitance detection, and specifically to a modeling and simulation method and system for mixed sodium ion capacitance models. Background Technology

[0002] In recent years, hybrid sodium-ion capacitors (HSICs) have attracted much attention in the energy storage field due to their excellent energy and power characteristics. However, to better understand and optimize the performance of these devices, accurate and detailed modeling and simulation are required. In particular, HSICs exhibit a significant double-layer capacitance (DLC) phenomenon during charging and discharging. This phenomenon can be described by Langmuir's adsorption-desorption law, but existing models do not fully reveal its electrochemical behavior and internal state, thus limiting the further development and application of HSICs. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a modeling and simulation method and system for a hybrid sodium ion capacitor model.

[0004] Specifically, the technical solution of the present invention is as follows:

[0005] In a first aspect, the present invention provides a modeling and simulation method for a hybrid sodium ion capacitance model, comprising:

[0006] A Langmuir adsorption-desorption law model and an electrochemical model of the mixed sodium ion capacitor are established. The Langmuir adsorption-desorption law model is a model based on the Langmuir adsorption-desorption law to describe the solid-phase mass transfer process of the mixed sodium ion capacitor.

[0007] By combining the Langmuir adsorption-desorption law model and the electrochemical model, a mixed sodium ion capacitance model is obtained.

[0008] The mixed sodium ion capacitance parameters in the mixed sodium ion capacitance model are calibrated and verified to obtain the verified mixed sodium ion capacitance model.

[0009] By simulating the verified hybrid sodium-ion capacitor model, the output response of the hybrid sodium-ion capacitor under different input conditions was obtained.

[0010] This implementation method describes the solid-phase mass transfer process of sodium-ion capacitors using the Langmuir adsorption-desorption law model. By mixing the Langmuir adsorption-desorption law model with an electrochemical model, the output response of the hybrid sodium-ion capacitor model under different input conditions can be accurately predicted.

[0011] The implementation method of modeling and simulation of some mixed sodium ion capacitor models.

[0012] The Langmuir adsorption-desorption law model includes: the Langmuir adsorption equation, the pseudo-first-order adsorption kinetic model, and the pseudo-second-order adsorption kinetic model.

[0013] The implementation method of modeling and simulation of some mixed sodium ion capacitor models.

[0014] The Langmuir adsorption equation is θ = K[A] / (1+K[A]);

[0015] The pseudo-first-order adsorption kinetic model is dq / dt=k1(q e -q);

[0016] The pseudo-second-order adsorption kinetic model is dq / dt=k2(q e -q) 2 Where θ is the adsorption degree, k1 is the pseudo-first-order adsorption rate constant, and q e q is the amount of adsorption at adsorption equilibrium, k2 is the amount of adsorption at any time, k2 is the pseudo-second-order adsorption rate constant, K is the Langmuir adsorption constant, and A is the concentration of the adsorbate.

[0017] The implementation method of modeling and simulation of some mixed sodium ion capacitor models.

[0018] The electrochemical model of the hybrid sodium-ion capacitor is a traditional electrochemical model that removes the solid-phase diffusion equation.

[0019] In the implementation method of some mixed sodium ion capacitor model modeling simulation methods, after calibrating and verifying the mixed sodium ion capacitor parameters in the mixed sodium ion capacitor model to obtain the verified mixed sodium ion capacitor model, the method further includes:

[0020] By simulating the verified mixed sodium ion capacitor model, the internal electrochemical state of the mixed sodium ion capacitor is obtained. The internal electrochemical state of the mixed sodium ion capacitor includes: ion concentration distribution, potential distribution, and adsorption state on the electrode surface.

[0021] This implementation method can also monitor the electrochemical behavior and internal state of mixed sodium ion capacitors using a mixed sodium ion capacitor model.

[0022] Secondly, the present invention provides a modeling and simulation system for a hybrid sodium ion capacitance model, comprising:

[0023] The model building module is used to build a Langmuir adsorption-desorption law model and an electrochemical model of the mixed sodium ion capacitor. The Langmuir adsorption-desorption law model is a model based on the Langmuir adsorption-desorption law to describe the solid-phase mass transfer process of the mixed sodium ion capacitor. The Langmuir adsorption-desorption law model and the electrochemical model of the mixed sodium ion capacitor are sent to the model mixing module.

