A modeling method and device for a zero-dimensional dynamic model of a SOFC power generation system

Abstract

The application belongs to the technical field of power generation system modeling, and specifically discloses a SOFC power generation system zero-dimensional dynamic model modeling method and device, which comprises the following steps: based on the fuel reforming reaction, the electrochemical reaction in the heat box of the SOFC power generation system and the energy conservation equation of each component, a zero-dimensional dynamic model is established; a soft delay parameter group is introduced into the zero-dimensional dynamic model, and a first-order inertia link is used to represent the change lag of the gas flow rate from the inlet to the outlet in each component; a hard delay parameter group is introduced into the zero-dimensional dynamic model, and a pure time delay parameter is used to represent the output response delay of each component due to the gas flow distance. The method can improve the modeling efficiency while taking into account the modeling accuracy.

Description

Technical Field

[0001] This application belongs to the field of power generation system modeling technology, and more specifically, relates to a method and apparatus for modeling a zero-dimensional dynamic model of an SOFC power generation system. Background Technology

[0002] A solid oxide fuel cell (SOFC) is an electrochemical device that can directly convert hydrocarbon fuels into electrical energy at high temperatures. To maintain the high-temperature reaction environment, the SOFC stack and some auxiliary components are integrated into a thermally insulated heatbox. A common waste heat utilization method involves using the high-temperature exhaust gas from the reaction to preheat the reactants at the heatbox inlet and then regenerating the gas through a gas turbine.

[0003] Due to their high operating temperatures and complex heat recovery piping, SOFC systems exhibit nonlinear and large hysteresis dynamic characteristics. After an instruction to adjust the reactant flow rate is issued, the exhaust gas discharged from the heat exchanger does not respond immediately; each heat exchange component amplifies this delay, leading to delays and oscillations when the exhaust gas is used to preheat the reactants. In existing zero-dimensional modeling studies, the nonlinear characteristics of SOFC systems are mainly represented by changes in reactant partial pressure in the stack model and energy conservation in the heat exchange components. This type of modeling method cannot reflect the aforementioned delay effects, resulting in low modeling accuracy. High-dimensional modeling of the system's auxiliary equipment can capture gas transport delays, but it significantly increases computational load and complexity, leading to low modeling efficiency. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this application is to provide a zero-dimensional dynamic modeling method and apparatus for SOFC power generation systems. This aims to solve the problem that existing modeling methods, which rely on reactant partial pressure changes in the stack model and energy conservation of heat exchange components, or perform high-dimensional modeling of system auxiliary equipment, cannot simultaneously achieve both modeling accuracy and efficiency.

[0005] To achieve the above objectives, in a first aspect, this application provides a method and apparatus for modeling a zero-dimensional dynamic model of an SOFC power generation system, comprising: A zero-dimensional dynamic model is established based on the fuel reforming reaction, electrochemical reaction, and energy conservation equations of each component in the hot box of the SOFC power generation system. A soft delay parameter set is introduced into the zero-dimensional dynamic model, and a first-order inertial element is used to characterize the lag in the change of gas velocity from inlet to outlet in each component. A set of hard delay parameters is introduced into the zero-dimensional dynamic model, and the pure time delay parameter is used to characterize the output response delay of each component caused by the gas flow distance.

[0006] This application introduces both soft-delay and hard-delay parameter sets into a zero-dimensional dynamic model, enabling the SOFC power generation system model to describe two delay phenomena in gas transport within the system without increasing the model's dimensionality. The soft-delay parameter set characterizes the gradual change in outlet velocity of each heat exchange component lagging behind the change in inlet velocity through a first-order inertial element. The hard-delay parameter set characterizes the pure time-delay response of each component due to the gas flow distance through pure time-delay parameters. The combined use of these two sets makes the model's mass transfer dynamics closer to real-world conditions, achieving high modeling accuracy without requiring high-dimensional modeling of all system auxiliary equipment. This reduces computational load and complexity, improving modeling efficiency while maintaining accuracy. It provides a computationally simple and dynamically realistic model foundation for the structural design, capacity configuration, and control optimization of SOFC power generation systems.

