SOFC cogeneration operation optimization method based on stack attenuation and bop off-design condition

Abstract

The present application relates to the technical field of solid oxide fuel cell (SOFC), in particular to a SOFC combined heat and power system operation optimization method based on stack attenuation and auxiliary equipment (BOP) non-design condition, including establishing auxiliary component system efficiency, pressure drop and heat transfer characteristic model under non-design condition, building SOFC combined heat and power system coupling stack voltage attenuation and auxiliary component non-design condition, using radial basis function-based proxy optimization algorithm to dynamically optimize target fuel utilization and target current density of each scheduling interval; finally, the optimization results are converted into fuel supply flow to realize full life cycle closed loop operation control and strategy correction. The present application can realize dynamic optimization scheduling of SOFC combined heat and power system full life cycle operation parameters under the condition of considering stack attenuation and auxiliary component non-design condition coupling effect, thereby providing effective support for improving system economy, power generation efficiency and long-term stable operation ability.

Description

Technical Field

[0001] This invention relates to the field of solid oxide fuel cell technology, and in particular to an optimization method for SOFC cogeneration operation based on stack decay and BOP off-design conditions. Background Technology

[0002] Solid oxide fuel cells (SOFCs) can achieve internal reforming of hydrocarbon and nitrogen-based fuels and directly convert the chemical energy of the fuel into electrical energy through electrochemical reactions. Compared with traditional combustion power generation systems, SOFCs have significant thermodynamic advantages, including high power generation efficiency and a wide range of applicable fuels. When using clean fuels such as hydrogen, biogas, and ammonia, they can also achieve near-zero carbon emissions, showing broad application prospects.

[0003] However, the high-temperature operating environment of SOFC systems places stringent requirements on the manufacturing processes and operational performance of the core materials and auxiliary components (BOP) of the fuel cell stack, resulting in high initial investment costs. At the same time, during long-term operation, the fuel cell stack is subject to the coupled effects of multiple factors such as microstructure evolution, thermal cycling stress, and fuel poisoning, which will lead to continuous performance degradation, manifested as an irreversible decrease in stack voltage, output power, and power generation efficiency. This severely restricts the commercialization and long-term stable operation of SOFC cogeneration systems. In addition, most existing research on SOFC operation strategy optimization is based on idealized assumptions: the system operating conditions are set to remain unchanged throughout the simulation analysis process, and it is assumed that there is no performance degradation of the fuel cell stack and auxiliary components (BOP). Although a few studies have analyzed fixed operating modes by combining stack decay curves, they are limited to simple strategies such as maintaining a constant average temperature, fixed output power, or adjusting a single current density. They fail to fully consider the potential for simultaneous and flexible control of multiple operating variables such as temperature, fuel utilization rate, and current density, and also fail to include the dynamic coupling effect of stack decay and auxiliary components under off-design conditions in the optimization scope. As a result, the generated operating strategies are difficult to adapt to the continuous evolution of system performance throughout the entire life cycle, and cannot achieve the comprehensive optimization of economy, power generation efficiency, and durability while ensuring long-term operational stability. At present, there is a need for an optimization method for SOFC cogeneration operation based on stack decay and BOP off-design conditions. Summary of the Invention

[0004] To address the technical challenge of balancing operational economy, power generation efficiency, and long-term stability in SOFC cogeneration systems, this invention provides an optimization method for SOFC cogeneration operation based on stack decay and BOP (Balance of Plant) off-design conditions.

[0005] This invention provides an optimization method for SOFC cogeneration operation based on stack decay and BOP (Balance of Plant) off-design conditions, employing the following technical solution: The optimization method for SOFC cogeneration operation based on stack decay and BOP off-design conditions includes: S1. Establish an off-design operating condition characteristic model of the auxiliary component system to characterize the efficiency, pressure drop and heat transfer dynamic characteristics of the auxiliary components under off-design conditions. S2. Construct a voltage decay model of the fuel cell stack that couples temperature, fuel utilization rate and current density, and obtain the voltage decay rate of the fuel cell stack under different operating conditions. S3. Couple the stack voltage decay model with the non-design operating condition characteristic model to build a non-design operating condition SOFC cogeneration system, and determine the system optimization variables, constraints and objective function; S4. Based on the SOFC cogeneration system under non-design conditions, an optimization algorithm is adopted to dynamically optimize the target fuel utilization rate and target current density in each scheduling interval with a preset time-sharing adjustment interval as the period. S5. Based on the optimized target fuel utilization rate and target current density, convert them into execution instructions for physical equipment and send them to the relevant hardware actuators of the SOFC cogeneration system.

[0006] Furthermore, the auxiliary components include at least a plate heat exchanger, a blower, a combustion chamber, and system piping; the establishment of the non-design operating condition characteristic model of the auxiliary component system includes, for each auxiliary component, based on the ratio of the actual mass flow rate under non-design conditions to the nominal mass flow rate under design conditions, correcting the corresponding design operating condition characteristic parameters to obtain the actual efficiency, pressure drop, or heat transfer dynamic characteristics under non-design conditions.

