A method of modeling a reversible solid oxide cell

Abstract

The application provides a modeling method of a reversible solid oxide cell, and belongs to the technical field of comprehensive energy system optimization; the modeling method comprises the following steps: establishing a physical model of the reversible solid oxide cell; establishing a high-dimensional operation domain model of the reversible solid oxide cell; establishing a high-dimensional operation domain proxy model of the reversible solid oxide cell based on a hybrid neural network; and combining a linearization method to reconstruct the model into a mixed integer linear programming form. The superiority of the high-dimensional operation domain proxy model of the reversible solid oxide cell based on the hybrid neural network in high fitting precision and small calculation burden is effectively characterized, and the feasibility of integrating the reversible solid oxide cell model into power system operation is evaluated.

Description

Technical Field

[0001] This invention belongs to the field of integrated energy system optimization technology, and specifically relates to a modeling method for reversible solid oxide batteries. Background Technology

[0002] As a promising technology, reversible solid oxide batteries (SOBs) can achieve bidirectional electro-hydrogen-thermal conversion in a single device, offering advantages such as compact structure and high round-trip efficiency. They can operate in both SOB electrolyzer and SOB fuel cell modes, combining hydrogen storage and thermal energy storage to support power system supply and demand balance. Refined modeling of SOBs is crucial for characterizing their flexible operation. Existing research has developed component-level electrochemical kinetic models for SOBs to simulate their transient performance. However, power system operation does not focus on the internal characteristics of SOBs, nor can it integrate such complex high-order nonlinear models. Furthermore, some studies use empirical formulas to characterize the energy conversion of SOBs, but fail to capture real electrochemical kinetics. In addition, some studies either fail to consider the extensive heat recovery of SOBs or employ complex linearization methods, failing to balance the flexibility of SOBs with the computational burden of the models.

[0003] To address the above issues, this invention proposes a physics-based, data-driven modeling method for reversible solid oxide batteries (SOBs) and reconstructs it into a MILP (Multi-Input Multi-Process) form for integration into power system optimization. The model considers extensive heat recovery to enhance flexibility and exhibits significant advantages in both computational accuracy and computational burden. The "physics-based" aspect is manifested in two ways: first, the model simulates the efficiency of the reversible SOB module using a physics-based approach; the empirical formula for SOB efficiency is obtained through simulations based on real equipment operating conditions and electrochemical kinetic models. Second, physical characteristics are considered in the data-driven modeling to enhance interpretability; the convex model construction of the reversible SOB considers the physical characteristics of the high-dimensional operating domain, employing a hybrid neural network as a proxy to improve accuracy and enhance interpretability.

[0004] A search revealed Chinese invention patent CN117423865A, which discloses a reversible solid oxide battery model and its modeling method based on dynamic thermoelectric characteristics, belonging to the field of energy conversion and storage technology. The patent establishes an RSOC model including a thermodynamic model, an electrochemical model, and a state-switching model. The state-switching model includes four operating states: power generation, electrolysis, shutdown, and thermal standby. By incorporating relaxation variables, the impedance characteristics of the RSOC as a load or generator under different states are calculated, and the relationships between the RSOC's temperature, current, and voltage over time are fitted.

[0005] Upon comparison, the aforementioned prior art documents differ from this application in the following ways:

[0006] 1. Patent CN117423865A does not comprehensively consider heat recovery, mainly focusing on the thermal management system composed of "reversible solid oxide battery stack + heat recovery system". This application, however, considers the extensive possibilities of heat recovery in electrolysis and power generation modes. It captures the external characteristics of the system through the actual operating conditions of the reversible solid oxide battery and the electrochemical kinetic simulation model. The heat of chemical reaction is characterized as part of the efficiency loss, and a first-order lumped heat model is used to describe the intrinsic relationship between temperature and heat.

[0007] 2. Patent CN117423865A's modeling is rather coarse. In terms of the thermo-electric energy conversion mechanism, it mainly provides a unified thermodynamic equilibrium and linearized electrochemical relationship for solid oxide fuel cell power generation and solid oxide electrolyzer modes, describing the electrolysis process as a single mode. In contrast, this application's modeling is more refined, further dividing electrolysis into endothermic and exothermic electrolysis, distinguishing the differences in the endothermic and exothermic mechanisms of the fuel cell stack under different electrolysis conditions. The operating regions of the two modes are separated by "state boundaries."