[0007] According to the zero-dimensional dynamic modeling method for SOFC power generation system provided in this application, the soft delay parameter set and the hard delay parameter set are both applied to each component in the exhaust gas preheating channel of SOFC power generation system.

[0008] This application limits both the soft and hard delay parameter sets to be applied to each component in the exhaust gas preheating channel, thus focusing the delay modeling on the exhaust gas preheating path with the longest gas transport distance and the most complex heat exchange relationship. The exhaust gas flows sequentially through components such as the heat box, preheater, mixer, steam generator, and gas turbine in a cascade manner. Each component amplifies the delay effect of gas transport. Introducing soft-hard delay combinations to each component in the exhaust gas preheating channel accurately reflects the accumulated delay and overshoot phenomena along the flow path, thereby realistically reflecting the dynamic characteristics such as temperature overshoot and flow oscillation during the exhaust gas preheating reactants process, making the model's mass transfer dynamics consistent with real-world operating conditions.

[0009] According to the zero-dimensional dynamic modeling method for SOFC power generation system provided in this application, no hard delay parameter set is introduced into the fuel flow stream, air flow stream and water flow stream of the SOFC power generation system.

[0010] This application demonstrates the following technical rationale by limiting the introduction of hard delay parameter sets to fuel, air, and water streams: The gas flow distances of fuel, air, and water streams are relatively short, and the pure time delay caused by the flow distance is negligible. Hard delay parameter sets are only introduced in the exhaust gas preheating channel, which has a long flow distance and a significant delay effect. This limitation ensures that the model accurately describes key delay phenomena while avoiding the introduction of unnecessary delay parameters to short-distance streams, reducing the redundancy and difficulty of model parameter identification, making the model structure more concise and reasonable, and the physical meaning of the parameters clearer.

[0011] According to the zero-dimensional dynamic modeling method for SOFC power generation system provided in this application, the soft delay parameter set includes the soft delay time of the hot box, the soft delay time of the preheater, the soft delay time of the mixer, the soft delay time of the steam generator, and the soft delay time of the gas turbine, and the hard delay parameter set includes the hard delay time of the hot box, the hard delay time of the preheater, the hard delay time of the mixer, the hard delay time of the steam generator, and the hard delay time of the gas turbine.

[0012] This application parameterizes the delay characteristics of each component in the exhaust gas preheating channel by explicitly listing the specific parameters contained in the soft delay parameter group and the hard delay parameter group. Each component is assigned an independent soft delay time and a hard delay time, allowing the differentiated delay characteristics of different components due to variations in pipe length, internal volume, and flow state to be characterized and adjusted separately. By changing the soft-hard delay parameter combinations of each component, different delay characteristics can be flexibly represented, providing refined parameter adjustment capabilities for dynamic modeling and control optimization of SOFC power generation systems with different system sizes, pipe layouts, and operating conditions.

[0013] Secondly, this application provides a zero-dimensional dynamic modeling device for an SOFC power generation system, comprising: The modeling module is used to establish a zero-dimensional dynamic model based on the fuel reforming reaction, electrochemical reaction, and energy conservation equations of each component in the hot box of the SOFC power generation system. The first introduction module is used to introduce a soft delay parameter set into the zero-dimensional dynamic model and to use a first-order inertial element to characterize the lag in the change of gas flow velocity from the inlet to the outlet in each component. The second introduction module is used to introduce a set of hard delay parameters into the zero-dimensional dynamic model, and to use pure time delay parameters to characterize the output response delay of each component caused by the gas flow distance.

[0014] According to the zero-dimensional dynamic modeling device for an SOFC power generation system provided in this application, the soft delay parameter set and the hard delay parameter set are both applied to the components in the exhaust gas preheating channel of the SOFC power generation system.

[0015] According to the zero-dimensional dynamic modeling device for SOFC power generation system provided in this application, no hard delay parameter set is introduced in the fuel stream, air stream and water stream of the SOFC power generation system.

[0016] According to the zero-dimensional dynamic modeling device for SOFC power generation system provided in this application, the soft delay parameter set includes the soft delay time of the hot box, the soft delay time of the preheater, the soft delay time of the mixer, the soft delay time of the steam generator, and the soft delay time of the gas turbine, and the hard delay parameter set includes the hard delay time of the hot box, the hard delay time of the preheater, the hard delay time of the mixer, the hard delay time of the steam generator, and the hard delay time of the gas turbine.