[0024] The model mixing module is used to mix the Langmuir adsorption-desorption law model and the electrochemical model to obtain a mixed sodium ion capacitance model; the mixed sodium ion capacitance model is then sent to the model verification module.

[0025] The model verification module is used to calibrate and verify the mixed sodium ion capacitor parameters in the mixed sodium ion capacitor model to obtain the verified mixed sodium ion capacitor model; and to send the verified mixed sodium ion capacitor model to the model simulation module.

[0026] The model simulation module is used to obtain the output response of the hybrid sodium-ion capacitor under different input conditions by simulating the verified hybrid sodium-ion capacitor model.

[0027] This implementation method describes the solid-phase mass transfer process of sodium-ion capacitors using the Langmuir adsorption-desorption law model. By mixing the Langmuir adsorption-desorption law model with an electrochemical model, the output response of the hybrid sodium-ion capacitor model under different input conditions can be accurately predicted.

[0028] Implementation methods for modeling and simulation systems of some mixed sodium ion capacitance models.

[0029] The Langmuir adsorption-desorption law model includes: the Langmuir adsorption equation, the pseudo-first-order adsorption kinetic model, and the pseudo-second-order adsorption kinetic model.

[0030] Implementation methods for modeling and simulation systems of some mixed sodium ion capacitance models.

[0031] The Langmuir adsorption equation is θ = K[A] / (1+K[A]);

[0032] The pseudo-first-order adsorption kinetic model is dq / dt=k1(q e -q);

[0033] The pseudo-second-order adsorption kinetic model is dq / dt=k2(q e -q) 2 Where θ is the adsorption degree, k1 is the pseudo-first-order adsorption rate constant, and q eq is the amount of adsorption at adsorption equilibrium, k2 is the amount of adsorption at any time, k2 is the pseudo-second-order adsorption rate constant, K is the Langmuir adsorption constant, and A is the concentration of the adsorbate.

[0034] Implementation methods for modeling and simulation systems of some mixed sodium ion capacitance models.

[0035] The electrochemical model of the hybrid sodium-ion capacitor is a traditional electrochemical model that removes the solid-phase diffusion equation.

[0036] Implementation methods for modeling and simulation systems of some mixed sodium ion capacitance models.

[0037] The model simulation module is also used to obtain the internal electrochemical state of the mixed sodium ion capacitor by simulating the verified mixed sodium ion capacitor model. The internal electrochemical state of the mixed sodium ion capacitor includes: ion concentration distribution, potential distribution, and adsorption state on the electrode surface.

[0038] Compared with the prior art, the present invention has at least one of the following beneficial effects:

[0039] 1. This invention describes the solid-phase mass transfer process of sodium-ion capacitors using the Langmuir adsorption-desorption law model. By mixing the Langmuir adsorption-desorption law model with an electrochemical model, the output response of the mixed sodium-ion capacitor model under different input conditions can be accurately predicted.

[0040] 2. This invention monitors the electrochemical behavior and internal state of mixed sodium ion capacitors using a mixed sodium ion capacitor model. Attached Figure Description

[0041] The preferred embodiments will now be described in a clear and easy-to-understand manner, in conjunction with the accompanying drawings, to further explain the above-mentioned characteristics, technical features, advantages, and implementation methods of the present invention.

[0042] Figure 1 This is a flowchart of a modeling and simulation method for a hybrid sodium ion capacitor model provided by the present invention;

[0043] Figure 2 This is a system block diagram of a modeling and simulation method for a hybrid sodium ion capacitor model provided by the present invention.

[0044] The following are the icon numbers: 10--Model building module; 20--Model mixing module; 30--Model verification module; 40--Model simulation module. Detailed Implementation

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the specific implementation methods of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings and other implementation methods can be obtained based on these drawings without any creative effort.

[0046] To keep the drawings concise, each figure only schematically shows the parts relevant to the invention, and these do not represent the actual structure of the product. Furthermore, to facilitate understanding, in some figures, only one of components with the same structure or function is schematically depicted, or only one is labeled. In this document, "one" not only means "only one," but can also mean "more than one."

