Methanol reforming fuel cell modeling and parameter identification method and application
By establishing a discrete-time state-space model and using particle swarm optimization to identify parameters, the shortcomings of thermal coupling and dynamic temperature description in methanol reforming fuel cell modeling are solved, and a high-precision model is applied to system simulation and control.
Patent Information
- Application Number
- CN202511705299.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-20
- Publication Date
- 2026-02-17
AI Technical Summary
Existing methanol reforming fuel cell modeling methods struggle to balance computational accuracy and real-time performance, lacking a systematic description of the thermal coupling and dynamic temperature changes between the combustion chamber and the reforming chamber, which makes control strategy design and optimization difficult.
Using combustion chamber temperature, reforming chamber inlet and outlet temperatures as state variables, a discrete time-domain state-space model is established. Parameters such as heat transfer area, heat transfer coefficient, and heat dissipation coefficient are identified through particle swarm optimization algorithm. An error objective function is constructed by combining experimental data to achieve a high-precision model description.
It achieves accurate characterization of the dynamic processes in the combustion chamber and reforming chamber, and provides a high-precision model for system simulation, control and operation optimization.
Smart Images
Figure CN121546098A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of fuel cell technology, specifically to a method and application for modeling and parameter identification of methanol reforming fuel cells. Background Technology
[0002] A methanol reforming high-temperature fuel cell system is a clean energy device that converts methanol-water solution into hydrogen-rich gas through a reforming reaction and then generates electricity electrochemically within the fuel cell stack. This system typically includes a combustion chamber, a reforming chamber, a heat exchanger, and a fuel cell stack. The combustion chamber provides heat by burning methanol or fuel cell stack exhaust gas, while the reforming chamber completes the methanol reforming reaction under suitable temperature conditions to generate hydrogen for the fuel cell. Due to the significant thermal coupling between the combustion chamber and the reforming chamber, and the accompanying feed disturbances and external environmental heat dissipation during system operation, its dynamic characteristics are complex and highly nonlinear.
[0003] Existing methanol reformer modeling methods often rely on simplified mechanistic or empirical models, which frequently struggle to balance computational accuracy and real-time performance. Furthermore, parameters often depend on experimental fitting, making it difficult to maintain universality across different operating conditions. In addition, there is a lack of unified descriptions of the temperature dynamics in the combustion and reforming chambers, and a lack of systematic modeling methods that reflect the effects of feed rate, air supply, and heat exchange on temperature changes. This poses challenges to the design and optimization of control strategies. Summary of the Invention
[0004] The purpose of this invention is to provide a modeling method that can clearly characterize the dynamic processes of the combustion chamber and reforming chamber, reflect the thermal coupling mechanism, and identify parameters through experimental data.
[0005] To achieve the above objectives, the present invention provides a method for modeling and parameter identification of methanol reforming fuel cells, comprising the following steps: Step S1, using combustion chamber temperature... Inlet temperature of the reforming chamber and outlet temperature Let the state variables be defined, and the state vector be defined as follows: ; Methanol or exhaust gas is fed into the combustion chamber. Air feed and methanol feed to the reforming chamber Let the input vector be defined as... ; Establish a discrete-time state-space model ; Step S2: Decompose the discrete-time state-space model into scalar equations; Step S3: Collect experimental data, which includes any one or more of the following: combustion chamber temperature, reforming chamber inlet and outlet temperatures, combustion chamber methanol or exhaust gas feed, air feed, and reforming chamber methanol feed. Step S4: Construct the error objective function and use the particle swarm optimization algorithm to identify parameters, thereby obtaining a model for simulation and control.
[0006] Optionally, in step S2, the scalar equation includes: Where a, b, and c represent position parameters, For the influence between state variables, This indicates that the reaction in the combustion chamber releases heat and transfers heat. This indicates the air-supporting combustion effect. This indicates the feed cooling effect. Indicates heat exchange or heat dissipation. For heat exchanger temperature, The ambient temperature.