[0007] Furthermore, the modification of the corresponding design condition characteristic parameters includes: For plate heat exchangers, based on the ratio of the actual mass flow rate of the cold and hot sides under non-design conditions to the nominal mass flow rate under design conditions, the preset convective heat transfer coefficient correction function is called to correct the convective heat transfer coefficient of the cold and hot sides, so as to obtain the total heat transfer coefficient and flow pressure drop under non-design conditions. For blowers, the load factor is determined based on the ratio of actual mass flow rate to rated mass flow rate. The total electrical efficiency under design conditions is then corrected based on the load factor to obtain the actual efficiency and shaft power under non-design conditions. For the combustion chamber, the pressure drop under the design conditions is corrected based on the ratio of the actual mass flow rate of the exhaust side under non-design conditions to the nominal mass flow rate under the design conditions, so as to obtain the actual pressure drop under non-design conditions. For the system pipeline, based on the ratio of the actual mass flow rate under non-design conditions to the nominal mass flow rate under design conditions, the pressure drop under design conditions is corrected to obtain the actual pressure drop under non-design conditions. The pressure drop of the pipeline system under non-design conditions satisfies the following: , in, The nominal pipeline pressure drop under design conditions. This represents the actual mass flow rate of the pipeline. This refers to the mass flow rate under the rated operating conditions of the pipeline.

[0008] Further, step S2 specifically includes: S21. Determine the input and output variables of the stack voltage decay model. The input variables include at least fuel utilization rate, current density and stack temperature. The output variables include at least one of voltage decay rate, performance loss rate, lifetime consumption factor, health status index and remaining usable lifetime. S22. Establish the mapping relationship between voltage decay rate and fuel utilization rate and current density. S23. Construct a fuel cell stack voltage decay model based on at least one of the following methods: experimental calibration data, physical degradation mechanism extraction, or operational data training. The fuel cell stack voltage decay model is an empirical model, a semi-empirical model, a data-driven model, or a fusion model formed by at least two combinations.

[0009] Furthermore, the stack voltage decay model updates the initial stack voltage for each scheduling interval according to the following sub-steps: In the i At the start of each scheduling interval, read the current cumulative runtime and obtain the candidate fuel utilization rate and candidate current density for that scheduling interval; Substitute the candidate fuel utilization rate and candidate current density into the stack voltage decay model to calculate the degradation rate of the scheduling interval, and calculate the voltage decay amount of the scheduling interval based on the degradation rate and the preset time step. Based on the voltage decay, update the [number] in a discrete time-varying form. i The starting stack voltage of +1 scheduling intervals is compared with a preset initial voltage threshold. If the current stack voltage is less than the preset threshold, the stack life is determined to have ended. i The expression for updating the initial heap voltage for +1 scheduling intervals is: , in, For the first i +1 scheduling interval's starting stack voltage, For the first i The stack voltage of each dispatch interval The degradation rate characterizes the proportion of voltage decay of the fuel cell stack per unit time. For the first i Fuel utilization rate of each dispatch interval For the fuel cell stack temperature, For time step.

[0010] Further, step S3 specifically includes: S31. Couple the stack voltage decay model with the auxiliary component non-design operating condition characteristic model to build a non-design operating condition SOFC cogeneration system with multiple continuous scheduling intervals within the life cycle as the time skeleton. S32. Within each dispatch interval, based on the stack voltage model under the current degradation state and the non-design operating condition characteristic model of auxiliary components, calculate the net power generation, net power generation efficiency, fuel consumption, parasitic work consumption, heat balance state and economic indicators of the dispatch interval. S33. The final state of the current scheduling interval is passed as the initial state of the next scheduling interval to realize the interval-by-interval recursive simulation of the operating state throughout the entire life cycle.

[0011] Furthermore, determining the system optimization variables, constraints, and objective function includes: The optimization variables include at least the target fuel utilization rate and the target current density within each scheduling interval; The constraints include at least the upper and lower limits of fuel utilization, the upper and lower limits of current density, and the stack temperature threshold within each scheduling interval. The objective function is selected from one of minimizing the levelized cost of electricity (LCOE), maximizing the average power generation efficiency over the entire life cycle, and maximizing the cumulative power generation over the life cycle.

[0012] Furthermore, the dynamic optimization of the target fuel utilization rate and target current density within each scheduling interval includes constructing a discrete time series containing n scheduling intervals based on the total operating life of the system and a preset time-sharing adjustment interval, and combining the target fuel utilization rate and current density of each interval to generate a time series decision vector. In the process of solving the time series decision vector, if the current candidate vector causes the output electrical efficiency of the SOFC cogeneration system under non-design conditions to be negative, or the system operating parameters exceed the preset constraint boundary, then a preset penalty value is applied to the objective function to eliminate the infeasible operating point. The time series decision vector satisfies: , in, The target fuel utilization rate for the nth scheduling interval is... Let n be the target current density of the nth scheduling interval, where n is the total number of scheduling intervals determined based on the total operating life of the system and the preset time-sharing adjustment interval.

[0013] Furthermore, the optimization algorithm is a surrogate optimization algorithm based on radial basis functions, and the surrogate optimization algorithm includes: S41. Use quasi-random sequences to generate initial evaluation points in the solution space, call the non-design condition SOFC cogeneration system to perform real evaluation on each initial evaluation point, and obtain the corresponding objective function value. S42. Based on the evaluated sample points, fit the response surface of the objective function with respect to the time series decision vector using radial basis functions, and dynamically update the response surface; S43. Combining the predicted objective function value of the response surface for candidate points and the distance information between candidate points and evaluated sample points, select new points to be evaluated for real evaluation and add them to the sample set to update the response surface. Iteratively execute S41 to S43 until the preset stopping condition is met, and output the optimal time series decision vector.

