Method and apparatus for controlling load variation of solid oxide fuel cell

Abstract

This application discloses a method and apparatus for variable load control of solid oxide fuel cells (SOFCs), relating to the field of power load control. The method includes establishing a nonlinear state-space model of the SOFC based on its heat flow model; transforming the nonlinear state-space model into a standard state-space model using the Jacobian matrix linearization method; and performing variable load control using a model predictive control algorithm based on the power output objective function, constraints, and the standard state-space model. This invention establishes a cross-scale heat flow model based on the overall heat transfer process of the SOFC, selects appropriate state variables and inputs, and establishes a nonlinear state-space model of the SOFC guided by variable load. The standard state-space model is obtained using Jacobian matrix linearization, and the power is adjusted under multiple constraints using a model predictive control algorithm to meet the expected load changes.

Description

Technical Field

[0001] This application relates to the field of power load control, and in particular to a method and apparatus for variable load control of a solid oxide fuel cell. Background Technology

[0002] Achieving large-scale renewable energy utilization is a crucial pathway to establishing new power systems. The high penetration rate of renewable energy, such as wind and solar power plants replacing traditional thermal energy, has significantly altered the frequency stability and load balance characteristics of power systems. Furthermore, the intermittency and randomness of wind and solar power pose significant challenges to power system stability, leading to increased grid frequency disturbances and load imbalances between generation and consumption sides.

[0003] Stable power supply and load balance in power systems are crucial for the sustainable development of modern society. Currently, there is a lack of corresponding generation flexibility resources to maintain the power system's load supply and demand balance. Therefore, finding suitable flexibility resources to ensure the power system can stably supply the required electricity and meet the load demand has become a key research focus. Solid oxide fuel cells (SOFCs) are an advanced energy conversion technology that can directly convert hydrogen energy into electrical energy, featuring high energy conversion efficiency and great flexibility in fuel selection. Their high operating temperature not only facilitates the direct use of various fuels but also significantly improves power efficiency, typically exceeding 60%, making them a feasible solution to supplement flexibility resources and effectively address load fluctuations in the power system and the uncertainties of new energy generation. Energy systems integrated with SOFCs represent a technology with great potential to meet the demand for faster load response.

[0004] Solid oxide fuel cells (SOFCs) are complex nonlinear systems with multiple dimensions and scales. Most existing research focuses on dynamic simulations of the fuel cells, providing relatively detailed data on temperature, concentration, velocity, and stress distribution. However, current control measures for SOFCs mainly concentrate on temperature-related thermal management strategies and output voltage optimization. Dynamic load control of SOFCs within safety constraints is of profound significance for supplementing grid flexibility resources at present. Summary of the Invention

[0005] The purpose of this application is to provide a method and apparatus for variable load control of solid oxide fuel cells, which can realize variable load control of solid oxide fuel cells and supplement grid resources more flexibly.

[0006] To achieve the above objectives, this application provides the following solution:

[0007] In a first aspect, this application provides a method for variable load control of a solid oxide fuel cell, comprising:

[0008] Based on the heat flow model of a solid oxide fuel cell, a nonlinear state-space model of a solid oxide fuel cell is established. The state variables in the nonlinear state-space model are the battery temperature, the air supply pipe temperature, the air duct wall temperature, and the fuel duct wall temperature. The inputs are the fuel mass flow rate and the air mass flow rate, and the output is the power.

[0009] The nonlinear state-space model is transformed into a standard state-space model using the Jacobian matrix linearization method.

[0010] Based on the power output objective function, constraints, and the standard state-space model, the optimal input is solved using a model predictive control algorithm to achieve variable load control; the standard state-space model is the predictive model in the model predictive control algorithm; the constraints include upper and lower limits of the state variables, upper and lower limits of the input, and upper and lower limits of the output.

[0011] Secondly, this application provides a variable load control device for a solid oxide fuel cell, comprising:

[0012] The nonlinear state-space model construction module is used to establish a nonlinear state-space model of a solid oxide fuel cell based on the heat flow model of the solid oxide fuel cell. The state variables in the nonlinear state-space model are the battery temperature, the air supply pipe temperature, the air pipe wall temperature, and the fuel pipe wall temperature. The inputs are the fuel mass flow rate and the air mass flow rate, and the output is the power.

[0013] The model linearization module is used to transform the nonlinear state-space model into a standard state-space model using the Jacobian matrix linearization method.

[0014] The variable load control module is used to solve for the optimal input quantity based on the power output objective function, constraints, and the standard state-space model using a model predictive control algorithm to achieve variable load control; the standard state-space model is the predictive model in the model predictive control algorithm; the constraints include upper and lower limits of the state variables, upper and lower limits of the input quantity, and upper and lower limits of the output quantity.

[0015] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described solid oxide fuel cell variable load control method.