[0008] 3. Patent CN117423865A only uses a tangent plane to fit the operating surface of the equipment, which is a relatively simple and crude method with low accuracy. This patent proposes a data-mechanism fusion-driven hybrid neural network proxy modeling method. It uses a physics-based model to simulate the efficiency of reversible solid oxide battery modules. The empirical formulas are obtained through simulation based on real equipment operating conditions and electrochemical kinetic models. The high-dimensional operating domain model is derived by discretely sampling its electrical power and temperature. The physical characteristics of the high-dimensional operating domain are considered in the convex model construction, and a hybrid neural network is used for proxy modeling, resulting in higher accuracy. Summary of the Invention

[0009] In view of the shortcomings of the prior art, the purpose of this invention is to provide a modeling method for reversible solid oxide batteries, which solves the problems in the prior art.

[0010] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0011] A modeling method for reversible solid oxide batteries includes the following steps:

[0012] S1. Establish a physical model for reversible solid oxide batteries;

[0013] S2. Establish a high-dimensional operating domain model for reversible solid oxide batteries;

[0014] S3. Establish a high-dimensional operating domain proxy model for reversible solid oxide batteries based on hybrid neural networks;

[0015] S4. Reconstruct the model into a mixed-integer linear programming form by combining linearization methods.

[0016] Furthermore, the physical model of the reversible solid oxide battery is as follows:

[0017] ;

[0018] In the formula, Open circuit voltage, For ohmic resistance, For current density, Let be the ideal gas constant. For operating temperature, For the number of transferred charges, It is Faraday's constant. The anode exchange current density, The cathode exchange current density, The limiting current density of water, To limit the current density of hydrogen, For pressure, For thickness, and These are dynamic parameters.

[0019] Furthermore, the battery power of reversible solid oxide batteries Due to battery voltage and current Calculate the product of:

[0020] ;

[0021] Considering the difference in maximum power between reversible solid oxide batteries in solid oxide electrolyzer and solid oxide fuel cell modes, Based on the operating mode, the efficiency is calculated as follows:

[0022] ;

[0023] ;

[0024] In the formula, and The figures represent the efficiencies in solid oxide electrolyzer and solid oxide fuel cell modes, respectively. and These represent the power outputs in solid oxide electrolyzer and solid oxide fuel cell modes, respectively. and The hydrogen flow rates are for solid oxide electrolyzer and solid oxide fuel cell modes, respectively. This is the lower heating value of hydrogen;

[0025] The safe power and temperature ranges that reversible solid oxide batteries need to meet when operating in different modes are as follows:

[0026] ;

[0027] ;

[0028] ;

[0029] In the formula, and These represent the lower and upper power limits for the solid oxide electrolyzer mode, respectively. and These represent the lower and upper power limits for solid oxide fuel cell mode, respectively. The operating temperature of a reversible solid oxide battery is limited by a lower temperature. and upper temperature limit constraint;

[0030] Efficiency based on electrochemical kinetics exhibits significant nonlinear characteristics. By capturing the external characteristics of the system through actual operating conditions of reversible solid oxide batteries and electrochemical kinetic simulation models, the efficiency is characterized by fitting a function of battery power versus temperature.

[0031] ;

[0032] ;

[0033] In the formula, and For the set of fitting parameters, , and These represent the operating domains of reversible solid oxide batteries in exothermic electrolysis, endothermic electrolysis, and fuel cell modes, respectively.

[0034] The operating regions for both endothermic and exothermic electrolysis are separated by state boundaries:

[0035] ;

[0036] ;

[0037] ;

[0038] In the formula, It is a fitting function used to describe the state boundary. , and These are the fitting parameters.