[0014] Further, step S5 specifically includes: S51, The central controller receives the optimized target fuel utilization rate and target current density; S52. Calculate the target fuel flow rate based on the target fuel utilization rate, and generate valve opening electrical signal commands for the fuel supply flow regulating valve, exhaust gas return regulating valve, steam / fuel ratio regulating valve, or fuel pressure regulating valve. S53. Calculate the target air flow rate based on the cathode oxygen supply demand and the excess air coefficient, and generate the speed control command for the variable frequency blower. S54. Calculate the target stack current based on the target current density, and generate current or power control commands for the external load regulation unit, DC / AC converter, inverter, or grid connection interface. S55 sends the valve opening electrical signal command, speed control command, and current or power control command to the corresponding hardware actuator of the SOFC combined heat and power system to realize closed-loop operation control and operation strategy correction throughout the entire life cycle.

[0015] In summary, the present invention has the following beneficial technical effects: 1. This invention couples the stack voltage decay model with the auxiliary component (BOP) off-design condition characteristic model to build a full life cycle off-design condition SOFC cogeneration system, realizing the coordinated characterization of stack decay and auxiliary component condition mismatch, and significantly improving the prediction accuracy of the system's long-term operating status.

[0016] 2. This invention achieves adaptive adjustment of the operating parameters of the SOFC cogeneration system throughout its entire life cycle by dynamically optimizing the target fuel utilization rate and target current density in each scheduling interval using a preset time-sharing adjustment interval as the cycle. This effectively overcomes the problems of accelerated performance degradation and economic deterioration caused by traditional fixed operation strategies.

[0017] 3. This invention employs a surrogate optimization algorithm based on radial basis functions, utilizes the response surface to guide the search direction and dynamically update it, thereby achieving efficient optimization of high-dimensional time series decision vectors. While ensuring optimization accuracy, it significantly reduces the computational overhead of full lifecycle simulation.

[0018] 4. This invention uses a central controller to convert the optimized target fuel utilization rate and target current density into execution instructions for physical devices, and continuously collects actual operating parameters for deviation detection and strategy correction, thereby realizing closed-loop operation control throughout the entire life cycle and effectively ensuring the operational stability and safety of the system at different degradation stages. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the overall process of the SOFC cogeneration system operation optimization method based on stack decay and BOP non-design conditions according to an embodiment of the present invention.

[0020] Figure 2 This is a graph showing the relationship between the fuel cell stack decay rate and fuel utilization rate and current density in an embodiment of the present invention.

[0021] Figure 3 This is a schematic diagram of the SOFC combined heat and power system according to an embodiment of the present invention.

[0022] Figure 4 This is a graph showing the relationship between the optimal LCOE and the computation time under different adjustment intervals in this embodiment of the invention.

[0023] Figure 5 This is an optimized operation plan diagram of the embodiment of the present invention with an adjustment interval of 3000h and minimizing LCOE.

[0024] Figure 6 This is a schematic diagram comparing the optimized effects of an embodiment of the present invention; wherein, Figure 6 (a) is a comparison chart of the optimized plan and the baseline. Figure 6 (b) is a comparison chart of the optimized plan and the best fixed conditions. Detailed Implementation

[0025] The present invention will be further described in detail below with reference to the accompanying drawings.

[0026] Example 1 Reference Figure 1 The SOFC cogeneration system operation optimization method based on stack decay and BOP off-design conditions in this embodiment includes: S1. Establish an off-design operating condition characteristic model of the auxiliary component (BOP) system to characterize the efficiency, pressure drop and heat transfer dynamic characteristics of the auxiliary component under off-design conditions. S2. Construct a voltage decay model of the fuel cell stack that couples temperature, fuel utilization rate and current density, and obtain the voltage decay rate of the fuel cell stack under different operating conditions. S3. Couple the stack voltage decay model with the non-design operating condition characteristic model to build a non-design operating condition SOFC cogeneration system, and determine the system optimization variables, constraints and objective function; S4. Based on the SOFC cogeneration system under non-design conditions, an optimization algorithm is adopted to dynamically optimize the target fuel utilization rate and target current density in each scheduling interval with a preset time-sharing adjustment interval as the period. S5. Based on the optimized target fuel utilization rate and target current density, convert them into execution instructions for physical equipment and send them to the relevant hardware actuators of the SOFC cogeneration system.

[0027] Specifically, the optimization method for SOFC cogeneration system operation based on stack decay and BOP off-design conditions includes the following: like Figure 1 As shown in Figure S1, firstly, an off-design operating condition characteristic model of the auxiliary component (BOP) system is established. This model is used to describe the efficiency changes, pressure drop changes, heat exchange capacity changes, and parasitic work changes of each auxiliary component under off-design conditions after the stack degradation causes the system to deviate from the initial design point. The auxiliary components include at least a plate heat exchanger, a blower, a combustion chamber, and system piping.

[0028] For plate heat exchangers, under non-design conditions, based on the ratio of the actual mass flow rate on the hot and cold sides to the nominal mass flow rate under design conditions, preset convective heat transfer coefficient correction functions are called to correct the convective heat transfer coefficients on the hot and cold sides, thereby obtaining the overall heat transfer coefficient and flow pressure drop. The overall heat transfer coefficient U is calculated using the following formula: , in, The convective heat transfer coefficient on the cold side is... The convective heat transfer coefficient on the hot side is given, and the convective heat transfer coefficients on the cold and hot sides are corrected according to the following formulas: , , in, The nominal convective heat transfer coefficient on the cold side under design conditions. This is a correction function for the cold-side convective heat transfer coefficient based on the mass flow rate ratio. This represents the cold-side mass flow rate under non-design conditions. The nominal mass flow rate on the cold side under design conditions. This is a correction function for the hot-side convective heat transfer coefficient based on the mass flow rate ratio. The nominal convective heat transfer coefficient on the hot side under design operating conditions. This represents the hot-side mass flow rate under non-design conditions. This is the nominal mass flow rate on the hot side under design conditions.