[0016] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described solid oxide fuel cell variable load control method.

[0017] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the above-described solid oxide fuel cell variable load control method.

[0018] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0019] This application provides a method and apparatus for variable load control of a solid oxide fuel cell (SOCF). Based on the heat flow model of the SOCF, a nonlinear state-space model of the SOCF is established. The state variables in the nonlinear state-space model are the cell temperature, air duct temperature, air duct wall temperature, and fuel duct wall temperature; the inputs are the fuel mass flow rate and air mass flow rate; and the output is power. The nonlinear state-space model is transformed into a standard state-space model using the Jacobian matrix linearization method. Based on the power output objective function, constraints, and the standard state-space model, a model predictive control algorithm is used for variable load control. This invention establishes a cross-scale heat flow model based on the overall heat exchange process of the SOCF, selects appropriate state variables and inputs, and establishes a nonlinear state-space model of the SOCF guided by variable load. The standard state-space model is obtained using Jacobian matrix linearization, and the power is adjusted under multiple constraints using a model predictive control algorithm to meet the expected load changes. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is an application environment diagram of a variable load control method for a solid oxide fuel cell according to an embodiment of this application;

[0022] Figure 2 A schematic flowchart illustrating a variable load control method for a solid oxide fuel cell provided in an embodiment of this application;

[0023] Figure 3 A schematic diagram of a physical model of a solid oxide fuel cell provided in an embodiment of this application;

[0024] Figure 4 This is a schematic diagram of the heat flow model of a solid oxide fuel cell provided in an embodiment of this application;

[0025] Figure 5 A schematic diagram of the Jacobian matrix linearization process provided in an embodiment of this application;

[0026] Figure 6 This is a functional module diagram of a solid oxide fuel cell variable load control device provided in another embodiment of this application.

[0027] Figure reference numerals: 1-First preheater; 2-Second preheater; 3-Electric stack; 4-Exhaust gas combustion module; 5-Electrical control module. Detailed Implementation

[0028] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0029] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0030] The solid oxide fuel cell variable load control method provided in this application embodiment can be applied to, for example... Figure 1 The application environment shown illustrates this. The terminal communicates with the server via a network. A data storage system stores the data the server needs to process. This system can be set up independently, integrated into the server, or located in the cloud or on another server. The terminal can send variable load control request commands to the server. Upon receiving the command, the server establishes a nonlinear state-space model of the solid oxide fuel cell based on its heat flow model. The state variables in this model are battery temperature, air duct temperature, air duct wall temperature, and fuel duct wall temperature; the inputs are fuel mass flow rate and air mass flow rate; and the output is power. Using the Jacobian matrix linearization method, the nonlinear state-space model is transformed into a standard state-space model. Based on the power output objective function, constraints, and the standard state-space model, a model predictive control algorithm is used for variable load control. The server can then feed back the output power of the solid oxide fuel cell calculated using the model predictive control algorithm to the terminal.

[0031] In one exemplary embodiment, such as Figure 2As shown, a variable load control method for a solid oxide fuel cell is provided. This method is executed by a computer device. In this embodiment, the method is applied to... Figure 1 The following steps, 101 to 103, are used as an example to illustrate the process of using a server in the example.

[0032] Step 101: Based on the heat flow model of the solid oxide fuel cell, establish a nonlinear state-space model of the solid oxide fuel cell; the state variables in the nonlinear state-space model are the battery temperature, the air supply pipe temperature, the air pipe wall temperature, and the fuel pipe wall temperature, the input quantities are the fuel mass flow rate and the air mass flow rate, and the output quantity is the power.

[0033] For the establishment of the heat flow model of the solid oxide fuel cell in step 101, the heat exchange module of the solid oxide fuel cell is first segmented, and a physical model of the solid oxide fuel cell is established by combining the heat exchange surface with the heat exchange links of air and fuel, such as... Figure 3 The diagram shows a physical model of a solid oxide fuel cell, including two preheaters (first preheater 1 and second preheater 2), a fuel cell stack 3, an exhaust gas combustion module 4, and an electronic control module 5.

[0034] Then, a heat flow model is established for the physical model. Specifically, the physical model of each segmented heat exchange section is simplified into a linear dynamic heat flow model. When evaluating the thermal storage performance and air and fuel heat exchange capacity of solid oxide fuel cells, the energy stored in the heat exchange fluid and on the key heat exchange walls plays a crucial role. Therefore, the following assumptions are made before the heat flow model:

[0035] 1) The content, flow rate, and temperature of the working gas in a solid oxide fuel cell remain constant over a short timescale.

[0036] 2) The energy stored in a solid oxide fuel cell is mainly from the stack and preheater components; other components can be ignored.

[0037] 3) Assume that the external supply is a continuous supply of air and fuel with a certain pressure, temperature and flow rate.