[0007] Optionally, step S3 includes a preheating stage and a power generation stage, respectively changing the input. and collect the corresponding The data is used for model identification.
[0008] Optionally, in step S4, parameter identification is achieved by minimizing the following objective function: in, The vector of parameters to be identified includes heat transfer area, heat transfer coefficient, and heat dissipation coefficient. and These are modeling data and experimental data, respectively.
[0009] Optionally, in step S4, parameter identification using the particle swarm optimization algorithm includes: initializing the parameter population and calculating the fitness. Update the speed and position, and iterate until the convergence condition is met.
[0010] Optionally, in step S4, physical constraints are applied to the parameters during the identification process. These physical constraints include the range of values, nonnegativity, and stability conditions to ensure the physical interpretability of the model.
[0011] Optionally, during the preheating stage, a methanol-water solution is used as the combustion input; during the power generation stage, fuel cell stack exhaust gas recovery is used as the combustion input.
[0012] Optionally, it also includes updating parameters using recursive or rolling identification methods to achieve dynamic correction of the model.
[0013] Optionally, it also includes model validation, which uses an independent dataset to compare simulation output with experimental output, calculate mean squared error and maximum error, and perform residual autocorrelation test.
[0014] This invention also provides an application of a methanol reforming fuel cell modeling and parameter identification method, which is used for fuel cell system simulation, controller design, fault diagnosis, and operation optimization.
[0015] Compared to the prior art, the beneficial effects of the present invention include at least the following: This invention provides a modeling method for a methanol reforming high-temperature fuel cell system, used to describe the coupling and dynamic characteristics of the combustion chamber and reforming chamber. The method selects the combustion chamber temperature, reforming chamber inlet temperature, and outlet temperature as state variables, and uses methanol or exhaust gas feed, air feed, and reforming chamber methanol feed as inputs to establish a discrete-time state-space model. This model comprehensively reflects the reaction exothermic effect, the effect of combustion air, environmental heat dissipation, and inter-chamber heat transfer, and incorporates corrections for inlet and outlet temperatures based on feed dilution and heat exchanger temperature. By constructing an error objective function between experimental and model outputs, and employing a particle swarm optimization algorithm to identify unknown parameters such as heat transfer area, heat transfer coefficient, and heat dissipation coefficient, a high-precision state-space model can be obtained. This method effectively reflects the dynamic processes of the preheating and power generation stages, providing a basis for system simulation, control, and operation. Attached Figure Description
[0016] Figure 1 This is a flowchart illustrating a modeling method for a methanol reforming high-temperature fuel cell system according to the present invention.
[0017] Figure 2 This is a flowchart illustrating the particle swarm optimization algorithm (PSO algorithm) used in this invention. Detailed Implementation
[0018] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.
[0019] This invention provides a method for modeling and parameter identification of methanol reforming fuel cells, comprising the following steps: Step S1, using combustion chamber temperature... Inlet temperature of the reforming chamber and outlet temperature Let the state variables be defined, and the state vector be defined as follows: ; Methanol or exhaust gas is fed into the combustion chamber. Air feed and methanol feed to the reforming chamber Let the input vector be defined as... ; Establish a discrete-time state-space model ; Step S2: Decompose the discrete-time state-space model into scalar equations; Step S3: Collect experimental data, which includes any one or more of the following: combustion chamber temperature, reforming chamber inlet and outlet temperatures, combustion chamber methanol or exhaust gas feed, air feed, and reforming chamber methanol feed. Step S4: Construct the error objective function and use the particle swarm optimization algorithm to identify parameters, thereby obtaining a model for simulation and control.
[0020] In some embodiments, according to heat transfer, in step S2, the scalar equation includes: Where a, b, and c represent position parameters, For the influence between state variables, This indicates that the reaction in the combustion chamber releases heat and transfers heat. This indicates the air-supporting combustion effect. This indicates the feed cooling effect. Indicates heat exchange or heat dissipation. For heat exchanger temperature, The ambient temperature.