[0047] It should also be further understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0048] In this document, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0049] Furthermore, in the description of this application, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0050] In one embodiment, refer to the appendix to the specification. Figure 1 The present invention provides a modeling and simulation method for a hybrid sodium ion capacitance model, comprising:

[0051] S110, Establish the Langmuir adsorption-desorption law model and the electrochemical model of the mixed sodium ion capacitor. The Langmuir adsorption-desorption law model is a model based on the Langmuir adsorption-desorption law to describe the solid-phase mass transfer process of the mixed sodium ion capacitor. The Langmuir adsorption-desorption law is mainly used to describe the adsorption behavior of gas or solution on solid surface. Its main points include: (1) The adsorption process occurs at specific sites on the solid surface, and each site can only adsorb one molecule; (2) The adsorption sites on the solid surface are uniform, that is, all sites have the same adsorption capacity; (3) There is no interaction between adsorbed molecules; (4) Adsorption is proportional to pressure at low pressure, while adsorption reaches saturation at high pressure, that is, all adsorption sites have been occupied.

[0052] In step S110, the Langmuir adsorption-desorption law model describes the double layer capacitance (DLC) phenomenon, which is the main electrochemical process occurring during the charging and discharging of hybrid sodium-ion capacitors. The Langmuir adsorption-desorption law model also includes the diffusion process of sodium ions in the electrodes. Since sodium-ion capacitors are highly similar to lithium-ion batteries, we can also simulate sodium-ion capacitors based on lithium-ion electrochemical models (such as pseudo-two-dimensional models); the pseudo-two-dimensional model is a widely used isothermal isocurrent model to describe the physicochemical processes of lithium batteries.

[0053] S120, by combining the Langmuir adsorption-desorption law model and the electrochemical model, a mixed sodium ion capacitance model is obtained.

[0054] In step S120, the Langmuir adsorption-desorption law model and the electrochemical model are combined. Specifically, the Langmuir adsorption-desorption law model is used to transform the description of solid-phase and interfacial processes in the lithium-ion electrochemical model into an adsorption kinetics description.

[0055] S130, the parameters of the mixed sodium ion capacitor in the mixed sodium ion capacitor model are calibrated and verified to obtain the verified mixed sodium ion capacitor model.

[0056] In step S130, experimental data are used to calibrate and validate the model parameters. This ensures that the model accurately reflects the electrochemical behavior of the mixed sodium-ion capacitor.

[0057] Specifically, the calibration and verification method can be achieved by collecting the terminal voltage of the mixed sodium-ion capacitor as the actual voltage condition and the current of the mixed sodium ions as the actual current condition; substituting the actual current condition into the mixed sodium-ion capacitor model, the mixed sodium-ion capacitor model generates a simulated voltage condition; and obtaining the accuracy of the mixed sodium-ion capacitor parameters in the current model based on the difference between the actual voltage condition and the simulated voltage condition.

[0058] S140, by simulating the verified hybrid sodium-ion capacitor model, the output response of the hybrid sodium-ion capacitor under different input conditions is obtained.

[0059] In step S140, the simulation of the output response of the mixed sodium-ion capacitor model is achieved through the following steps: First, the initial and boundary conditions of the mixed sodium-ion capacitor model are set. These conditions can be determined based on the actual operating state and environmental conditions of the mixed sodium-ion capacitor. Second, a suitable numerical solution method is selected. Choosing the right numerical solution method is crucial for solving the model. Commonly used numerical methods include the finite difference method, the finite element method, and the finite volume method. For models involving differential equations, time integration methods such as the Euler method and the Runge-Kutta method can be used. Third, after selecting a suitable numerical method, the method is implemented using computer programming to numerically solve the model. This step usually requires writing or using existing numerical calculation software, such as MATLAB or Python. The results obtained from the numerical solution are analyzed to verify whether they meet expectations and whether they match experimental data. If the results deviate significantly from expectations or experimental data, it is necessary to return to resetting the model parameters or adjusting the model.

[0060] This embodiment describes the solid-phase mass transfer process of a sodium-ion capacitor using the Langmuir adsorption-desorption law model. By mixing the Langmuir adsorption-desorption law model with an electrochemical model, the output response of the hybrid sodium-ion capacitor model under different input conditions can be accurately predicted.