[0038] Based on the above assumptions, a heat flow model is established, and the heat release from the internal chemical reaction of a solid oxide fuel cell can be expressed as:

[0039] Q gen =Q chem -Q elec (1)

[0040] Among them, Q chem It is the usable work released by a chemical reaction, and its calculation formula is:

[0041] Q chem=nΔH (2)

[0042] Where ΔH is the enthalpy change of the chemical reaction inside the solid oxide fuel cell; n represents the number of moles of reactants. Q elec The output electrical power of a solid oxide fuel cell is defined as:

[0043] Q elec =I·V out (3)

[0044] Where I represents the output current; V out This indicates the output voltage.

[0045] The radiative heat transfer between the fuel cell stack and the air supply duct AST is expressed as:

[0046]

[0047] In the formula, Q rad It is the radiative heat transfer between the fuel cell stack and the air supply duct AST, ε AST σ represents the emissivity of the air supply duct; σ represents the Stefan-Boltzmann constant.

[0048] Based on the heat transfer above, calculate the heat flow model parameters. The fuel cell stack is the core structure of a solid oxide fuel cell and is crucial for regulating load changes in the solid oxide fuel cell system. The simplified energy conservation equation for the fuel cell stack is:

[0049]

[0050] In the formula, C AST This indicates the heat capacity of the fuel cell stack's air supply duct, expressed in J / kg·K; T AST Q represents the temperature of the fuel cell stack's air supply duct, in Kelvin (K). rad This represents the radiative heat transfer between the fuel cell stack and the air duct, measured in J; T. aircell,o R represents the air outlet temperature of the fuel cell stack's air supply duct, in Kelvin (K). con,AST,outer This indicates the thermal resistance of air exchanged with heat outside the fuel cell stack's air supply duct, expressed in K·s / J; T air,i R represents the transient temperature of the air inside the fuel cell stack's air supply duct, expressed in Kelvin (K). con,AST,inner This indicates the thermal resistance of air in the fuel cell stack's air supply duct, expressed in K·s / J; C cell T represents the heat capacity of the fuel cell stack, expressed in J / kg·K; cell Q represents the temperature of the fuel cell stack, in Kelvin (K). chem Q represents the available work released in a chemical reaction, measured in J. elec Q represents the output power of a solid oxide fuel cell, expressed in J. radThis represents the radiative heat transfer between the fuel cell stack and the air duct, measured in J; T. aircell,i T represents the transient temperature of the air inside the fuel cell stack, measured in Kelvin (K). fuel,i R represents the transient temperature of the fuel, measured in Kelvin (K). con,air R represents the thermal resistance between air and the battery stack, expressed in K·s / J. con,fuel This represents the thermal resistance between the fuel and the fuel cell stack, expressed in K·s / J.

[0051] Heat flows through thermal resistance, which is represented in the fuel cell stack as follows:

[0052]

[0053]

[0054] For the preheater of a solid oxide fuel cell, the simplified energy conservation equation is:

[0055]

[0056] In the formula, C airtube This indicates the heat capacity of the air duct, expressed in J / kg·K; T airtube This indicates the wall temperature of the air duct, expressed in Kelvin (K); T. bur This indicates the preheater flue gas inlet temperature, in Kelvin (K); T air1 R represents the air temperature at the fuel cell inlet, in Kelvin (K). conv,bur,airtube R represents the thermal resistance between flue gas and air ducts, expressed in K·s / J. conv,air,tube This represents the thermal resistance between air and air ducts, expressed in K·s / J; C fueltube The heat capacity of the fuel pipes in the preheater is expressed in J / kg·K; T fueltube This indicates the temperature of the fuel pipe wall in the preheater, in Kelvin (K); T bur The temperature at the flue gas inlet of the preheater is expressed in Kelvin (K); T fuel1 R represents the fuel temperature at the fuel stack inlet, in Kelvin (K). conv,bur,fueltube R represents the thermal resistance between the flue gas and the preheater fuel pipeline, expressed in K·s / J. conv,fuel,tube This indicates the heat exchange resistance between the fuel and the preheater fuel pipeline, expressed in K·s / J.

[0057] The thermal resistance in the preheater is expressed as follows:

[0058]

[0059]

[0060] The heat flow model is essentially determined by the energy conservation equations of formulas (4), (5), (10), and (11), thus yielding the heat flow model for solid oxide fuel cells, as follows: Figure 4 As shown.

[0061] Therefore, step 101, based on the heat flow model of the solid oxide fuel cell, establishes a nonlinear state-space model of the solid oxide fuel cell, specifically including:

[0062] (1) The heat exchange module of the solid oxide fuel cell is segmented, and a physical model of the solid oxide fuel cell is established by combining the heat exchange surface with the heat exchange links of air and fuel.