[0039] The heat of chemical reaction in reversible solid oxide batteries and The portion characterized as efficiency loss:

[0040] ;

[0041] ;

[0042] Furthermore, since reversible solid oxide batteries exhibit different thermal dynamics under different operating modes, a first-order lumped thermal model is used to describe the intrinsic relationship between temperature and heat:

[0043] ;

[0044] Heat loss It includes both convective and radiative losses:

[0045] ;

[0046] In the formula, For temperature changes, For the heat capacity of the reversible solid oxide battery system, For time intervals, For exposed heat exchange area, The convective heat transfer coefficient is... For surface emissivity, This is the Stefan–Boltzmann constant. The average operating temperature of the reversible solid oxide battery. For ambient temperature, For heat recovery in reversible solid oxide batteries , and The electrical, hydrogen, and heat released by the reversible solid oxide battery are represented by negative values, indicating absorption from the outside. and This represents the number of cells connected in series in a reversible solid oxide battery stack and the number of connections in the stack within the reversible solid oxide battery system.

[0047] Furthermore, the high-dimensional operating domain model of the reversible solid oxide battery is derived by discretely sampling the electrical power and temperature of the reversible solid oxide battery.

[0048] Furthermore, the high-dimensional operating domain model of the reversible solid oxide battery is proxies by a hybrid neural network with enhanced interpretability, as follows:

[0049] Considering that the input convex neural network maintains convexity with respect to the input, it is used to proxy The hydrogen and heat below; while deep neural networks have a powerful ability to fit non-convex functions, used to proxy The hydrogen and heat below; and The efficiency of the reversible solid oxide battery remains constant, and hydrogen and heat exhibit a linear relationship with power and temperature, requiring no proxy.

[0050] The architectures of input convex neural networks and deep neural networks are as follows:

[0051] ;

[0052] ;

[0053] In the formula, and For the network's input and output, and These are the inputs to the convex neural network and the outputs of the k-th layer of the deep neural network, respectively. and The input convex neural network and the deep neural network are respectively non-linear activation functions of the k-th layer. The ReLU activation function is used in the hidden layer and the linear activation function is used in the output layer. The weights of the k-th layer of the input convex neural network are given by the input. and These are the weights of the k-th layer of the input convex neural network and the deep neural network, respectively. and These are the input convex neural network and the deep neural network, respectively. Layer bias, and These represent the number of layers in the input convex neural network and the deep neural network, respectively.

[0054] Furthermore, the nonlinearity in the input convex neural network and deep neural network is caused by the activation function, and the ReLU activation function is precisely equivalently transformed using the Big-M method; the state boundary is characterized by the type 2 special ordered set constraint of the Big-M method:

[0055] ;

[0056] ;

[0057] It is a special type of sequence set constraint;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] ;

[0063] ;

[0064] In the formula, It is a segmentation point Weight variables, It is a segmentation point unit power, It is the number of segmentation points. yes Piecewise linear interpolation approximation, It is a binary selection variable representing the operand region; 1 indicates that in Operation, 0 indicates in operate, It is a constant. and These are hydrogen and heat, respectively, in the context of a deep neural network agent.

[0065] The high-dimensional operating domain of the agent-based reversible solid oxide battery is reconstructed as follows:

[0066] ;

[0067] ;

[0068] In the formula, and A vector composed of binary variables. It is a constant.

[0069] Furthermore, in solid oxide electrolyzer mode, reversible solid oxide batteries can only operate at... or Internally, the Big-M method combined with two types of special ordered sets is used for characterization; the operating domain of the reversible solid oxide battery in the solid oxide fuel cell mode can be directly proxies using an input convex neural network; the high-dimensional operating domain model of the reversible solid oxide battery is reconstructed as follows:

[0070] ;

[0071] In the formula, and These are input convex neural networks and deep neural networks, respectively.

[0072] The external characteristic model of a reversible solid oxide battery is as follows:

[0073] ;

[0074] In the formula, , and The electrical, hydrogen, and heat released by the reversible solid oxide battery are represented by negative values, indicating absorption from the outside. and To represent the operating mode of a reversible solid oxide battery, a binary variable is obtained. and This represents the number of cells connected in series in a reversible solid oxide battery stack and the number of connections in the stack within the reversible solid oxide battery system.

[0075] Furthermore, the external characteristic model involves the product of binary variables and continuous variables, which is handled using a linearization method:

[0076] ;

[0077] ;

[0078] ;

[0079] ;

[0080] In the formula, , , , , and As an auxiliary variable; and These represent the minimum and maximum unit power values ​​under the two modes, respectively; and These correspond to the minimum and maximum values ​​of hydrogen, respectively; and This represents the minimum and maximum values ​​of thermal energy. The corresponding set includes two modes: solid oxide electrolyzer (EC) mode and solid oxide fuel cell (FC) mode.