[0021] In some embodiments, step S3 includes a preheating stage and a power generation stage, which respectively change the input. and collect the corresponding The data is used for model identification.
[0022] In some embodiments, in step S4, parameter identification is achieved by minimizing the following objective function: in, The vector of parameters to be identified includes heat transfer area, heat transfer coefficient, and heat dissipation coefficient. and These are modeling data and experimental data, respectively.
[0023] like Figure 2As shown, the particle swarm optimization algorithm of the present invention includes: initializing the particle swarm, setting parameters such as population size and number of iterations, randomly generating the initial position and velocity of particles, and determining whether the termination condition has been met: if so, outputting the global optimal solution and ending; if not, calculating the fitness of each particle, updating the individual optimal position (retaining the particle's own historical best position), updating the global optimal position (retaining the best position among all particles), updating the particle velocity and position (adjusting based on the individual optimal and global optimal), and then looping until the termination condition is determined again.
[0024] During the identification process, physical constraints are imposed on the parameters, including the range of values, nonnegativity, and stability conditions, to ensure the physical interpretability of the model.
[0025] Example This embodiment uses a methanol reforming high-temperature fuel cell system with a rated power of 3kW as an example to illustrate the specific application of the method of the present invention. Please refer to... Figure 1 The flowchart shown is a modeling and parameter identification method for methanol reforming fuel cells, including: Step S100: The system mainly includes a methanol-water solution feed pump, a combustion chamber, an air supply system, a heat exchanger, and a high-temperature fuel cell stack. The system was built in a laboratory environment. Thermocouples were placed on the fuel cell stack and at the inlet and outlet of the heat exchanger to collect the stack temperature in real time. Heat exchanger inlet temperature and outlet temperature The opening degree of the methanol pump in the combustion chamber was measured using a flow meter. airflow and the opening degree of the methanol pump in the reforming chamber The experimental sampling period was set to 1 second.
[0026] Based on the system's energy balance relationship, the following discrete state equations are established: Wherein, the state vector Step S200: Set the control input vector Expand it into a scalar equation: Among them, parameters These correspond to the heat transfer coupling term, flow input coefficient, and heat dissipation term, respectively. For ambient temperature, This refers to the temperature of the combustion exhaust gas.
[0027] During the experiment, the system operation was divided into two stages: preheating and power generation. In the preheating stage, the methanol pump speed was adjusted. and airflow Temperature response data under different operating conditions is collected; during the power generation phase, the recovered exhaust gas from the fuel cell stack is used as the combustion input to adjust the coolant pump speed. Record the dynamic temperature changes of the fuel cell stack and heat exchanger.
[0028] Step S300, in order to obtain the model parameters θ = { }, Establish the objective function: Particle swarm optimization (PSO) is used to identify the parameters. The specific configuration is as follows: population size is set to 30, maximum number of iterations is 200, inertia weight w decreases linearly between 0.9 and 0.4, individual learning factor c1 and swarm learning factor c2 are both set to 2.0, and the parameter search space is set to non-negative real numbers in the range [0, 10] based on the actual physical meaning. During the iteration process, the position of each particle represents a set of parameters to be identified, and the velocity update formula is... in, This is the optimal solution in the particle's history. This is the optimal solution for the population. and It is a random number between [0,1].
[0029] After iteration, the model parameters converged, and the final model had a mean squared error (RMSE) of approximately 10 °C on the independent validation dataset, validating the effectiveness and applicability of the model.
[0030] The established model can accurately describe the temperature dynamics of a 3kW methanol reforming fuel cell system and can be further used for model-based predictive control, operating status monitoring, and energy management optimization.