[0063] (2) The physical models of each heat exchange component in the physical model of the solid oxide fuel cell are simplified into linear heat flow models.

[0064] (3) Based on the heat flow model of solid oxide fuel cells, a nonlinear state-space model of solid oxide fuel cells is established.

[0065] Specifically, based on the heat flow model of a solid oxide fuel cell, the temperature at key points within the stack (stack cell temperature T) is determined. cell Temperature T of fuel cell stack air supply duct AST ) and the critical point temperature inside the preheater (the air duct wall temperature T of the first preheater) airtube1 The air duct wall temperature T of the second preheater airtube2 The wall temperature T of the fuel pipeline in the first preheater fueltube1 The wall temperature T of the fuel pipe in the second preheater fueltube2 ), and determine the initial mass flow rates D of air and fuel. air D fuel .

[0066] The inputs to the solid oxide fuel cell control system include: the air supply subsystem's required air mass flow rate, pressure, and inlet temperature for system operation, and the fuel supply subsystem's required fuel mass flow rate, pressure, humidity, and inlet temperature for system operation.

[0067] Since the initial values ​​of the input variable u and the state variable x of the control system use the given values ​​of the standard operating condition, that is, the model is described by the data of the stable operating condition reached after the battery cold start, and the study faces a wide range of loads and many operating conditions, in order to accurately represent the changes of parameters under different operating conditions, multiple state variables are selected, and the correlation function between them and the operating parameters is found to obtain the target nonlinear state-space equation, so as to ensure the accuracy of the model. Figure 4 As shown in the established heat flow model, fuel mass flow rate and air mass flow rate are selected as the input quantities u for the variable load control of this invention: u = [Dair D fuel ] T . Figure 4 In the middle, T air,in T represents the initial temperature of the air entering the preheater. fuel,in This indicates the initial temperature of the fuel entering the preheater. (C) dl The equivalent capacitance R represents the double-layer charging effect. act R ohm R conc The equivalent resistance representing the activation voltage drop, ohmic voltage drop, and concentration voltage drop. V cell Q represents the output voltage of the SOFC. elec E represents electrical output power. cell This represents the electromotive force between the cathode and the anode.

[0068] Selecting the battery stack temperature T cell Temperature T of fuel cell stack air supply duct AST Preheater air duct temperature T airtube1 ,T airtube2 Preheater fuel pipeline temperature T fueltube1 ,T fueltube2 There are a total of 6 heat exchange surfaces, with the temperature as the state variable x: x = [T AST ,T cell ,T airtube1 ,T airtube2 ,T fueltube1 ,T fueltube2 ] T .

[0069] Meanwhile, power P was selected as the output quantity y to explore the flexibility of variable load adjustment under different operating conditions of solid oxide fuel cells.

[0070] Based on the energy conservation equations of formulas (4), (5), (10), and (11), a preliminary nonlinear state-space model is obtained:

[0071]

[0072] in, Used to evaluate the heat storage capacity of heat exchange working fluids and battery heat exchange surfaces. These are the state matrix and the input matrix, respectively. and This describes the changes in output caused by changes in input and state variables. The matrix is ​​usually a zero matrix. Due to the hybridity of the parameters, the above matrix parameters are currently all non-linear.

[0073] Based on the heat flow model of a solid oxide fuel cell, and combining equations (4) to (15), the detailed expression of its nonlinear state transition equation is obtained from the functional relationship of the temperature state variable x:

[0074]

[0075] The B matrix and the input u in formula (17) are intertwined and cannot be separated, which is why a linearization step is needed later.

[0076] Simultaneously, by placing the selected output quantity y and input quantity u into the output equation, a detailed expression for its nonlinear output equation is obtained:

[0077]