[0061] This embodiment provides a modeling and simulation method for a hybrid sodium ion capacitor model based on the aforementioned embodiments.

[0062] The Langmuir adsorption-desorption law model includes: the Langmuir adsorption equation, the pseudo-first-order adsorption kinetic model, and the pseudo-second-order adsorption kinetic model.

[0063] The Langmuir adsorption equation is θ = K[A] / (1+K[A]);

[0064] The pseudo-first-order adsorption kinetic model is dq / dt=k1(q e -q);

[0065] The pseudo-second-order adsorption kinetic model is dq / dt=k2(q e -q) 2 Where θ is the adsorption degree, k1 is the pseudo-first-order adsorption rate constant, and q eq is the amount of adsorption at adsorption equilibrium, k2 is the amount of adsorption at any time, k2 is the pseudo-second-order adsorption rate constant, K is the Langmuir adsorption constant, and A is the concentration of the adsorbate.

[0066] In this embodiment, the pseudo-first-order adsorption kinetic model is the pseudo-first-order adsorption kinetic equation, also known as the Langmuir rank equation, which is one of the earliest and most commonly used equations describing liquid-phase adsorption processes. This equation assumes that the adsorption rate is proportional to the concentration of the remaining unadsorbed adsorbent. The pseudo-second-order adsorption kinetic model is based on the assumption that the adsorption rate is proportional to the square of the concentration of the remaining unadsorbed adsorbent.

[0067] This embodiment provides a modeling and simulation method for a hybrid sodium ion capacitor model based on the aforementioned embodiments.

[0068] The electrochemical model of the hybrid sodium-ion capacitor is a traditional electrochemical model that removes the solid-phase diffusion equation.

[0069] This embodiment provides an electrochemical model for a hybrid sodium-ion capacitor that removes the solid-phase diffusion equation from the traditional electrochemical model. The mathematical solution process for lithium-ion batteries in traditional electrochemical models includes solid-phase mass transfer, solid-phase potential, liquid-phase mass transfer, liquid-phase potential, and charge conservation. However, for sodium-ion capacitors, except for solid-phase mass transfer, the solution for the remaining processes is essentially the same as for lithium-ion batteries. The solid-phase mass transfer process of sodium-ion capacitors can be described by adsorption kinetics, specifically using Langmuir adsorption theory, that is, combining the electrochemical model of the hybrid sodium-ion capacitor with the Langmuir adsorption-desorption law model. When the physical processes of the hybrid sodium-ion capacitor predominate, the Langmuir adsorption equation in the Langmuir adsorption-desorption law model is preferentially used for model solving; when the chemical processes of the hybrid sodium-ion capacitor predominate, the BV equation (Butler-Volmer equation) in the electrochemical model of the hybrid sodium-ion capacitor is preferentially used for model solving.

[0070] This embodiment provides a modeling and simulation method for a hybrid sodium ion capacitance model based on the aforementioned embodiments. After step S130, it further includes:

[0071] By simulating the validated hybrid sodium ion capacitor model, the internal electrochemical state of the hybrid sodium ion capacitor was obtained. The internal electrochemical state of the hybrid sodium ion capacitor includes: ion concentration distribution, potential distribution, and adsorption state on the electrode surface.

[0072] This embodiment uses a mixed sodium ion capacitor model to monitor the electrochemical behavior and internal state of a mixed sodium ion capacitor.

[0073] In one embodiment, refer to the appendix to the specification. Figure 2 A modeling and simulation system for a hybrid sodium-ion capacitance model, characterized in that it includes:

[0074] Model building module 10 is used to build the Langmuir adsorption-desorption law model and the electrochemical model of the mixed sodium ion capacitor. The Langmuir adsorption-desorption law model is a model based on the Langmuir adsorption-desorption law to describe the solid-phase mass transfer process of the mixed sodium ion capacitor. The Langmuir adsorption-desorption law model and the electrochemical model of the mixed sodium ion capacitor are sent to the model mixing module.