[0029] The flow pressure drop DP of a plate heat exchanger under off-design conditions is calculated using the following formula: , in, This represents the total pressure drop of the fluid. The nominal pressure drop under design conditions. For volumetric flow rate, The nominal volumetric flow rate under design conditions. This represents the mass flow rate of the plate heat exchanger under actual operating conditions. This is the mass flow rate of the plate heat exchanger under rated operating conditions.

[0030] In SOFC (Solar-Electric Combined Heat and Power) systems, the blower supplies oxidant air to the cathode of the fuel cell stack, and its operating performance directly affects the system's parasitic power consumption and the stability of the cathode oxygen supply. Because fuel cell stack degradation causes the actual system operating conditions to continuously deviate from the design point, the blower's mass flow rate changes accordingly. If the efficiency is still calculated based on the design operating conditions, significant deviations will occur. Therefore, it is necessary to establish a non-design operating condition characteristic model to correct its efficiency and power consumption.

[0031] The blower efficiency varies with load rate, and is corrected using an empirical mapping fitted from measured data. The load rate (LR) is defined as the ratio of the actual mass flow rate to the rated mass flow rate, used to quantify the degree to which the blower deviates from its design operating conditions. , in, The load factor is the efficiency ratio, calculated based on the efficiency variation characteristics of the blower in different load ranges. Determined by the following piecewise linear function: , Based on the above efficiency ratio, the actual efficiency of the blower under non-design operating conditions... and shaft power Calculate using the following formulas respectively: , , in, This refers to the mass flow rate of the blower under actual operating conditions. This refers to the mass flow rate of the blower under rated operating conditions. For efficiency ratio, This refers to the equipment efficiency under actual operating conditions. The total electrical efficiency of the motor-blower system under design operating conditions. To increase the pressure of the blower, This represents the actual shaft power of the blower.

[0032] In a SOFC (Solar-Electric Combined Heat and Power) system, the combustion chamber is used to burn unreacted fuel in the anode exhaust gas and oxygen in the cathode exhaust gas to maintain system thermal balance. When stack degradation causes the system operating conditions to deviate from the design point, the anode exhaust gas flow rate changes, and the gas mass flow rate in the combustion chamber changes accordingly, thus affecting the combustion chamber pressure drop. Ignoring this off-design condition effect will lead to distortion in the system back pressure calculation, affecting the matching accuracy of fuel and air supply. Therefore, under off-design conditions, the pressure drop is corrected based on the ratio of the actual exhaust mass flow rate to the nominal mass flow rate under design conditions. (Combustion chamber pressure drop) Calculate using the following formula: , in, This refers to the pressure drop in the combustion chamber under non-design conditions. The nominal combustion chamber pressure drop under design conditions. This represents the actual mass flow rate on the exhaust side. This is the nominal exhaust-side mass flow rate under design conditions.

[0033] For the system piping, the SOFC combined heat and power system includes multiple connecting pipelines for transporting fuel, air, and exhaust gases. During the stack decay process, the mass flow rate of each branch varies with operating conditions. The pipeline pressure drop is proportional to the square of the mass flow rate. Pressure drop changes under off-design conditions directly affect the resistance distribution and equilibrium state of the system's fluid network. Therefore, a general correction formula is used for the pressure drop of each pipeline section under off-design conditions: , in, This represents the pipeline pressure drop under actual operating conditions. The nominal pipeline pressure drop under design conditions. This represents the actual mass flow rate of the pipeline. This refers to the mass flow rate under the rated operating conditions of the pipeline.

[0034] S2. After establishing the non-design operating condition characteristic model of the auxiliary components as described in Step 1, further establish the fuel cell stack steady-state performance model and the fuel cell stack voltage decay model. The fuel cell stack steady-state performance model is the basis for calculating the fuel cell stack output voltage and system energy balance, while the fuel cell stack voltage decay model is used to characterize the performance degradation law of the fuel cell stack during long-term operation.

[0035] like Figure 2 As shown, a steady-state performance model of the fuel cell stack is first established. This model, based on electrochemical mechanisms, characterizes the stack output voltage as the sum of reversible voltage, activation overpotential, ohmic overpotential, and concentration overpotential. Reversible voltage... The calculation is as follows: , in, For the change of Gibbs free energy, It is Faraday's constant. Let be the ideal gas constant. For the fuel cell stack temperature, The mole fraction of hydrogen in the main stream. The partial pressure of oxygen. This represents the mole fraction of water vapor in the main stream.

[0036] Activation overpotential Calculate using the following formula: , Where n is the number of electrons transferred in the electrochemical reaction; n=2 when the reaction side is fuel, and n=4 when the reaction side is air. For exchange current density, For current density, ohmic overpotential satisfy: , in, For electrolyte thickness, Electrolyte reference conductivity, concentration overpotential Calculate using the following formula: , in, This refers to the mole fraction of oxygen in the main stream. This represents the mole fraction of oxygen at the three-phase interface. This represents the mole fraction of hydrogen at the three-phase interface. The mole fraction of hydrogen in the main stream. This represents the mole fraction of water vapor at the three-phase interface. The mole fraction of water vapor in the main stream; in addition, the mole fraction of oxygen at the three-phase interface. Hydrogen mole fraction at the three-phase interface Mole fraction of water vapor at the three-phase interface and oxygen boundary layer thickness parameters They respectively satisfy: , , , , in, The thickness of the anode diffusion layer. For the thickness of the fuel diffusion layer, For oxygen boundary layer thickness parameters, The effective diffusion coefficient of hydrogen is... The mole fraction of nitrogen gas. The effective diffusion coefficient of oxygen. The effective diffusion coefficient between oxygen and nitrogen. For the operating pressure, the system thermal balance is calculated using the following formula: , , in, To generate heat power for the system, This indicates the chemical energy from the imported fuel. This indicates the chemical energy carried away by unreacted fuel at the outlet. Indicates the output voltage. Indicates the output current. This refers to the output power of the fuel cell stack.