[0017] Thirdly, this application provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory. When the program stored in the memory is executed, the processor is used to execute the zero-dimensional dynamic model modeling method for SOFC power generation systems described in the first aspect or any possible implementation of the first aspect.

[0018] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the zero-dimensional dynamic model modeling method for SOFC power generation systems described in the first aspect or any possible implementation of the first aspect.

[0019] Fifthly, this application provides a computer program product that, when run on a processor, causes the processor to execute the zero-dimensional dynamic model modeling method for SOFC power generation systems described in the first aspect or any possible implementation of the first aspect.

[0020] It is understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0021] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: This application introduces both soft-delay and hard-delay parameter sets into a zero-dimensional dynamic model, enabling the SOFC power generation system model to describe two delay phenomena in gas transport within the system without increasing the model's dimensionality. The soft-delay parameter set characterizes the gradual change in outlet velocity of each heat exchange component lagging behind the change in inlet velocity through a first-order inertial element. The hard-delay parameter set characterizes the pure time-delay response of each component due to the gas flow distance through pure time-delay parameters. The combined use of these two sets makes the model's mass transfer dynamics closer to real-world conditions, achieving high modeling accuracy without requiring high-dimensional modeling of all system auxiliary equipment. This reduces computational load and complexity, improving modeling efficiency while maintaining accuracy. It provides a computationally simple and dynamically realistic model foundation for the structural design, capacity configuration, and control optimization of SOFC power generation systems. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a flowchart illustrating the zero-dimensional dynamic modeling method for SOFC power generation systems provided in this application embodiment; Figure 2 This is a schematic diagram of the SOFC power generation system provided in the embodiments of this application; Figure 3 This is a schematic diagram of the gas transport delay model of the SOFC power generation system provided in the embodiments of this application; Figure 4 This is a schematic diagram comparing the dynamic response of the system provided in the embodiments of this application. Figure 4 (a) in the figure is a comparison chart of excess air coefficients. Figure 4 (b) in the figure is a comparison chart of fuel utilization rates. Figure 4 (c) in the figure is a comparison chart of the flow rates of the three streams. Figure 4 (d) in the figure is a comparison chart of the flow rates of stream 7. Figure 4 (e) in the figure is a comparison of the voltage of a single SOFC stack. Figure 4 (f) in the figure is a temperature comparison chart of the SOFC hot box. Figure 4 (g) in the figure is a temperature comparison chart of stream 12. Figure 4 (h) in the figure is a temperature comparison chart of stream 13. Figure 4 (i) in the figure is a temperature comparison chart of stream 14. Figure 4 (j) in the figure is a temperature comparison chart of stream 15. Figure 4 (k) in the graph is a comparison of the flow rates of stream 15. Figure 4 (l) in the figure is a comparison chart of gas turbine output power; Figure 5 This is a schematic diagram of the structure of the zero-dimensional dynamic modeling device for SOFC power generation system provided in the embodiments of this application; Figure 6 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0025] In this article, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The symbol " / " in this article indicates that the related objects are in an "or" relationship; for example, A / B means A or B.

[0026] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0027] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0028] Next, combined Figures 1-4 The zero-dimensional dynamic modeling method for SOFC power generation systems provided in the embodiments of this application is introduced.

[0029] Figure 1 This is a flowchart illustrating the zero-dimensional dynamic modeling method for SOFC power generation systems provided in this application embodiment, as shown below. Figure 1 As shown, the method includes the following steps: Step S1: Based on the fuel reforming reaction, electrochemical reaction, and energy conservation equations of each component in the hot box of the SOFC power generation system, establish a zero-dimensional dynamic model. Step S2: Introduce a soft delay parameter set into the zero-dimensional dynamic model and use a first-order inertial element to characterize the lag in the change of gas velocity from inlet to outlet in each component. Step S3: Introduce a set of hard delay parameters into the zero-dimensional dynamic model and use pure time delay parameters to characterize the output response delay of each component caused by the gas flow distance.