[0081] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0082] 1. This invention proposes a high-dimensional operating domain model for reversible solid oxide batteries.

[0083] 2. This invention proposes a high-dimensional operating domain proxy model for reversible solid oxide batteries based on hybrid neural networks.

[0084] 3. Compared with deep neural networks, input convex neural networks and triangular segmentation methods, the present invention has the advantages of high fitting accuracy and low computational burden. Attached Figure Description

[0085] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0086] Figure 1 This is a flowchart of the modeling method for the reversible solid oxide battery of the present invention;

[0087] Figure 2 This is a schematic diagram of the high-dimensional operating domain model of the reversible solid oxide battery of the present invention;

[0088] in, Figure 2 (a) in the text represents the hydrogen input in solid oxide fuel cell mode; Figure 2 (b) in the figure represents the heat output in solid oxide fuel cell mode; Figure 2 (c) in the figure represents hydrogen output in solid oxide electrolyzer mode; Figure 2 In the figure, (d) represents the heat output in the solid oxide electrolyzer mode.

[0089] Figure 3 This is a schematic diagram of the improved IEEE 33-node system architecture used in this invention;

[0090] Figure 4 This is a schematic diagram of the operating point distribution of the reversible solid oxide battery of the present invention;

[0091] in, Figure 4 (a) in the text represents the hydrogen input in solid oxide fuel cell mode; Figure 4 (b) in the figure represents the heat output in solid oxide fuel cell mode; Figure 4 (c) in the figure represents hydrogen output in solid oxide electrolyzer mode; Figure 4 In the figure, (d) represents the heat output in the solid oxide electrolyzer mode. Detailed Implementation

[0092] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. 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.

[0093] Example 1:

[0094] like Figure 1 As shown, this embodiment illustrates a modeling method for reversible solid oxide batteries, comprising the following steps:

[0095] S1, Establish a physical model for reversible solid oxide batteries;

[0096] The physical model of a reversible solid oxide battery is as follows:

[0097] ;

[0098] In the formula, Open circuit voltage, For ohmic resistance, For current density, Let be the ideal gas constant. For operating temperature, For the number of transferred charges, It is Faraday's constant. The anode exchange current density, The cathode exchange current density, The limiting current density of water, To limit the current density of hydrogen, For pressure, For thickness, and These are dynamic parameters.

[0099] Furthermore, the battery power of reversible solid oxide batteries Due to battery voltage and current Calculate the product of:

[0100] ;

[0101] Considering the difference in maximum power between reversible solid oxide batteries in solid oxide electrolyzer and solid oxide fuel cell modes, Based on the operating mode, the efficiency is calculated as follows:

[0102] ;

[0103] ;

[0104] In the formula, and The figures represent the efficiencies in solid oxide electrolyzer and solid oxide fuel cell modes, respectively. and The power outputs are for solid oxide electrolyzer and solid oxide fuel cell modes, respectively. and The hydrogen flow rates are for solid oxide electrolyzer and solid oxide fuel cell modes, respectively. This is the lower heating value of hydrogen;

[0105] The safe power and temperature ranges that reversible solid oxide batteries need to meet when operating in different modes are as follows:

[0106] ;

[0107] ;

[0108] ;

[0109] In the formula, and These represent the lower and upper power limits for the solid oxide electrolyzer mode, respectively. and These represent the lower and upper power limits for solid oxide fuel cell mode, respectively. The operating temperature of a reversible solid oxide battery is limited by a lower temperature. and upper limit constraint;

[0110] Efficiency based on electrochemical kinetics exhibits significant nonlinear characteristics. By capturing the external characteristics of the system through actual operating conditions of reversible solid oxide batteries and electrochemical kinetic simulation models, the efficiency is characterized by fitting a function of battery power versus temperature.

[0111] ;

[0112] ;

[0113] In the formula, and For the set of fitting parameters, , and These represent the operating domains of reversible solid oxide batteries in exothermic electrolysis, endothermic electrolysis, and fuel cell modes, respectively.

[0114] The operating regions for both endothermic and exothermic electrolysis are separated by state boundaries:

[0115] ;

[0116] ;

[0117] ;

[0118] In the formula, It is a fitting function used to describe the state boundary. , and These are the fitting parameters.