[0037] Based on the aforementioned steady-state performance model of the fuel cell stack, a voltage decay model is further constructed. Due to the combined effects of multiple factors such as microstructural evolution, thermal cycling, and fuel poisoning during long-term operation, the output voltage, output power, and power generation efficiency of the fuel cell stack will continuously decline. If this degradation effect is ignored, subsequent system optimization will be based on idealized stack performance, leading to a severe mismatch between operating strategies and actual operating conditions. Therefore, a fuel cell stack voltage decay model is needed to quantify this degradation process.

[0038] Determine the input and output variables of the fuel cell stack voltage decay model. The input variables should include at least the fuel utilization rate. The output variables include, but are not limited to, current density J and stack temperature T; at least the voltage decay rate. The parameters include performance degradation rate, lifetime attrition factor, health status index, and remaining usable lifetime. A mapping relationship is established between voltage decay rate and fuel utilization rate and current density. The decay rate increases with increasing fuel utilization rate and increases exponentially with increasing current density. Based on at least one of the following methods—experimental calibration data, physical degradation mechanism extraction, or operational data training—a stack voltage decay model is constructed. This model can be an empirical model, a semi-empirical model, a data-driven model, or a fusion model combining at least two of these. In this embodiment, based on a semi-empirical model derived from experimental data regression, the following decay rate prediction function is constructed: , in, The degradation rate is expressed in units of 1000 m / s. , For fuel utilization rate, For the fuel cell stack temperature, denoted as current density.

[0039] Based on the aforementioned decay rate, a time-varying voltage model for the SOFC stack is established to describe the continuous decay process of the stack voltage over cumulative operating time. This continuous form is as follows: , Since this embodiment employs a time-segmented operation strategy for discretized scheduling throughout the entire lifecycle, the aforementioned continuous model needs to be adapted to a discrete time-varying form to allow for recursive updates of the stack voltage at the boundaries of each scheduling interval. The discrete time-varying form is as follows: , in, For continuous time t The voltage of the fuel cell stack, The initial voltage, For the first i +1 scheduling interval's starting stack voltage, For the first i The stack voltage of each dispatch interval For the first i Fuel utilization rate of each dispatch interval For time step, For a moment Fuel utilization rate.

[0040] Finally, update the starting heap voltage for each scheduling interval using the following sub-steps: At the start of the i-th scheduling interval, read the current cumulative runtime. And obtain the candidate fuel utilization rate for that scheduling interval. and candidate current density ;Will and Substitute the values ​​into the decay rate prediction function to calculate the degradation rate for this scheduling interval. According to the degradation rate With preset time step Calculate the voltage attenuation in this scheduling interval. Based on the voltage decay, update the starting pile voltage of the (i+1)th scheduling interval in a discrete time-varying manner; determine the current pile voltage. Should it be reduced to the initial voltage? If the voltage decay rate is below 80%, the stack is considered to have reached the end of its lifespan. This voltage decay model outputs not only the decay rate, but also the lifespan consumption factor, health status index, or remaining usable lifespan, and sets corresponding parameter sets for different fuel modes, different stack types, or different anode cycle structures.

[0041] S3. After establishing the steady-state performance model and voltage decay model of the fuel cell stack, the non-design operating condition characteristic model of the auxiliary component (BOP), the steady-state performance model of the fuel cell stack, and the voltage decay model of the fuel cell stack established in step one are coupled to build a non-design operating condition SOFC cogeneration system. This system uses multiple continuous scheduling intervals within the life cycle as the time skeleton. In each scheduling interval, the starting voltage of the fuel cell stack in the current degradation state is determined based on the fuel cell stack voltage model. The non-design operating condition characteristic model of the auxiliary component is called to determine the actual efficiency, voltage drop, and heat transfer coefficient of each auxiliary component. The fuel cell stack electrochemical equation, system thermal balance equation, and fluid network equation are combined to solve the net power generation, net power generation efficiency, fuel consumption, parasitic work consumption, thermal balance state, and economic indicators of the scheduling interval. The final state of the current scheduling interval is transferred to the next scheduling interval as the initial state to realize the interval-by-interval recursive simulation of the operating state throughout the entire life cycle. The optimization variables include at least the target fuel utilization rate and target current density in each scheduling interval, and may further include one or more of the following: target temperature, air flow rate, fuel flow rate, anode exhaust gas recirculation ratio, adjustment interval length, or baseline design point parameters.

[0042] After the system model is built, the system constraints and objective function are determined. The constraints include at least the upper and lower limits of fuel utilization, current density, stack temperature, and system stability boundary conditions for each scheduling interval; the objective function is selected from any of the following: (1) Minimize the levelized cost of electricity (LCOE), the objective function satisfies: , (2) Maximize the average power generation efficiency over the entire life cycle. The objective function satisfies: , (3) Maximize the cumulative power generation over the lifetime. The objective function satisfies: , in, To levelize the cost of electricity, Total lifetime revenue requirement. Let be the net output power of the i-th scheduling interval. Let be the duration of the i-th scheduling interval. The average power generation efficiency over the entire life cycle. Let be the hydrogen mass flow rate for the i-th scheduling interval. The lower heating value of hydrogen. This represents the cumulative power generation over the product's lifetime. This represents the total number of scheduling intervals.