[0030] Figure 2 This is a schematic diagram of the SOFC power generation system provided in the embodiments of this application, as shown below. Figure 2 As shown, the SOFC power generation system structure includes the following components: a heat box, a methane source, a pure water source, a preheater, a mixer, a steam generator, and a gas turbine. The heat box mainly consists of a reformer, multiple fuel cell stacks, and an afterburner.

[0031] The SOFC power generation system uses methane as fuel, which is mixed with a certain proportion of steam and heated in a mixer before being sent to the hot box for reforming. Air flow is regulated by a compressor and supplied to the hot box after being heated by exhaust gas in a preheater. Steam is generated by absorbing heat from the exhaust gas from pure water in a steam generator. Inside the hot box, the air and fuel mixture is further heated. The fuel mixture is reformed in the reformer to produce reformed gas, primarily composed of hydrogen and carbon monoxide. The air and reformed gas are then supplied to each fuel cell stack for electrochemical reactions. Unreacted gases are collected in an afterburner and completely combusted to maintain the high temperature of the hot box. Exhaust gas from the hot box passes in a cascaded manner through the preheater, mixer, and steam generator to preheat the reactants. After further power generation by the gas turbine, the gas exits the system.

[0032] Zero-dimensional means ignoring the spatial distribution differences of the components within the system and treating the entire power generation system as a lumped parameter object with uniform parameters that only change with time.

[0033] Optionally, the zero-dimensional dynamic model mainly consists of the fuel reforming reaction, electrochemical reaction, and energy conservation equations for each component within the hotbox, as shown in Table 1 below: Table 1 Zero-dimensional dynamic model

[0034] in, Let be the forward kinetic rate constant of reaction 1. This represents the partial pressure of hydrogen in the reformer. This represents the partial pressure of methane in the reformer. The partial pressure of water in the reformer. This represents the partial pressure of carbon monoxide in the reformer. Let be the thermodynamic equilibrium constant of reaction 1. Let be the forward kinetic rate constant of reaction 2. Let be the thermodynamic equilibrium constant of reaction 2. Let be the forward kinetic rate constant of reaction 3. This represents the partial pressure of carbon dioxide in the reformer. Let be the thermodynamic equilibrium constant for reaction 3. The adsorption constant of carbon monoxide surface. The surface adsorption constant of hydrogen gas is given. The adsorption constant of methane surface. The adsorption constant of water surface This is the universal gas constant. For the fuel cell stack temperature, It is Faraday's constant. This represents the partial pressure of hydrogen in the fuel cell stack. This represents the partial pressure of oxygen in the fuel cell stack. The partial pressure of water in the fuel cell stack. The anode charge transfer coefficient, For single-pile current, For the effective membrane area, The anode reference exchange current density, The cathode charge transfer coefficient, The cathode reference exchange current density, As the anode pre-index factor, For the fuel cell stack pressure, This is the anodic activation energy. For cathode pre-index factor, The activation energy of the cathode, The limiting current density of water, The limiting current density of hydrogen gas is given by ( ). The limiting current density for oxygen. The effective diffusion coefficient of the anode is . For the anode thickness, The effective diffusion coefficient of the cathode, For cathode thickness, For electrolyte thickness, The anode conductivity is... The electrolyte conductivity, The cathode conductivity, For the number of fuel cells, This refers to the number of individual cells in the fuel cell stack. For single cell voltage, For the output power efficiency of the fuel cell stack, The flow rate of methane in stream 9, Methane has a low calorific value. The flow rate of hydrogen in stream 9, Hydrogen has a low calorific value. The flow rate of carbon monoxide in stream 9, The calorific value of carbon monoxide. The average heat capacity of the hot box. For the quality of the hot box, This refers to the temperature of the hot box. The flow rate of methane in stream 7, For the flow rate of flow segment 3, The enthalpy of the flow stream 3, For the flow rate of stream 7, The enthalpy of the flow stream 7, For the flow rate of stream 11, The enthalpy of the flow 11, This represents the total output power of the fuel cell stack. The outer surface area of ​​the hot box. For reference temperature, For the thermal resistance of the hot box, The average heat capacity of the heat exchanger. For the quality of the preheater, The temperature of the flow stream 12, For the flow rate of stream 12, The enthalpy of the flow is 12. For heat exchange at the hot end of the preheater, The temperature of stream 3, For the flow rate of flow stream 2, The enthalpy of the second flow segment, For heat exchange efficiency, For mixer quality, The temperature of the flow stream 13, For the flow rate of stream 13, The enthalpy of the flow is 13. For heat exchange at the hot end of the mixer, The temperature of the flow stream 7, For the flow rate of flow segment 4, The enthalpy of the flow stream 4, For the flow rate of stream 6, The enthalpy of the flow stream 6, For the quality of the steam generator, The temperature of the flow stream 14, For the flow rate of stream 14, The enthalpy of the flow is 14. For heat exchange at the hot end of the steam generator, The temperature of the flow stream 6, For the flow rate of stream 5, The enthalpy of the flow stream 5, The specific heat capacity of air, For the flow rate of flow segment 1, The temperature of stream 1, For isentropic efficiency, The pressure of stream 2, The pressure of stream 1, The adiabatic coefficient is... The specific heat capacity of the exhaust gas. For the flow rate of stream 14, The temperature of the flow stream 14, The pressure of the flow stream 15, The pressure of the flow stream 14.