[0075] The model mixing module 20 is used to mix the Langmuir adsorption-desorption law model and the electrochemical model to obtain a mixed sodium ion capacitance model; and to send the mixed sodium ion capacitance model to the model verification module.

[0076] The model verification module 30 is used to calibrate and verify the mixed sodium ion capacitor parameters in the mixed sodium ion capacitor model to obtain the verified mixed sodium ion capacitor model; and to send the verified mixed sodium ion capacitor model to the model simulation module.

[0077] The model simulation module 40 is used to simulate the verified hybrid sodium-ion capacitor model to obtain the output response of the hybrid sodium-ion capacitor under different input conditions.

[0078] This embodiment describes the solid-phase mass transfer process of a sodium-ion capacitor using the Langmuir adsorption-desorption law model. By mixing the Langmuir adsorption-desorption law model with an electrochemical model, the output response of the hybrid sodium-ion capacitor model under different input conditions can be accurately predicted.

[0079] This embodiment provides a modeling and simulation system for a hybrid sodium ion capacitor model based on the aforementioned embodiments.

[0080] The Langmuir adsorption-desorption law model includes: the Langmuir adsorption equation, the pseudo-first-order adsorption kinetic model, and the pseudo-second-order adsorption kinetic model.

[0081] The Langmuir adsorption equation is θ = K[A] / (1+K[A]);

[0082] The pseudo-first-order adsorption kinetic model is dq / dt=k1(q e -q);

[0083] The pseudo-second-order adsorption kinetic model is dq / dt=k2(q e -q) 2 Where θ is the adsorption degree, k1 is the pseudo-first-order adsorption rate constant, and q e q is the amount of adsorption at adsorption equilibrium, k2 is the amount of adsorption at any time, k2 is the pseudo-second-order adsorption rate constant, K is the Langmuir adsorption constant, and A is the concentration of the adsorbate.

[0084] In this embodiment, the pseudo-first-order adsorption kinetic model is the pseudo-first-order adsorption kinetic equation, also known as the Langmuir rank equation, which is one of the earliest and most commonly used equations describing liquid-phase adsorption processes. This equation assumes that the adsorption rate is proportional to the concentration of the remaining unadsorbed adsorbent. The pseudo-second-order adsorption kinetic model is based on the assumption that the adsorption rate is proportional to the square of the concentration of the remaining unadsorbed adsorbent.

[0085] This embodiment provides a modeling and simulation system for a hybrid sodium ion capacitor model based on the aforementioned embodiments.

[0086] The electrochemical model of the hybrid sodium-ion capacitor is a traditional electrochemical model that removes the solid-phase diffusion equation.

[0087] This embodiment provides an electrochemical model for a hybrid sodium-ion capacitor that removes the solid-phase diffusion equation from the traditional electrochemical model. The mathematical solution process for lithium-ion batteries in traditional electrochemical models includes solid-phase mass transfer, solid-phase potential, liquid-phase mass transfer, liquid-phase potential, and charge conservation. However, for the mathematical solution of sodium-ion capacitors, except for solid-phase mass transfer, the solution for the remaining processes is essentially the same as for lithium-ion batteries. The solid-phase mass transfer process of sodium-ion capacitors can be described by adsorption kinetics, specifically using Langmuir adsorption theory, that is, combining the electrochemical model of the hybrid sodium-ion capacitor with the Langmuir adsorption-desorption law model.

[0088] This embodiment provides a modeling and simulation system for a hybrid sodium ion capacitor model based on the aforementioned embodiments.

[0089] The model simulation module 40 is also used to obtain the internal electrochemical state of the mixed sodium ion capacitor by simulating the verified mixed sodium ion capacitor model. The internal electrochemical state of the mixed sodium ion capacitor includes: the concentration distribution of ions, the potential distribution, and the adsorption state of the electrode surface.