[0043] S4. After completing the construction of the SOFC cogeneration system under non-design conditions and determining the optimization variables, constraints and objective functions as described in step three, further optimization algorithms are adopted to dynamically optimize the target fuel utilization rate and target current density in each scheduling interval with a preset time-sharing adjustment interval as the period.

[0044] First, based on the total system lifespan and the preset time-sharing adjustment interval, a discrete time series containing n scheduling intervals is constructed. The target fuel utilization rate and current density of each interval are then combined to generate a time series decision vector. The time-sharing adjustment interval can be a fixed or variable value, and can be set at the hourly, daily, weekly, monthly, or event-triggered levels. In this embodiment, the SOFC combined heat and power system is specifically as follows: Figure 3 As shown, the preset time-sharing adjustment interval is set between 200 and 3000 hours, and the boundary conditions for the control variables are: 2000A / m²≤J≤5000A / m². The time series decision vector satisfies: , in, The target fuel utilization rate for the nth scheduling interval is... Let n be the target current density of the nth scheduling interval, where n is the total number of scheduling intervals determined based on the total system lifespan and the preset time-sharing adjustment interval. During the process of solving the time-series decision vector, if the current candidate vector causes the output electrical efficiency of the SOFC combined heat and power system under non-design conditions to be negative, or if the system operating parameters exceed the preset constraint boundaries, a preset penalty value is applied to the objective function to exclude the infeasible operating point, ensuring the continuity of global optimization. The penalty value is on a much larger scale than the normal objective function value, effectively preventing the optimization algorithm from continuing to search for that operating condition region.

[0045] The optimization algorithm is a surrogate optimization algorithm based on radial basis functions. The surrogate optimization algorithm first generates initial evaluation points in the solution space using a quasi-random sequence, then calls the non-design condition SOFC cogeneration system to perform a real evaluation on each initial evaluation point, obtaining the corresponding objective function value. Subsequently, based on the evaluated sample points, it uses radial basis functions to fit the response surface of the objective function with respect to the time series decision vector, and dynamically updates the response surface. Then, combining the predicted objective function values ​​of the response surface on candidate points and the distance information between the candidate points and the evaluated sample points, it selects new points to be evaluated from candidate points with better prediction performance and higher spatial dispersion, performs a real evaluation, and adds them to the sample set to update the response surface. The above steps are iteratively executed until a preset stopping condition is met, outputting the optimal time series decision vector.

[0046] S5. The central controller acquires the target fuel utilization rate and target current density, converts them into execution instructions for physical devices, and sends them to the relevant hardware actuators of the SOFC system to achieve closed-loop operation control and strategy correction throughout the entire life cycle.

[0047] After optimizing and obtaining the target fuel utilization rate and target current density for each scheduling interval, the central controller executes the scheduling sequence generated by the scheduling control and outputs control commands within the corresponding time interval. The central controller can be any one of an industrial controller, an edge computing unit, a host computer control platform, a DCS, a PLC, or an embedded controller.

[0048] Specifically, the central controller converts the target fuel utilization rate into one or more of the following: fuel flow setpoint, air flow setpoint, anode exhaust gas recirculation valve opening, humidifier operating status, or fuel supply pressure setpoint; it converts the target current density into a load current setpoint, power converter power command, or grid-connected inverter output setpoint; and then sends these commands to one or more of the following: mass flow controller, blower driver, regulating valve, electric heater, burner actuator, DC / AC converter, inverter, or electronic load. In this way, abstract optimization variables are mapped into executable physical control actions.

[0049] Preferably, the central controller collects one or more of the following feedback quantities in real time: stack voltage, current, temperature, fuel flow rate, air flow rate, stack inlet / outlet pressure, heat exchanger hot and cold side temperatures, blower power, fuel consumption, and system net output power. The central controller calculates the current actual fuel utilization rate, actual current density, actual efficiency, and real-time health status based on the feedback quantities and compares them with target values. When the deviation exceeds a preset operating detection threshold, the operating condition is determined to be infeasible, and the deviation information is fed back to step S4 to trigger re-optimization, thus preventing the optimization algorithm from continuing to search the operating condition region. In this example, the preset operating detection thresholds include voltage deviation exceeding 5%; voltage drop deviation exceeding 10% of the nominal voltage drop; inlet temperature deviation exceeding 15°C; and blower load rate exceeding 90% of the rated load rate, with a penalty value of [missing value]. .

[0050] Example 2 The difference between this embodiment and Embodiment 1 is that this embodiment provides a simulation experiment of an operation optimization method for SOFC cogeneration system based on stack decay and BOP non-design conditions; like Figure 4As shown, in this embodiment, a combination of single-objective optimization and multi-index cross-evaluation is used to optimize and evaluate the system operation strategy. Specifically, three independent optimization models are constructed with the objectives of minimizing the levelized cost of electricity (LCOE), maximizing the average power generation efficiency over the entire lifecycle, and maximizing the cumulative power generation over the lifecycle. These models are then solved using the non-design condition SOFC cogeneration system described in step three to obtain the optimal operation scheduling strategy corresponding to each objective. Subsequently, within a unified lifecycle simulation and techno-economic analysis framework, the three indicators of each optimal strategy are compared horizontally to comprehensively evaluate the techno-economic performance under different optimization objectives.