[0035] It is evident that the system dynamics of the zero-dimensional dynamic model are primarily reflected through the partial pressure and temperature changes of the reactants within the stack, as well as the heat transfer balance equations within the auxiliary components. This modeling method neglects the gas transport delay in the SOFC power generation system. The flow rates of each gas stream in the exhaust gas preheating reactant section change instantaneously, while only the temperature slowly changes to a stable value according to energy conservation.

[0036] In reality, because gas transport occurs over a certain distance, the flow rate of exhaust gas discharged from the hot box does not change immediately when the reactant flow rate changes. This response delay is called "hard delay," characterized by the fact that each component... There is a response time delay in all of them. D i .

[0037] Furthermore, the flow behavior within each heat exchanger is more complex, causing changes in outlet velocity to lag behind changes in inlet velocity. The more components the gas passes through, the longer it takes for the gas flow rate to reach a steady state. This phenomenon is called "soft delay," denoted by a time constant τ. i It is represented by a first-order inertial element.

[0038] by Figure 2 Taking the preheater in the middle as an example, The relationship between the time-varying gas transport delay and the gas flow rate through this component is described as follows:

[0039]

[0040] in, This refers to the soft delay time of the preheater (exhaust gas side). for The flow rate of the 12th of the time stream, for The flow of 11 at all times, For the preheater hard delay time, Let the Laplace transform image function of the flow rate of stream 12 be given. Let the Laplace transform image function of the flow rate of stream 11 be... Let be the complex variable after the Laplace transform.

[0041] Figure 3 This is a schematic diagram of the gas transport delay model of the SOFC power generation system provided in the embodiments of this application, such as... Figure 3 As shown, the current The required reference flow rates of hydrogen and oxygen, as well as the reference flow rate of exhaust gas discharged from the hot box, are calculated as follows:

[0042]

[0043]

[0044] in and These are reference values ​​for fuel efficiency and excess air coefficient, respectively, generated by the controller that controls the temperature of the heatbox and exhaust gas. and These represent the methane reforming rate and the oxygen content in the air, respectively. This refers to the water-to-carbon ratio.

[0045] In one embodiment of this application, the parameters in Table 2 below are used as the basic modeling parameters of the system and applied to the zero-dimensional dynamic model shown in Table 1: Table 2 Basic Modeling Parameters

[0046] The zero-dimensional dynamic modeling method for SOFC power generation systems provided in this application introduces both soft-delay and hard-delay parameter sets into the zero-dimensional dynamic model. This allows the SOFC power generation system model to describe two delay phenomena in gas transport within the system without increasing the model's dimensionality. Specifically, the soft-delay parameter set characterizes the gradual change in outlet velocity of each heat exchange component lagging behind the change in inlet velocity through first-order inertial elements, while the hard-delay parameter set characterizes the pure time-delay response of each component due to the gas flow distance through pure time-delay parameters. The combined use of these two sets makes the model's mass transfer dynamic characteristics closer to real-world operating conditions. It achieves high modeling accuracy without requiring high-dimensional modeling of all system auxiliary equipment, reducing computational load and complexity. This approach improves modeling efficiency while maintaining accuracy, providing a computationally simple and dynamically realistic model foundation for the structural design, capacity configuration, and control optimization of SOFC power generation systems.