[0119] The heat of chemical reaction in reversible solid oxide batteries and The portion characterized as efficiency loss:

[0120] ;

[0121] ;

[0122] Furthermore, since reversible solid oxide batteries exhibit different thermal dynamics under different operating modes, a first-order lumped thermal model is used to describe the intrinsic relationship between temperature and heat:

[0123] ;

[0124] Heat loss It includes both convective and radiative losses:

[0125] ;

[0126] In the formula, For temperature changes, For the heat capacity of the reversible solid oxide battery system, For time intervals, For exposed heat exchange area, The convective heat transfer coefficient is... For surface emissivity, This is the Stefan–Boltzmann constant. The average operating temperature of the reversible solid oxide battery. For ambient temperature, For heat recovery of reversible solid oxide batteries.

[0127] S2, Establishing a high-dimensional operational domain modeling method for reversible solid oxide batteries based on physical models;

[0128] like Figure 2 As shown, where, Figure 2 (a) in the text represents the hydrogen input in solid oxide fuel cell mode; Figure 2 (b) in the figure represents the heat output in solid oxide fuel cell mode; Figure 2 (c) in the figure represents hydrogen output in solid oxide electrolyzer mode; Figure 2 In the model, (d) represents the heat output in the solid oxide electrolyzer mode. In the high-dimensional operating domain model of the reversible solid oxide battery, the hydrogen input and heat output in the solid oxide fuel cell mode are smooth convex surfaces, while the hydrogen output and heat output in the solid oxide electrolyzer mode are non-smooth non-convex surfaces. By discretely sampling the power and temperature of the reversible solid oxide battery, the high-dimensional operating domain model of the reversible solid oxide battery is derived.

[0129] S3, Establish a high-dimensional operating domain proxy model for reversible solid oxide batteries based on hybrid neural networks;

[0130] Considering that the input convex neural network maintains convexity with respect to the input, it is used to proxy The hydrogen and heat below; while deep neural networks have a powerful ability to fit non-convex functions, used to proxy The hydrogen and heat below; and The efficiency of the reversible solid oxide battery remains constant, and hydrogen and heat exhibit a linear relationship with power and temperature, requiring no proxy.

[0131] The architectures of input convex neural networks and deep neural networks are as follows:

[0132] ;

[0133] ;

[0134] In the formula, and For the network's input and output, and These are the inputs to the convex neural network and the outputs of the k-th layer of the deep neural network, respectively. and The input convex neural network and the deep neural network are respectively non-linear activation functions of the k-th layer. The ReLU activation function is used in the hidden layer and the linear activation function is used in the output layer. The weights of the k-th layer of the input convex neural network are given by the input. and These are the weights of the k-th layer of the input convex neural network and the deep neural network, respectively. and These are the input convex neural network and the deep neural network, respectively. Layer bias, and These represent the number of layers in the input convex neural network and the deep neural network, respectively.

[0135] Considering that the input convex neural network maintains convexity with respect to the input, it is used to proxy The hydrogen and heat below; while deep neural networks have a powerful ability to fit non-convex functions, used to proxy The hydrogen and heat below. The efficiency of the reversible solid oxide battery remains constant, and the hydrogen and heat exhibit a linear relationship with power and temperature, requiring no proxy.

[0136] S4, combining linearization methods, reconstructs the model into a mixed-integer linear programming form. The nonlinearity in the input convex neural network and deep neural network is caused by the activation function; the ReLU activation function undergoes an exact equivalent transformation using the Big-M method; the state boundary is characterized by the type 2 special ordered set constraint of the Big-M method.

[0137] ;

[0138] ;

[0139] It is a special type of sequence set constraint;

[0140] ;

[0141] ;

[0142] ;

[0143] ;

[0144] ;

[0145] ;

[0146] In the formula, It is a segmentation point Weight variables, It is a segmentation point unit power, It is the number of segmentation points. yes Piecewise linear interpolation approximation, It is a binary selection variable representing the operand region; 1 indicates that in Operation, 0 indicates in operate, It is a constant. and These are hydrogen and heat, respectively, in the context of a deep neural network agent.

[0147] The high-dimensional operating domain of the agent-based reversible solid oxide battery is reconstructed as follows:

[0148] ;

[0149] ;

[0150] In the formula, and A vector composed of binary variables. It is a constant.