[0051] To establish a baseline, a full-condition screening was first conducted under fixed operating conditions. Fuel utilization was then assessed. With current density J As fixed control variables, typical combinations were selected within the feasible region for full life-cycle simulation, and the levelized cost of electricity (LCOE), average generation efficiency over the entire life-cycle, and cumulative power generation for each combination were calculated. Table 1 shows the screening results under fixed operating conditions: Based on the above screening results, a compromise operating condition that balances electrical efficiency, power generation output, and levelized cost of electricity (LCOE) is selected as the baseline according to actual needs. In this embodiment, the following is selected: The baseline is the operating condition with J=3000A / m2. Under this baseline operating condition, the total lifetime electrical efficiency is at a medium level, the cumulative power generation is relatively high, and the levelized cost of electricity is relatively low.

[0052] Furthermore, a surrogate optimization algorithm based on radial basis functions is used to dynamically optimize the lifecycle operation strategy with the objective function of minimizing the levelized cost of electricity (LCOE). The time-of-use adjustment interval is set to 3000 hours, the maximum number of evaluations is 2500, and the optimized operation plan minimizes LCOE and LOCE as follows: Figure 5 As shown, the boundary conditions for the control variables are 2000A / m²≤J≤5000A / m². During the optimization process, the surrogate optimization algorithm generates initial sample points through a quasi-random sequence, calls the non-design condition SOFC cogeneration system for real evaluation, and dynamically updates the response surface based on the radial basis function, gradually converging to the optimal time series decision vector.

[0053] like Figure 6 As shown, after optimization, the dynamic optimization results are compared with the baseline operating condition and the optimal fixed condition operating condition, respectively. The optimal fixed condition operating condition refers to the fixed condition corresponding to the minimum levelized cost of electricity (LCOE) obtained under fixed operating conditions. Combined with J. Comparative results show that the dynamic scheduling strategy, considering stack voltage decay and the off-design operating characteristics of auxiliary components, has a significantly lower levelized cost of electricity (LCOE) than the baseline condition and any fixed operating point. Furthermore, it can adaptively adjust operating parameters according to the stack degradation state throughout its entire lifespan, effectively delaying performance degradation and improving system economy. These results demonstrate that, given a clear understanding of the stack voltage decay pattern and the off-design behavior of auxiliary components, the time-segmented dynamic scheduling strategy outperforms any fixed operating behavior, verifying the effectiveness of the optimization method described in this invention.

[0054] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. An optimization method for SOFC cogeneration operation based on stack decay and BOP (Balance of Plant) off-design conditions, characterized in that, include: S1. Establish an off-design operating condition characteristic model of the auxiliary component system to characterize the efficiency, pressure drop and heat transfer dynamic characteristics of the auxiliary components under off-design conditions. S2. Construct a voltage decay model of the fuel cell stack that couples temperature, fuel utilization rate and current density, and obtain the voltage decay rate of the fuel cell stack under different operating conditions. S3. Couple the stack voltage decay model with the non-design operating condition characteristic model to build a non-design operating condition SOFC cogeneration system, and determine the system optimization variables, constraints and objective function; S4. Based on the SOFC cogeneration system under non-design conditions, an optimization algorithm is adopted to dynamically optimize the target fuel utilization rate and target current density in each scheduling interval with a preset time-sharing adjustment interval as the period. S5. Based on the optimized target fuel utilization rate and target current density, convert them into execution instructions for physical equipment and send them to the relevant hardware actuators of the SOFC cogeneration system.

2. The SOFC cogeneration operation optimization method based on stack decay and BOP off-design conditions as described in claim 1, characterized in that, The auxiliary components include at least a plate heat exchanger, a blower, a combustion chamber, and system piping; the establishment of the non-design operating condition characteristic model of the auxiliary component system includes, for each auxiliary component, based on the ratio of the actual mass flow rate under non-design conditions to the nominal mass flow rate under design conditions, correcting the corresponding design operating condition characteristic parameters to obtain the actual efficiency, pressure drop, or heat transfer dynamic characteristics under non-design conditions.

3. The SOFC cogeneration operation optimization method based on stack decay and BOP off-design conditions as described in claim 2, characterized in that, The correction of the corresponding design condition characteristic parameters includes: For plate heat exchangers, based on the ratio of the actual mass flow rate of the cold and hot sides under non-design conditions to the nominal mass flow rate under design conditions, the preset convective heat transfer coefficient correction function is called to correct the convective heat transfer coefficient of the cold and hot sides, so as to obtain the total heat transfer coefficient and flow pressure drop under non-design conditions. For blowers, the load factor is determined based on the ratio of actual mass flow rate to rated mass flow rate. The total electrical efficiency under design conditions is then corrected based on the load factor to obtain the actual efficiency and shaft power under non-design conditions. For the combustion chamber, the pressure drop under the design conditions is corrected based on the ratio of the actual mass flow rate of the exhaust side under non-design conditions to the nominal mass flow rate under the design conditions, so as to obtain the actual pressure drop under non-design conditions. For the system pipeline, based on the ratio of the actual mass flow rate under non-design conditions to the nominal mass flow rate under design conditions, the pressure drop under design conditions is corrected to obtain the actual pressure drop under non-design conditions. The pressure drop of the pipeline system under non-design conditions satisfies the following: ； in, The nominal pipeline pressure drop under design conditions. This represents the actual mass flow rate of the pipeline. This refers to the mass flow rate under the rated operating conditions of the pipeline.

4. The SOFC cogeneration operation optimization method based on stack decay and BOP off-design conditions as described in claim 1, characterized in that, Step S2 specifically includes: S21. Determine the input and output variables of the stack voltage decay model. The input variables include at least fuel utilization rate, current density and stack temperature. The output variables include at least one of voltage decay rate, performance loss rate, lifetime consumption factor, health status index and remaining usable lifetime. S22. Establish the mapping relationship between voltage decay rate and fuel utilization rate and current density. S23. Construct a fuel cell stack voltage decay model based on at least one of the following methods: experimental calibration data, physical degradation mechanism extraction, or operational data training. The fuel cell stack voltage decay model is an empirical model, a semi-empirical model, a data-driven model, or a fusion model formed by at least two combinations.