[0047] In some embodiments, both the soft delay parameter set and the hard delay parameter set are applied to the components in the exhaust gas preheating channel of the SOFC power generation system.

[0048] In the exhaust gas preheating channel, the exhaust gas passing through each component (heatbox, preheater, mixer, steam generator, gas turbine) is simulated using a combination of soft and hard delays. This results in significant time differences in gas temperature changes during the preheating process.

[0049] Furthermore, the delays of the two fluids within the preheater, mixer, and steam generator are independent of each other. Taking the steam generator as an example, the steam delay and the exhaust gas delay are represented by different first-order inertial elements. This can be achieved by changing the soft-hard delay combination of each component. and This can represent different delay characteristics.

[0050] In some embodiments, no hard delay parameter set is introduced into the fuel stream, air stream, and water stream of the SOFC power generation system.

[0051] In the fuel, air, and water streams, no hard delay is introduced because the gas flow distance is relatively short.

[0052] In some embodiments, the soft delay parameter set includes the soft delay time of the hot box, the soft delay time of the preheater, the soft delay time of the mixer, the soft delay time of the steam generator, and the soft delay time of the gas turbine; the hard delay parameter set includes the hard delay time of the hot box, the hard delay time of the preheater, the hard delay time of the mixer, the hard delay time of the steam generator, and the hard delay time of the gas turbine.

[0053] In one embodiment of this application, the parameters in Table 3 below are used as the system's soft-hard latency parameter set: Table 3 Soft-Hard Delay Parameter Group

[0054] In one embodiment of this application, a dynamic characteristic comparison analysis is performed using the five sets of soft-hard delay parameter groups shown in Table 4. The system models under these five sets of soft-hard delay parameter groups all employ the same PI controller. A PI control loop adjusts... To stabilize the exhaust gas temperature at 493K, another PI control loop adjusts... The temperature of the hot box was maintained at 1023K. The system operated stably with a single-pile current of 85 A, and a step current of 95 A was applied at 1200 seconds to observe the subsequent dynamic changes of the system.

[0055] Table 4 Five groups of soft-hard delay parameters

[0056] Figure 4 This is a schematic diagram comparing the dynamic response of the system provided in the embodiments of this application. Figure 4 (a) in the figure is a comparison chart of excess air coefficients. Figure 4 (b) in the figure is a comparison chart of fuel utilization rates. Figure 4 (c) in the figure is a comparison chart of the flow rates of the three streams. Figure 4 (d) in the figure is a comparison chart of the flow rates of stream 7. Figure 4 (e) in the figure is a comparison of the voltage of a single SOFC stack. Figure 4 (f) in the figure is a temperature comparison chart of the SOFC hot box. Figure 4 (g) in the figure is a temperature comparison chart of stream 12. Figure 4(h) in the figure is a temperature comparison chart of stream 13. Figure 4 (i) in the figure is a temperature comparison chart of stream 14. Figure 4 (j) in the figure is a temperature comparison chart of stream 15. Figure 4 (k) in the graph is a comparison of the flow rates of stream 15. Figure 4 (l) in the figure is a comparison chart of gas turbine output power, such as Figure 4 As shown, the monitoring locations and corresponding physical quantities are labeled in the lower left corner and on the y-axis of each subplot, respectively. In the no-delay model, the exhaust gas flow response exhibits only a slight lag relative to the reactants. This is due to fuel reforming and electrochemical reactions within the hot box. Therefore, the exhaust gas temperature in each preheating component decreases after the current step. The exhaust gas temperature emanating from the steam generator drops from 493 K to 482 K, prompting the controller to rapidly reduce... This increases heat generation. Simultaneously, higher current exacerbates electrochemical polarization losses, leading to a gradual decrease in the stack's output voltage. The combined effect of reduced heat and decreased voltage increases the heat within the chamber, causing the temperature to rise. This prompts the controller to increase... This removes excess heat from the hot chamber. As the exhaust gas temperature gradually stabilizes, Increase The temperature decreased. After approximately 400 s, the system reached a new steady state. Due to the absence of gas transport delay outside the combustion chamber, the preheater, mixer, and steam generator exhibited nearly identical heat transfer characteristics. This indicates that describing the auxiliary components of a SOFC power generation system solely based on energy conservation is insufficient to capture its true thermodynamic dynamics.