[0151] Reversible solid oxide batteries can only operate in solid oxide electrolyzer mode. or Internally, the Big-M method combined with two types of special ordered sets is used for characterization; the operating domain of the reversible solid oxide battery in the solid oxide fuel cell mode can be directly proxies using an input convex neural network; the high-dimensional operating domain model of the reversible solid oxide battery is reconstructed as follows:

[0152] ;

[0153] In the formula, and These are input convex neural networks and deep neural networks, respectively.

[0154] The external characteristic model of a reversible solid oxide battery is as follows:

[0155] ;

[0156] In the formula, , and The electrical, hydrogen, and heat released by the reversible solid oxide battery are represented by negative values, indicating absorption from the outside. and To represent the operating mode of a reversible solid oxide battery, a binary variable is obtained. and This represents the number of cells connected in series in a reversible solid oxide battery stack and the number of connections in the stack within the reversible solid oxide battery system.

[0157] The external characteristic model involves the product of binary variables and continuous variables, which is handled using a linearization method:

[0158] ;

[0159] ;

[0160] ;

[0161] ;

[0162] In the formula, , , , , and As an auxiliary variable; and These represent the minimum and maximum unit power values ​​under the two modes, respectively; and These correspond to the minimum and maximum values ​​of hydrogen, respectively; and This represents the minimum and maximum values ​​of thermal energy.

[0163] Example 2:

[0164] like Figure 3 As shown, this embodiment presents an improved IEEE 33-node system based on the one used in Embodiment 1.

[0165] In this example, nodes 6, 18, 24, and 32 are equipped with 3 MW wind turbines (WT) and 0.5 MWh batteries (BT, with a maximum charge / discharge time of 2 hours). The reversible solid oxide battery system deployed at node 10 comprises 20 battery stacks, each consisting of 60 series-connected battery cells. Supporting facilities include a 1.5-ton hydrogen storage unit (HS, with a maximum charge / discharge time of 8 hours) and a 60 MWh thermal storage unit (triangular segmentation method, with a maximum charge / discharge time of 6 hours). The energy balance cycle for the battery stacks and thermal storage is intraday (24 hours), while the hydrogen storage operates on a weekly cycle (168 hours).

[0166] like Figure 4 As shown, where, Figure 4 (a) in the text represents the hydrogen input in solid oxide fuel cell mode; Figure 4 (b) in the figure represents the heat output in solid oxide fuel cell mode; Figure 4 (c) in the figure represents hydrogen output in solid oxide electrolyzer mode; Figure 4 (d) in the figure represents the heat output in the solid oxide electrolyzer mode, illustrating the operating point of the reversible solid oxide battery over time. The operating point can be accurately identified within the high-density operating region, particularly in areas with steep curvature, confirming the effectiveness of the proposed method. Furthermore, the operating point distribution indicates that the reversible solid oxide battery can smoothly switch between endothermic, exothermic, and exothermic fuel cell modes, fully demonstrating the versatility of the model.

[0167] The mean absolute percentage errors (MAR) of high-dimensional operating domain model surrogates using input convex neural networks, deep neural networks, and triangulation methods were compared. When fitting hydrogen and pyrolysis, deep neural networks achieved the highest accuracy, with MAR of 0.0725% and 0.1713%, respectively. The triangulation method had a fitting error three times that of deep neural networks. Input convex neural networks exhibited the lowest MAR, at 0.3441% for hydrogen and 0.8034% for pyrolysis, representing an improvement of more than tenfold over the triangulation method. This demonstrates the high accuracy and interpretability-enhancing capabilities of the physics-based interpretability-enhancing hybrid neural network surrogate method.

[0168] This study compares the wind power curtailment and model solution time of various agent-based methods. Using the proposed interpretable enhanced hybrid neural network agent, the weekly wind power curtailment is 996.24 MWh. The curtailment errors of the input convex neural network and deep neural network agents are -12.77 MWh and -2.33 MWh, respectively, while the error of the triangulation method increases with the number of triangular segments. Furthermore, the solution time of the interpretable enhanced hybrid neural network agent is 130.59 seconds, comparable to that of the input convex neural network; while the triangulation method shows a sharp increase in error with the number of triangular segments. Compared to the interpretable enhanced hybrid neural network, other methods often underestimate the wind power curtailment (operating costs), and the interpretable enhanced hybrid neural network also has a lower computational burden.