[0078] In the formula, T cell The temperature of the fuel cell stack is expressed in Kelvin (K); T AST This indicates the temperature of the fuel cell stack's air supply duct, in Kelvin (K); T airtube1 This indicates the temperature of the air duct wall in the first preheater, in Kelvin (K); T airtube2 This indicates the temperature of the air duct wall in the second preheater, in Kelvin (K); T fueltube1 This indicates the wall temperature of the fuel pipes in the first preheater, in Kelvin (K); T fueltube2 This indicates the wall temperature of the fuel pipes in the second preheater, in Kelvin (K); T air,i The transient temperature of the air inside the fuel cell stack's air supply duct is expressed in Kelvin (K); T air,o The initial temperature of the air inside the fuel cell stack's air supply duct is expressed in Kelvin (K); T aircell,i T represents the transient temperature of the air inside the fuel cell stack, measured in Kelvin (K). fuel,i The transient temperature of the fuel is expressed in Kelvin (K); T fuel,o Indicates the initial temperature of the fuel, in K; T air1 This indicates the air temperature at the fuel cell stack inlet, in Kelvin (K); T fuel1 This indicates the fuel temperature at the fuel stack inlet, measured in Kelvin (K); T bur1 This indicates the flue gas inlet temperature of the first preheater, in Kelvin (K); T bur2 R represents the flue gas inlet temperature of the second preheater, in Kelvin (K). con,AST,inner R represents the thermal resistance of air in the fuel cell stack's air supply duct, expressed in K·s / J. con,AST,outer R represents the thermal resistance of air outside the fuel cell stack's air supply duct, expressed in K·s / J. conv,bur,airtube1 R represents the thermal resistance between the flue gas and the air duct of the first preheater, expressed in K·s / J. conv,air,tube1 R represents the thermal resistance between air and the air duct of the first preheater, expressed in K·s / J. conv,bur,airtube2R represents the thermal resistance between the flue gas and the air duct of the second preheater, expressed in K·s / J. conv,air,tube2 R represents the thermal resistance between the air and the air duct of the second preheater, expressed in K·s / J. conv,bur,fueltube1 R represents the thermal resistance between the flue gas and the fuel pipeline of the first preheater, expressed in K·s / J. conv,fuel,tube1 R represents the thermal resistance between the fuel and the fuel pipeline of the first preheater, expressed in K·s / J. conv,bur,fueltube2 R represents the thermal resistance between the flue gas and the fuel pipeline of the second preheater, expressed in K·s / J. conv,fuel,tube2 R represents the thermal resistance between the fuel and the fuel pipeline of the second preheater, expressed in K·s / J. con,air R represents the thermal resistance between air and the battery stack, expressed in K·s / J. con,fuel This indicates the thermal resistance between the fuel and the battery, expressed in K·s / J; C AST This indicates the heat capacity of the air supply duct, expressed in J / kg·K; C cell This indicates the battery's heat capacity, expressed in J / kg·K; C airtube1 The heat capacity of the air duct of the first preheater is expressed in J / kg·K; C airtube2 The heat capacity of the air duct of the second preheater is expressed in J / kg·K; C fueltube1 This indicates the heat capacity of the fuel pipeline in the first preheater, expressed in J / kg·K; C fueltube2 Q represents the heat capacity of the fuel pipes in the second preheater, expressed in J / kg·K. gen Q represents the heat released by the chemical reaction inside the battery, measured in J. chem Q represents the available work released in a chemical reaction, measured in J. rad This represents the radiative heat transfer between the fuel cell stack and the air duct, measured in J; D air D represents the air input mass flow rate; fuel This indicates the mass flow rate of the fuel input.

[0079] One important reason for establishing a state-space expression is to accurately characterize the heat storage capacity of key components in a solid oxide fuel cell at each stage, and to correct it based on model data, thereby obtaining accurate heat transfer in real time. This allows for the establishment of a precise control system model for the solid oxide fuel cell that can accurately assess its heat transfer capacity. The state transition equations and output equations of the heat transfer system above can be simplified as follows:

[0080]

[0081] Here, f(x,u,t) is the nonlinear state equation describing the dynamic behavior of a solid oxide fuel cell, and g(x,u,t) is the nonlinear output equation.

[0082] Step 102: The nonlinear state-space model is transformed into a standard state-space model using the Jacobian matrix linearization method.

[0083] Based on the nonlinear state-space model of the solid oxide fuel cell established in the previous step, the stable point after startup is selected as the standard operating condition (SOP), and the standard state-space model is obtained using the Jacobian matrix linearization method. Specifically, the stable point reached after cold start is selected as the SOP, and linearization is performed at the SOP using the Jacobian matrix. When characterizing the state equations under different load conditions, since the values ​​of the state variables have a real-time impact on the properties of the solid oxide fuel cell control system, the Jacobian matrix is ​​used to... Linearization of key parameter matrices, such as Figure 5 As shown, this characterizes the properties of the solid oxide fuel cell control system under different load conditions. Figure 5 In this context, G is the heat capacity factor, a nonlinear quantity in the energy flow model.

[0084]

[0085] In equation (20), A and B are the Jacobian matrices of the state equation with respect to the state variables and control variables (input quantities), respectively. C and D are the Jacobian matrices of the output equation with respect to the state variables and control variables, respectively. (x0,u0) are the state variables and input quantities of the selected standard operating point, thus obtaining the linearized standard state space model, as shown in equation (21).

[0086]

[0087] Step 103: Based on the power output objective function, constraints, and the standard state-space model, the optimal input quantity is solved using a model predictive control algorithm to achieve variable load control; the standard state-space model is the predictive model in the model predictive control algorithm; the constraints include upper and lower limits of the state variables, upper and lower limits of the input quantity, and upper and lower limits of the output quantity.