[0090] It should be noted that the above embodiments can be freely combined as needed. The above are merely preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A modeling and simulation method for a hybrid sodium-ion capacitor model, characterized in that, include: A Langmuir adsorption-desorption law model and an electrochemical model of the mixed sodium ion capacitor are established. The Langmuir adsorption-desorption law model is a model based on the Langmuir adsorption-desorption law to describe the solid-phase mass transfer process of the mixed sodium ion capacitor. By combining the Langmuir adsorption-desorption law model and the electrochemical model, a mixed sodium ion capacitance model is obtained. The mixed sodium ion capacitance parameters in the mixed sodium ion capacitance model are calibrated and verified to obtain the verified mixed sodium ion capacitance model. The output response of the hybrid sodium ion capacitor under different input conditions was obtained by simulating the verified hybrid sodium ion capacitor model. The Langmuir adsorption-desorption law model includes: the Langmuir adsorption equation, the pseudo-first-order adsorption kinetic model, and the pseudo-second-order adsorption kinetic model; The Langmuir adsorption equation is θ = K[A] / (1 + K[A]); The pseudo-first-order adsorption kinetic model is ; The pseudo-second-order adsorption kinetic model is ; Where θ is the adsorption degree. It is a pseudo-first-order adsorption rate constant. It is the amount of adsorption at adsorption equilibrium. It represents the amount of adsorption at any given time. It is the pseudo-second-order adsorption rate constant, where K is the Langmuir adsorption constant and [A] is the concentration of the adsorbate.

2. The modeling and simulation method for a hybrid sodium ion capacitor model according to claim 1, characterized in that, The electrochemical model of the hybrid sodium-ion capacitor is a traditional electrochemical model that removes the solid-phase diffusion equation.

3. The modeling and simulation method for a hybrid sodium ion capacitor model according to claim 1, characterized in that, After calibrating and verifying the mixed sodium ion capacitance parameters in the mixed sodium ion capacitance model to obtain the verified mixed sodium ion capacitance model, the method further includes: By simulating the verified mixed sodium ion capacitor model, the internal electrochemical state of the mixed sodium ion capacitor is obtained. The internal electrochemical state of the mixed sodium ion capacitor includes: ion concentration distribution, potential distribution, and adsorption state on the electrode surface.

4. A modeling and simulation system for a hybrid sodium-ion capacitance model, characterized in that, include: The model building module is used to build a Langmuir adsorption-desorption law model and an electrochemical model of the mixed sodium ion capacitor. The Langmuir adsorption-desorption law model is a model based on the Langmuir adsorption-desorption law to describe the solid-phase mass transfer process of the mixed sodium ion capacitor. The Langmuir adsorption-desorption law model and the electrochemical model of the mixed sodium ion capacitor are sent to the model mixing module. The model mixing module is used to mix the Langmuir adsorption-desorption law model and the electrochemical model to obtain a mixed sodium ion capacitance model; the mixed sodium ion capacitance model is then sent to the model verification module. The model verification module is used to calibrate and verify the mixed sodium ion capacitor parameters in the mixed sodium ion capacitor model to obtain the verified mixed sodium ion capacitor model; and to send the verified mixed sodium ion capacitor model to the model simulation module. The model simulation module is used to obtain the output response of the hybrid sodium ion capacitor under different input conditions by simulating the verified hybrid sodium ion capacitor model. The Langmuir adsorption-desorption law model includes: the Langmuir adsorption equation, the pseudo-first-order adsorption kinetic model, and the pseudo-second-order adsorption kinetic model; The Langmuir adsorption equation is θ = K[A] / (1 + K[A]); The pseudo-first-order adsorption kinetic model is ; The pseudo-second-order adsorption kinetic model is Where θ is the adsorption degree. It is a pseudo-first-order adsorption rate constant. It is the amount of adsorption at adsorption equilibrium. It represents the amount of adsorption at any given time. It is the pseudo-second-order adsorption rate constant, where K is the Langmuir adsorption constant and [A] is the concentration of the adsorbate.

5. The modeling and simulation system for a hybrid sodium ion capacitor model according to claim 4, characterized in that, The electrochemical model of the hybrid sodium-ion capacitor is a traditional electrochemical model that removes the solid-phase diffusion equation.

6. The modeling and simulation system for a hybrid sodium-ion capacitor model according to claim 4, characterized in that, The model simulation module is also used to obtain the internal electrochemical state of the mixed sodium ion capacitor by simulating the verified mixed sodium ion capacitor model. The internal electrochemical state of the mixed sodium ion capacitor includes: ion concentration distribution, potential distribution, and adsorption state on the electrode surface.

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