5. The SOFC cogeneration operation optimization method based on stack decay and BOP off-design conditions as described in claim 4, characterized in that, The stack voltage decay model updates the initial stack voltage for each scheduling interval according to the following sub-steps: At the start of the i-th scheduling interval, read the current cumulative runtime and obtain the candidate fuel utilization rate and candidate current density for that scheduling interval; Substitute the candidate fuel utilization rate and candidate current density into the stack voltage decay model to calculate the degradation rate of the scheduling interval, and calculate the voltage decay amount of the scheduling interval based on the degradation rate and the preset time step. Based on the voltage decay, update the [number] in a discrete time-varying form. i The starting stack voltage of +1 scheduling intervals is compared with a preset initial voltage threshold. If the current stack voltage is less than the preset threshold, the stack life is determined to have ended. i The expression for updating the initial heap voltage for +1 scheduling intervals is: ； in, For the first i +1 scheduling interval's starting stack voltage, For the first i The stack voltage of each dispatch interval The degradation rate characterizes the proportion of voltage decay of the fuel cell stack per unit time. For the first i Fuel utilization rate of each dispatch interval For the fuel cell stack temperature, For time step.

6. The SOFC cogeneration operation optimization method based on stack decay and BOP off-design conditions as described in claim 1, characterized in that, Step S3 specifically includes: S31. Couple the stack voltage decay model with the auxiliary component non-design operating condition characteristic model to build a non-design operating condition SOFC cogeneration system with multiple continuous scheduling intervals within the life cycle as the time skeleton. S32. Within each dispatch interval, based on the stack voltage model under the current degradation state and the non-design operating condition characteristic model of auxiliary components, calculate the net power generation, net power generation efficiency, fuel consumption, parasitic work consumption, heat balance state and economic indicators of the dispatch interval. S33. The final state of the current scheduling interval is passed as the initial state of the next scheduling interval to realize the interval-by-interval recursive simulation of the full life cycle operation state.

7. The SOFC cogeneration operation optimization method based on stack decay and BOP off-design conditions as described in claim 6, characterized in that, The determination of system optimization variables, constraints, and objective function includes: The optimization variables include at least the target fuel utilization rate and the target current density within each scheduling interval; The constraints include at least the upper and lower limits of fuel utilization, the upper and lower limits of current density, and the stack temperature threshold within each scheduling interval. The objective function is selected from one of minimizing the levelized cost of electricity (LCOE), maximizing the average power generation efficiency over the entire life cycle, and maximizing the cumulative power generation over the life cycle.

8. The SOFC cogeneration operation optimization method based on stack decay and BOP off-design conditions as described in claim 1, characterized in that, The dynamic optimization of target fuel utilization and target current density within each scheduling interval includes constructing a discrete time series containing n scheduling intervals based on the total system lifespan and a preset time-sharing adjustment interval, and combining the target fuel utilization and current density of each interval to generate a time series decision vector. In the process of solving the time series decision vector, if the current candidate vector causes the output electrical efficiency of the SOFC cogeneration system under non-design conditions to be negative, or the system operating parameters exceed the preset constraint boundary, then a preset penalty value is applied to the objective function to eliminate the infeasible operating point. The time series decision vector satisfies: ； in, The target fuel utilization rate for the nth scheduling interval is... Let n be the target current density of the nth scheduling interval, where n is the total number of scheduling intervals determined based on the total operating life of the system and the preset time-sharing adjustment interval.

9. The SOFC cogeneration operation optimization method based on stack decay and BOP off-design conditions as described in claim 8, characterized in that, The optimization algorithm is a surrogate optimization algorithm based on radial basis functions, and the surrogate optimization algorithm includes: S41. Use quasi-random sequences to generate initial evaluation points in the solution space, call the non-design condition SOFC cogeneration system to perform real evaluation on each initial evaluation point, and obtain the corresponding objective function value. S42. Based on the evaluated sample points, use radial basis functions to fit the response surface of the objective function with respect to the time series decision vector, and dynamically update the response surface; S43. Combining the predicted objective function value of the response surface for candidate points and the distance information between candidate points and evaluated sample points, select new points to be evaluated for real evaluation and add them to the sample set to update the response surface. Iteratively execute S41 to S43 until the preset stopping condition is met, and output the optimal time series decision vector.

10. The SOFC cogeneration operation optimization method based on stack decay and BOP off-design conditions as described in claim 1, characterized in that, Step S5 specifically includes: S51, The central controller receives the optimized target fuel utilization rate and target current density; S52. Calculate the target fuel flow rate based on the target fuel utilization rate, and generate valve opening electrical signal commands for the fuel supply flow regulating valve, exhaust gas return regulating valve, steam / fuel ratio regulating valve, or fuel pressure regulating valve. S53. Calculate the target air flow rate based on the cathode oxygen supply demand and the excess air coefficient, and generate the speed control command for the variable frequency blower. S54. Calculate the target stack current based on the target current density, and generate current or power control commands for the external load regulation unit, DC / AC converter, inverter, or grid connection interface. S55 sends the valve opening electrical signal command, speed control command, and current or power control command to the corresponding hardware actuator of the SOFC combined heat and power system to realize closed-loop operation control and operation strategy correction throughout the entire life cycle.

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