[0088] Based on the standard state-space model established in the previous step, a variable load control system that can flexibly adjust within a safe range is designed using model predictive control algorithms. The objective function is constructed as follows:

[0089]

[0090] In equation (22), h represents the controlled object (either nonlinear equation or standard state-space equation); r is the sample target, the value of the target r is different in different stages of load variation, and needs to be determined according to the demand of the electricity consumer, thus exhibiting sample randomness; N is the prediction time domain, and m is the control time domain. The load response weight matrix and the fuel input control weight matrix are defined as Ei, Ej ...P,i and E U,j E represents the weight matrix factor, which includes E P,i and E U,j y(k+i|k) represents the system output predicted at the current time step k for the i-th future step, where y represents the predicted output and |k indicates that the predicted output is based on information from time step k. r(k+i) represents the reference trajectory or setpoint at time step k+i, which is the target the system expects to achieve. Δu(k+j-1) represents the change in control input between time steps k+j-1 and k+j. This change is calculated by the difference between the currently predicted control input u(k+j) and the predicted control input u(k+j-1) of the previous time step, i.e., Δu(k+j-1) = u(k+j) - u(k+j-1).

[0091] Once the objective function is established, certain constraints need to be set as safety boundaries to ensure that the power varies within a safe and expected range. Solid oxide fuel cells require load variations within their rated power range, and the temperature cannot change frequently or fluctuate drastically. Furthermore, the air and fuel input quantities must be within safe limits. Therefore, the constraints are as follows:

[0092] u min,e ≤u e ≤u max,e

[0093] y min ≤y≤y max

[0094] T min,e ≤x e ≤T max,e (twenty three)

[0095] In equation (23), constraints are applied to the input, output, and state variables, respectively. min,e and u max,e These represent the input quantity u. e Minimum and maximum values ​​of y; min and y max These represent the minimum and maximum values ​​of the output quantity y, respectively; T min,e and T max,e Representing state variables x respectively e The minimum and maximum temperature values.

[0096] This invention establishes a complete solid oxide fuel cell control system including an objective function and constraints. It then utilizes a model predictive control algorithm to adjust power within a safety boundary, minimizing the objective function to obtain the optimal input quantities (i.e., the optimal air and fuel input mass flow rates) while satisfying the constraints. Based on these optimal input quantities, the air and fuel input mass flow rates of the solid oxide fuel cell are adjusted to ensure the output power approaches the sample target and meets the expected load changes. The principle of the model predictive control algorithm requires a standard state-space model equation. This equation is substituted into the algorithm, and the objective function and constraints are used to optimize and solve for the optimal input quantities, achieving the desired variable load control (power control).

[0097] By implementing steps 101 to 103 above, this invention establishes a control system that comprehensively considers key structures such as the solid oxide fuel cell stack and preheater. Based on a cross-scale heat flow model established for the overall heat exchange process of the solid oxide fuel cell, appropriate state variables and input quantities are selected, and a nonlinear state-space model is established with variable load as the guide. A standard state-space model is obtained by linearization using the Jacobian matrix, controller parameters are designed, and a model predictive control algorithm is used to adjust the power under multiple constraints to meet expected changes. Here, "cross-scale" refers to its ability to effectively handle the complex characteristics of multi-parameter, multi-level, and multi-process electrochemistry and external heat exchange within the SOFC (solid oxide fuel cell), integrating the external heat and mass transfer processes in the SOFC system.

[0098] Based on the same inventive concept, this application also provides a solid oxide fuel cell variable load control device for implementing the aforementioned solid oxide fuel cell variable load control method. The solution provided by this device is similar to the solution described in the above method; therefore, the specific limitations in one or more embodiments of the solid oxide fuel cell variable load control device provided below can be found in the limitations of the solid oxide fuel cell variable load control method described above, and will not be repeated here.

[0099] In one exemplary embodiment, such as Figure 6 As shown, a solid oxide fuel cell variable load control device is provided, comprising:

[0100] The nonlinear state-space model construction module M1 is used to establish a nonlinear state-space model of a solid oxide fuel cell based on the heat flow model of the solid oxide fuel cell. The state variables in the nonlinear state-space model are the battery temperature, the air supply pipe temperature, the air pipe wall temperature, and the fuel pipe wall temperature. The input quantities are the fuel mass flow rate and the air mass flow rate, and the output quantity is the power.

[0101] The model linearization module M2 is used to transform the nonlinear state-space model into a standard state-space model using the Jacobian matrix linearization method.

[0102] The variable load control module M3 is used to solve for the optimal input quantity based on the power output objective function, constraints, and the standard state-space model using a model predictive control algorithm to achieve variable load control; the standard state-space model is the predictive model in the model predictive control algorithm; the constraints include upper and lower limits of the state variables, upper and lower limits of the input quantity, and upper and lower limits of the output quantity.