[0169] Example 3:

[0170] The modeling method of the present invention can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CD-ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code originally stored on a remote recording medium or a non-transitory machine-readable medium and subsequently stored on a local recording medium, downloaded via a network. Thus, the method described herein can be processed by software stored on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that the computer, processor, microprocessor controller, or programmable hardware includes storage components (e.g., RAM, ROM, flash memory, etc.) capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the method described herein. Furthermore, when a general-purpose computer accesses the code used to implement the method shown herein, the execution of the code transforms the general-purpose computer into a dedicated computer for executing the method shown herein.

[0171] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A modeling method for reversible solid oxide batteries, characterized in that, Includes the following steps: S1. Establish a physical model for reversible solid oxide batteries; S2. Establish a high-dimensional operating domain model for reversible solid oxide batteries; S3. Establish a high-dimensional operating domain proxy model for reversible solid oxide batteries based on hybrid neural networks; S4. Reconstruct the model into a mixed-integer linear programming form using linearization methods; The high-dimensional operating domain model of the reversible solid oxide battery is proxies by a hybrid neural network with enhanced interpretability, as follows: Considering that the input convex neural network maintains convexity with respect to the input, it is used to proxy The hydrogen and heat below; while deep neural networks have a powerful ability to fit non-convex functions, used to proxy The hydrogen and heat below; and The efficiency of the reversible solid oxide battery remains constant, and hydrogen and heat exhibit a linear relationship with power and temperature, requiring no proxy. The architectures of input convex neural networks and deep neural networks are as follows: ； ； In the formula, and For the network's input and output, and These are the inputs to the convex neural network and the outputs of the k-th layer of the deep neural network, respectively. and The input convex neural network and the deep neural network are respectively non-linear activation functions of the k-th layer. The ReLU activation function is used in the hidden layer and the linear activation function is used in the output layer. The weights of the k-th layer of the input convex neural network are given by the input. and These are the weights of the k-th layer of the input convex neural network and the deep neural network, respectively. and These are the input convex neural network and the deep neural network, respectively. Layer bias, and These represent the number of layers in the input convex neural network and the deep neural network, respectively. The nonlinearity in the input convex neural network and deep neural network is caused by the activation function, and the ReLU activation function is precisely equivalently transformed using the Big-M method; the state boundary is characterized by the type 2 special ordered set constraint of the Big-M method: ； ； It is a special type of sequence set constraint; ； ； ； ； ； ； ； In the formula, It is a segmentation point Weight variables, It is a segmentation point unit power, It is the number of segmentation points. yes Piecewise linear interpolation approximation, It is a binary selection variable representing the operand region; 1 indicates that in Operation, 0 indicates in operate, It is a constant. and These are hydrogen and heat in the context of a deep neural network agent. This refers to the operating temperature of reversible solid oxide batteries. and The figures represent the efficiencies in solid oxide electrolyzer and solid oxide fuel cell modes, respectively. This refers to the power output in solid oxide electrolysis cell mode. This represents the hydrogen flow rate in solid oxide electrolyzer mode. This is the lower heating value of hydrogen. It is a fitting function used to describe the state boundary. , and These are the fitting parameters. The heat of chemical reaction in a reversible solid oxide battery; The high-dimensional operating domain of the agent-based reversible solid oxide battery is reconstructed as follows: ； ； In the formula, and A vector composed of binary variables. It is a constant.

2. The modeling method for a reversible solid oxide battery according to claim 1, characterized in that, The physical model of the reversible solid oxide battery is as follows: ； In the formula, Open circuit voltage, For ohmic resistance, For current density, Let be the ideal gas constant. This refers to the operating temperature of reversible solid oxide batteries. For the number of transferred charges, It is Faraday's constant. The anode exchange current density, The cathode exchange current density, The limiting current density of water, To limit the current density of hydrogen, For pressure, For thickness, and These are dynamic parameters.