[0031] In summary, this invention discloses a method and application for modeling and parameter identification of a methanol reforming fuel cell, comprising the following steps: Step S2, defining a state vector with combustion chamber temperature, reforming chamber inlet temperature, and outlet temperature as state variables; and defining an input vector with combustion chamber methanol or exhaust gas feed, air feed, and reforming chamber methanol feed as inputs to establish a discrete-time state-space model; Step S3, decomposing the discrete-time state-space model into scalar equations; Step S4, collecting experimental data, which includes any one or more of combustion chamber temperature, reforming chamber inlet and outlet temperatures, combustion chamber methanol or exhaust gas feed, air feed, and reforming chamber methanol feed; and Step S5, constructing an error objective function and using a particle swarm optimization algorithm for parameter identification to obtain a model for simulation and control. This method effectively reflects the dynamic process of the preheating and power generation stages, providing support for system simulation, control, and operation optimization.
[0032] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.
Claims
1. A method for modeling and parameter identification of methanol reforming fuel cells, characterized in that, Includes the following steps: Step S1, with combustion chamber temperature Inlet temperature of the reforming chamber and outlet temperature Let the state variables be defined, and the state vector be defined as follows: ; Methanol or exhaust gas is fed into the combustion chamber. Air feed and methanol feed to the reforming chamber Let the input vector be defined as... ; Establish a discrete-time state-space model ; Step S2: Decompose the discrete-time state-space model into scalar equations; Step S3: Collect experimental data, which includes any one or more of the following: combustion chamber temperature, reforming chamber inlet and outlet temperatures, combustion chamber methanol or exhaust gas feed, air feed, and reforming chamber methanol feed. Step S4: Construct the error objective function and use the particle swarm optimization algorithm to identify parameters, thereby obtaining a model for simulation and control.
2. The method for modeling and parameter identification of methanol reforming fuel cells as described in claim 1, characterized in that, In step S2, the scalar equation includes: Where a, b, and c represent position parameters, For the influence between state variables, This indicates that the reaction in the combustion chamber releases heat and transfers heat. This indicates the air-supporting combustion effect. This indicates the feed cooling effect. Indicates heat exchange or heat dissipation. For heat exchanger temperature, The ambient temperature.
3. The method for modeling and parameter identification of methanol reforming fuel cells as described in claim 1, characterized in that, Step S3 includes a preheating stage and a power generation stage, which involve changing the input respectively. and collect the corresponding The data is used for model identification.
4. The method for modeling and parameter identification of methanol reforming fuel cells as described in claim 1, characterized in that, In step S4, parameter identification is achieved by minimizing the following objective function: in, The vector of parameters to be identified includes heat transfer area, heat transfer coefficient, and heat dissipation coefficient. and These are modeling data and experimental data, respectively.
5. The method for modeling and parameter identification of methanol reforming fuel cells as described in claim 1, characterized in that, Step S4, parameter identification using the particle swarm optimization algorithm, includes: initializing the parameter population and calculating fitness. Update the speed and position, and iterate until the convergence condition is met.
6. The method for modeling and parameter identification of methanol reforming fuel cells as described in claim 1, characterized in that, In step S4, physical constraints are applied to the parameters during the identification process. These physical constraints include the range of values, nonnegativity, and stability conditions to ensure the physical interpretability of the model.
7. The method for modeling and parameter identification of methanol reforming fuel cells as described in claim 3, characterized in that, In the preheating stage, methanol-water solution is used as the combustion input; in the power generation stage, fuel cell stack exhaust gas recovery is used as the combustion input.
8. The method for modeling and parameter identification of methanol reforming fuel cells as described in claim 1, characterized in that, It also includes updating parameters using recursive or rolling identification methods to achieve dynamic model correction.
9. The method for modeling and parameter identification of methanol reforming fuel cells as described in claim 1, characterized in that, It also includes model validation, which uses an independent dataset to compare simulation output with experimental output, calculate mean square error and maximum error, and perform residual autocorrelation test.
10. An application of the methanol reforming fuel cell modeling and parameter identification method as described in any one of claims 1 to 9, characterized in that, The methanol reforming fuel cell modeling and parameter identification method described herein is used for fuel cell system simulation, controller design, fault diagnosis, and operation optimization.