[0103] In one exemplary embodiment, a computer device is provided, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the solid oxide fuel cell variable load control method.

[0104] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the above-described solid oxide fuel cell variable load control method.

[0105] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the above-described solid oxide fuel cell variable load control method.

[0106] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0107] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for variable load control of a solid oxide fuel cell, characterized in that, The solid oxide fuel cell variable load control method includes: Based on the heat flow model of a solid oxide fuel cell, a nonlinear state-space model of a solid oxide fuel cell is established. The state variables in the nonlinear state-space model are the battery temperature, the air supply pipe temperature, the air duct wall temperature, and the fuel duct wall temperature. The inputs are the fuel mass flow rate and the air mass flow rate, and the output is the power. The nonlinear state-space model is transformed into a standard state-space model using the Jacobian matrix linearization method. Based on the power output objective function, constraints, and the standard state-space model, the optimal input is solved using a model predictive control algorithm to achieve variable load control; the standard state-space model is the predictive model in the model predictive control algorithm; the constraints include upper and lower limits of the state variables, upper and lower limits of the input, and upper and lower limits of the output. Specifically, based on the heat flow model of a solid oxide fuel cell, a nonlinear state-space model of the solid oxide fuel cell is established, including: The heat exchange module of a solid oxide fuel cell is segmented, and a physical model of the solid oxide fuel cell is established by combining the heat exchange surface with the heat exchange links of air and fuel. The physical models of each heat exchange component in the physical model of the solid oxide fuel cell are simplified into linear heat flow models. Based on the heat flow model of solid oxide fuel cells, a nonlinear state-space model of solid oxide fuel cells is established.

2. The variable load control method for a solid oxide fuel cell according to claim 1, characterized in that, The heat flow model of the solid oxide fuel cell includes the energy conservation equation of the fuel cell stack and the energy conservation equation of the preheater. The energy conservation equation for the fuel cell stack is: In the formula, C AST Indicates the heat capacity of the fuel cell stack's air supply duct; T AST Q represents the temperature of the fuel cell stack's air supply duct in K; rad T represents the radiative heat transfer between the fuel cell stack and the air duct; aircell,o R represents the air outlet temperature of the fuel cell stack's air supply duct; con,AST,outer This indicates the thermal resistance of air exchange outside the fuel cell stack's air supply duct; T air,i R represents the transient temperature of the air inside the fuel cell stack's air supply duct; con,AST,inner Indicates the thermal resistance of air in the fuel cell stack's air supply duct; C cell Indicates the heat capacity of the battery stack; T cell Indicates the temperature of the fuel cell stack; Q chem Q represents the available work released in a chemical reaction. elec Q represents the output electrical power of a solid oxide fuel cell; rad This indicates the radiative heat transfer between the fuel cell stack and the air duct. T aircell,i T represents the transient temperature of the air inside the fuel cell stack. fuel,i Indicates the transient temperature of the fuel; R con,air R represents the thermal resistance between air and the battery stack. con,fuel This indicates the thermal resistance between the fuel and the fuel cell stack. The energy conservation equation for the preheater is: In the formula, C airtube T represents the heat capacity of the air duct in the preheater. airtube T represents the wall temperature of the air duct in the preheater. bur Indicates the preheater flue gas inlet temperature; T air1 Indicates the air temperature at the fuel cell inlet; R conv,bur,airtube R represents the thermal resistance of the flue gas to the air duct of the preheater; conv,air,tube Indicates the heat exchange resistance between air and the preheater air duct; C fueltube T represents the heat capacity of the fuel pipes in the preheater. fueltube T represents the wall temperature of the fuel pipes in the preheater. bur T represents the flue gas inlet temperature of the preheater. fuel1 Indicates the fuel temperature at the fuel stack inlet; R conv,bur,fueltube R represents the thermal resistance between the flue gas and the preheater fuel pipeline; conv,fuel,tube This indicates the thermal resistance of the fuel to the preheater fuel pipeline.