3. The modeling method for a reversible solid oxide battery according to claim 2, characterized in that, Battery power of reversible solid oxide batteries Due to battery voltage and current Calculate the product of: ； Considering the difference in maximum power between reversible solid oxide batteries in solid oxide electrolyzer and solid oxide fuel cell modes, Based on the operating mode, the efficiency is calculated as follows: ； ； In the formula, and The figures represent the efficiencies in solid oxide electrolyzer and solid oxide fuel cell modes, respectively. and These represent the power outputs in solid oxide electrolyzer and solid oxide fuel cell modes, respectively. and The hydrogen flow rates are for solid oxide electrolyzer and solid oxide fuel cell modes, respectively. This is the lower heating value of hydrogen; The safe power and temperature ranges that reversible solid oxide batteries need to meet when operating in different modes are as follows: ； ； ； In the formula, and These represent the lower and upper power limits for the solid oxide electrolyzer mode, respectively. and These represent the lower and upper power limits for solid oxide fuel cell mode, respectively. The operating temperature of a reversible solid oxide battery is limited by a lower temperature. and upper temperature limit constraint; Efficiency based on electrochemical kinetics exhibits significant nonlinear characteristics. By capturing the external characteristics of the system through actual operating conditions of reversible solid oxide batteries and electrochemical kinetic simulation models, the efficiency is characterized by fitting a function of battery power versus temperature. ； ； In the formula, and For the set of fitting parameters, , and These represent the operating domains of reversible solid oxide batteries in exothermic electrolysis, endothermic electrolysis, and fuel cell modes, respectively. The operating regions for both endothermic and exothermic electrolysis are separated by state boundaries: ； ； ； In the formula, It is a fitting function used to describe the state boundary. , and These are the fitting parameters.

4. The modeling method for a reversible solid oxide battery according to claim 3, characterized in that, The heat of chemical reaction in reversible solid oxide batteries and The portion characterized as efficiency loss: ； ； Furthermore, since reversible solid oxide batteries exhibit different thermal dynamics under different operating modes, a first-order lumped thermal model is used to describe the intrinsic relationship between temperature and heat: ； Heat loss It includes both convective and radiative losses: ； In the formula, For temperature changes, For the heat capacity of the reversible solid oxide battery system, For time intervals, For exposed heat exchange area, The convective heat transfer coefficient is... For surface emissivity, This is the Stefan–Boltzmann constant. The average operating temperature of the reversible solid oxide battery. For ambient temperature, For heat recovery in reversible solid oxide batteries , and The electrical, hydrogen, and heat released by the reversible solid oxide battery are represented by negative values, indicating absorption from the outside. and This represents the number of cells connected in series in a reversible solid oxide battery stack and the number of connections in the stack within the reversible solid oxide battery system.

5. The modeling method for a reversible solid oxide battery according to claim 1, characterized in that, The high-dimensional operating domain model of the reversible solid oxide battery is derived by discretely sampling the power and temperature of the reversible solid oxide battery.

6. The modeling method for a reversible solid oxide battery according to claim 5, characterized in that, Reversible solid oxide batteries can only operate in solid oxide electrolyzer mode. or Internally, the Big-M method combined with two types of special ordered sets is used for characterization; the operating domain of the reversible solid oxide battery in the solid oxide fuel cell mode can be directly proxies using an input convex neural network; the high-dimensional operating domain model of the reversible solid oxide battery is reconstructed as follows: ； In the formula, and These are input convex neural networks and deep neural networks, respectively. The external characteristic model of a reversible solid oxide battery is as follows: ； In the formula, , and The electrical, hydrogen, and heat released by the reversible solid oxide battery are represented by negative values, indicating absorption from the outside. and To represent the operating mode of a reversible solid oxide battery, a binary variable is obtained. and This represents the number of cells connected in series in a reversible solid oxide battery stack and the number of connections in the stack within the reversible solid oxide battery system.

7. The modeling method for a reversible solid oxide battery according to claim 6, characterized in that, The external characteristic model involves the product of binary variables and continuous variables, which is handled using a linearization method: ； ； ； ； In the formula, , , , , and As an auxiliary variable; and These represent the minimum and maximum unit power values ​​under the two modes, respectively; and These correspond to the minimum and maximum values ​​of hydrogen, respectively; and This represents the minimum and maximum values ​​of thermal energy. The corresponding set includes two modes: solid oxide electrolyzer (EC) mode and solid oxide fuel cell (FC) mode.

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