[0057] The model under the S0.5H0 parameter group exhibited temperature overshoot. The temperatures of streams 12-15 overshooted by 0.9 K, 2.4 K, 4.3 K, and 9.1 K, respectively. The increasing overshoot along the flow path indicates that the soft delay effect of the exhaust gas accumulates among the components. The exhaust gas flow rate from the steam generator exhibits a significant lag compared to the steam flow rate, causing its temperature to drop rapidly to 450.7 K. When the soft delay parameter returned to its nominal value (S1H0 parameter group), to compensate for the rapid drop in exhaust gas temperature, The significant decrease caused strong oscillations in the flow channels, affecting both velocity and temperature. Overshoot for air and fuel reached 24.3% and 12.1%, respectively.

[0058] The presence of soft delay increases the lag in the rate of change of exhaust gas flow relative to the inlet reactants, while their responses remain synchronous. In contrast, hard delay disrupts this synchronicity. When the hard delay parameters are small (i.e., the S1H0.5 parameter set), the system behavior is similar to that of the S1H0 parameter set, reaching a new steady state after approximately 600 to 700 s. However, larger hard delays significantly alter this behavior. Taking a steam generator as an example, when the steam flow rate suddenly increases, the exhaust gas flow rate through the steam generator remains constant for a period of time. This leads to a sharp drop in the temperature of stream 14. In the model with only soft delay, although the exhaust gas temperature also drops rapidly, the synchronous increase in flow rate results in a relatively slower temperature drop. Therefore, under the S1H1 parameter set, The temperature drops rapidly, leading to a faster increase in system heat generation. After the exhaust gas passes through the hard delay phase, the heat carried increases, and the temperature of stream 14 rises rapidly. After a trough, The rapid increase suppresses the oscillations caused by soft delay. Therefore, different sets of soft-hard delay parameters exhibit completely different system gas transport delay effects.

[0059] The following describes the SOFC power generation system zero-dimensional dynamic modeling device provided in this application. The SOFC power generation system zero-dimensional dynamic modeling device described below and the SOFC power generation system zero-dimensional dynamic modeling method described above can be referred to in correspondence.

[0060] Figure 5 This is a schematic diagram of the structure of a zero-dimensional dynamic modeling device for an SOFC power generation system provided in an embodiment of this application, as shown below. Figure 5 As shown, the device 500 includes: Modeling module 510 is used to establish a zero-dimensional dynamic model based on the fuel reforming reaction, electrochemical reaction and energy conservation equations of each component in the hot box of the SOFC power generation system. The first introduction module 520 is used to introduce a soft delay parameter set into the zero-dimensional dynamic model and to use a first-order inertial element to characterize the lag in the change of gas flow velocity from the inlet to the outlet in each component. The second introduction module 530 is used to introduce a set of hard delay parameters into the zero-dimensional dynamic model, and to use pure time delay parameters to characterize the output response delay of each component caused by the gas flow distance.

[0061] In some embodiments, no hard delay parameter set is introduced into the fuel stream, air stream, and water stream of the SOFC power generation system.

[0062] In some embodiments, the soft delay parameter set includes the soft delay time of the hot box, the soft delay time of the preheater, the soft delay time of the mixer, the soft delay time of the steam generator, and the soft delay time of the gas turbine; the hard delay parameter set includes the hard delay time of the hot box, the hard delay time of the preheater, the hard delay time of the mixer, the hard delay time of the steam generator, and the hard delay time of the gas turbine.

[0063] The following describes the SOFC power generation system zero-dimensional dynamic modeling device provided in this application. The SOFC power generation system zero-dimensional dynamic modeling device described below and the SOFC power generation system zero-dimensional dynamic modeling method described above can be referred to in correspondence.