3. The variable load control method for a solid oxide fuel cell according to claim 1, characterized in that, The standard state-space model is as follows: y = Cx + Du; in, In the formula, x = [T AST ,T cell ,T airtube1 ,T airtube2 ,T fueltube1 ,T fueltube2 ] T ; x is the state variable; ; is the input quantity, u = [D air D fuel ] T ; y is the output quantity; (x0, u0) are the state variables and input quantities of the selected standard operating point; and Used to describe the change in output caused by changes in input and state variables; T cell Indicates the temperature of the fuel cell stack; T AST Indicates the temperature of the fuel cell stack's air supply duct; T airtube1 T represents the temperature of the air duct wall in the first preheater. airtube2 T represents the temperature of the air duct wall in the second preheater. fueltube1 T represents the wall temperature of the fuel pipe in the first preheater. fueltube2 T represents the wall temperature of the fuel pipe in the second preheater. air,i T represents the transient temperature of the air inside the fuel cell stack's air supply duct; air,o Indicates the initial temperature of the air inside the fuel cell stack's air supply duct; T aircell,i T represents the transient temperature of the air inside the fuel cell stack. fuel,i T represents the transient temperature of the fuel. fuel,o Indicates the initial temperature of the fuel; T air1 Indicates the air temperature at the fuel cell inlet; T fuel1 Indicates the fuel temperature at the fuel stack inlet; T bur1 T represents the flue gas inlet temperature of the first preheater; bur2 R represents the flue gas inlet temperature of the second preheater. con,AST,inner R represents the thermal resistance of air in the fuel cell stack's air supply duct. con,AST,outer R represents the thermal resistance of air outside the fuel cell stack's air supply duct. conv,bur,airtube1 R represents the thermal resistance between the flue gas and the air duct of the first preheater; conv,air,tube1 This indicates the thermal resistance of heat exchange between the air and the air duct of the first preheater; R conv,bur,airtube2 This indicates the thermal resistance of the flue gas to the air duct of the second preheater. R conv,air,tube2 This indicates the thermal resistance of the air exchange between the air and the air duct of the second preheater. R conv,bur,fueltube1 This indicates the thermal resistance of the flue gas to the fuel pipe of the first preheater. R conv,fuel,tube1 This indicates the thermal resistance of the fuel exchange between the fuel and the fuel pipeline of the first preheater; R conv,bur,fueltube2 This indicates the thermal resistance of the flue gas to the fuel pipe of the second preheater. R conv,fuel,tube2 R represents the thermal resistance between the fuel and the fuel pipeline of the second preheater. con,air R represents the thermal resistance between air and the battery stack. con,fuel Indicates the thermal resistance between the fuel and the battery; C AST Indicates the heat capacity of the air supply duct; C cell Indicates battery heat capacity; C airtube1 C represents the heat capacity of the air duct of the first preheater; airtube2 Indicates the heat capacity of the air duct of the second preheater; C fueltube1 C represents the heat capacity of the fuel pipes in the first preheater. fueltube2 Q represents the heat capacity of the fuel pipes in the second preheater; gen Q represents the heat released by the chemical reaction inside the battery; chem Q represents the available work released in a chemical reaction. rad D represents the radiative heat transfer between the fuel cell stack and the air duct; air D represents the air input mass flow rate; fuel This indicates the mass flow rate of the fuel input.

4. The variable load control method for a solid oxide fuel cell according to claim 1, characterized in that, The power output objective function is: In the formula, h represents the standard state-space model; E represents the weight matrix factor, which includes E P,i and E U,j r represents the target sample; N represents the prediction time domain; m represents the control time domain; E P,i and E U,j These are the load response weight matrix and the fuel input control weight matrix, respectively; y(k+i|k) represents the system output predicted at the current time step k for the i-th future step; r(k+i) represents the reference trajectory at time step k+i; Δu(k+j-1) represents the change in control input between time steps k+j-1 and k+j.

5. A variable load control device for a solid oxide fuel cell, characterized in that, The solid oxide fuel cell variable load control device includes: The nonlinear state-space model construction module is used to establish a nonlinear state-space model of a solid oxide fuel cell based on the heat flow model of the solid oxide fuel cell. The state variables in the nonlinear state-space model are the battery temperature, the air supply pipe temperature, the air pipe wall temperature, and the fuel pipe wall temperature. The inputs are the fuel mass flow rate and the air mass flow rate, and the output is the power. Specifically, based on the heat flow model of a solid oxide fuel cell, a nonlinear state-space model of the solid oxide fuel cell is established, including: The heat exchange module of a solid oxide fuel cell is segmented, and a physical model of the solid oxide fuel cell is established by combining the heat exchange surface with the heat exchange links of air and fuel. The physical models of each heat exchange component in the physical model of the solid oxide fuel cell are simplified into linear heat flow models. Based on the heat flow model of solid oxide fuel cells, a nonlinear state-space model of solid oxide fuel cells is established. The model linearization module is used to transform the nonlinear state-space model into a standard state-space model using the Jacobian matrix linearization method. The variable load control module is used to solve for the optimal input quantity based on the power output objective function, constraints, and the standard state-space model using a model predictive control algorithm to achieve variable load control; the standard state-space model is the predictive model in the model predictive control algorithm; the constraints include upper and lower limits of the state variables, upper and lower limits of the input quantity, and upper and lower limits of the output quantity.

6. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the solid oxide fuel cell variable load control method according to any one of claims 1-4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the variable load control method for solid oxide fuel cells according to any one of claims 1-4.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the variable load control method for solid oxide fuel cells according to any one of claims 1-4.

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