[0064] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0065] Based on the methods in the above embodiments, Figure 6 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 6 As shown in the illustration, this application provides an electronic device that may include a processor 610, a communication interface 620, a memory 630, and a communication bus 640. The processor 610, communication interface 620, and memory 630 communicate with each other via the communication bus 640. The processor 610 can call logical instructions stored in the memory 630 to execute the zero-dimensional dynamic modeling method for SOFC power generation systems described in the above embodiment.

[0066] Furthermore, the logical instructions in the aforementioned memory 630 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the zero-dimensional dynamic model modeling method for SOFC power generation systems described in the various embodiments of this application.

[0067] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program. When the computer program runs on a processor, it causes the processor to execute the zero-dimensional dynamic model modeling method for SOFC power generation systems in the above embodiments.

[0068] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the SOFC power generation system zero-dimensional dynamic model modeling method in the above embodiments.

[0069] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0070] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0071] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0072] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0073] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for modeling a zero-dimensional dynamic model of an SOFC power generation system, characterized in that, include: A zero-dimensional dynamic model is established based on the fuel reforming reaction, electrochemical reaction, and energy conservation equations of each component in the hot box of the SOFC power generation system. A soft delay parameter set is introduced into the zero-dimensional dynamic model, and a first-order inertial element is used to characterize the lag in the change of gas velocity from inlet to outlet in each component. A set of hard delay parameters is introduced into the zero-dimensional dynamic model, and the pure time delay parameter is used to characterize the output response delay of each component caused by the gas flow distance.

2. The zero-dimensional dynamic modeling method for SOFC power generation systems according to claim 1, characterized in that, Both the soft delay parameter set and the hard delay parameter set are applied to various components in the exhaust gas preheating channel of the SOFC power generation system.

3. The zero-dimensional dynamic modeling method for SOFC power generation systems according to claim 1, characterized in that, No hard delay parameter set is introduced into the fuel stream, air stream, and water stream of the SOFC power generation system.

4. The zero-dimensional dynamic modeling method for SOFC power generation systems according to claim 1, characterized in that, The soft delay parameter set includes the soft delay time of the hot box, the soft delay time of the preheater, the soft delay time of the mixer, the soft delay time of the steam generator, and the soft delay time of the gas turbine. The hard delay parameter set includes the hard delay time of the hot box, the hard delay time of the preheater, the hard delay time of the mixer, the hard delay time of the steam generator, and the hard delay time of the gas turbine.

5. A zero-dimensional dynamic modeling device for an SOFC power generation system, characterized in that, include: The modeling module is used to establish a zero-dimensional dynamic model based on the fuel reforming reaction, electrochemical reaction, and energy conservation equations of each component in the hot box of the SOFC power generation system. The first introduction module is used to introduce a soft delay parameter set into the zero-dimensional dynamic model and to use a first-order inertial element to characterize the lag in the change of gas flow velocity from the inlet to the outlet in each component. The second introduction module is used to introduce a set of hard delay parameters into the zero-dimensional dynamic model, and to use pure time delay parameters to characterize the output response delay of each component caused by the gas flow distance.

6. The zero-dimensional dynamic modeling device for SOFC power generation system according to claim 1, characterized in that, Both the soft delay parameter set and the hard delay parameter set are applied to various components in the exhaust gas preheating channel of the SOFC power generation system.

7. The zero-dimensional dynamic modeling device for SOFC power generation system according to claim 1, characterized in that, No hard delay parameter set is introduced into the fuel stream, air stream, and water stream of the SOFC power generation system.

8. The zero-dimensional dynamic modeling device for SOFC power generation system according to claim 1, characterized in that, The soft delay parameter set includes the soft delay time of the hot box, the soft delay time of the preheater, the soft delay time of the mixer, the soft delay time of the steam generator, and the soft delay time of the gas turbine. The hard delay parameter set includes the hard delay time of the hot box, the hard delay time of the preheater, the hard delay time of the mixer, the hard delay time of the steam generator, and the hard delay time of the gas turbine.

9. An electronic device, characterized in that, include: At least one memory for storing computer programs; At least one processor is configured to execute a program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the zero-dimensional dynamic model modeling method for SOFC power generation systems as described in any one of claims 1-4.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is run on the processor, the processor performs the zero-dimensional dynamic modeling method for SOFC power generation systems as described in any one of claims 1-4.

Images