A Health Management Method for Multi-Stack Fuel Cell Power Generation Systems Based on Hierarchical Collaborative Optimization

Abstract

This invention proposes a health management method for multi-stack fuel cell power generation systems based on hierarchical collaborative optimization, belonging to the field of fuel cell technology. The method includes the following steps: Based on the operating parameters of the multi-stack fuel cell power generation system, a degradation model for the fuel cell stack and a capacity decay model for the battery energy storage system are established to obtain the lifespan cost of the fuel cell stack and the battery energy storage system; at a first time scale, based on the hydrogen consumption cost, the lifespan cost of the fuel cell stack, and the lifespan cost of the battery energy storage system, a rolling optimization problem is modeled to obtain a power reference trajectory and a state-of-charge reference trajectory for the battery energy storage system; at a second time scale, a Tube-model predictive control is used to construct an invariant tubular set and tighten the constraints, and an actual control law is generated based on the load prediction error for real-time rolling optimization to correct the power reference trajectory and the state-of-charge reference trajectory.

Description

Technical Field

[0001] This invention relates to the field of fuel cell technology, and in particular to a health management method for multi-stack fuel cell power generation systems based on hierarchical collaborative optimization. Background Technology

[0002] Driven by global carbon neutrality and sustainable development strategies, hydrogen energy has garnered significant attention due to its clean, efficient, and renewable characteristics. Hydrogen fuel cells, as one of the core methods of hydrogen energy utilization, are widely used in the transportation industry and are extending into fields such as the power system. To meet the grid's demands for higher capacity and long-term operation, multi-fuel cell stack architectures have become the mainstream solution for stationary power generation and grid support applications. However, in actual long-term operation, the performance degradation rates of different fuel cell stacks often differ, leading to a shortened overall lifespan of multi-fuel cell power generation systems and increased operation and maintenance costs, thus hindering their large-scale deployment in grid support scenarios.

[0003] Regarding energy management of fuel cell systems, existing technologies still have some shortcomings in practical applications. On the one hand, existing technologies are mostly concentrated in the transportation sector, focusing on dealing with dynamic operating conditions and short-term power fluctuations, which is difficult to meet the application requirements of long-term continuous operation and relatively stable load characteristics in grid-supported scenarios. On the other hand, although some existing technologies consider the stack degradation characteristics, there is a lack of research on long-term health management for the consistency of lifespan degradation among stacks, which limits the application effectiveness and life cycle value of multi-stack fuel cell power generation systems in grid-supported scenarios.

[0004] Therefore, this application provides a health management method for multi-stack fuel cell power generation systems based on hierarchical collaborative optimization. By analyzing the operating parameters of the fuel cell stack power generation system, constructing a degradation model, and obtaining the power reference trajectory and state of charge reference trajectory of the fuel cell stack, it is necessary to improve the overall system performance, operational stability and lifespan through rolling optimization at different levels and correction of the power reference trajectory and state of charge reference trajectory. Summary of the Invention

[0005] In view of this, the present invention proposes a hierarchical collaborative optimization-based health management method for multi-stack fuel cell power generation systems. This method involves configuring a two-level coupling: an intraday rolling optimization layer responsible for long-term overall optimization and a real-time rolling optimization layer responsible for disturbance rejection correction. The synergistic effect of the two layers enables multi-stack systems to meet grid demands while also taking into account health and economy, thereby improving the overall system performance and operational stability.

[0006] This invention provides a health management method for multi-stack fuel cell power generation systems based on hierarchical collaborative optimization, comprising the following steps: S1: Based on the operating parameters of the multi-stack fuel cell power generation system, establish a degradation model for the fuel cell stack and a capacity decay model for the battery energy storage system, and obtain the life cost of the fuel cell stack and the life cost of the battery energy storage system. S2: On the first time scale, based on the hydrogen consumption cost, the life cost of the fuel cell stack, and the life cost of the battery energy storage system, the intraday rolling optimization problem is modeled, and intraday rolling optimization is performed under the set constraints to obtain the power reference trajectory of the fuel cell stack and the state of charge reference trajectory of the battery energy storage system. S3: On the second time scale, an invariant tubular set is constructed using Tube-model predictive control and constraint tightening is applied. Based on the load prediction error, an actual control law is generated for real-time rolling optimization, and robust corrections are made to the power reference trajectory and the state of charge reference trajectory.

[0007] Based on the above technical solutions, preferably, the establishment of the fuel cell stack degradation model in step S1 involves linearly degrading the performance of the fuel cell stack FCS under given operating conditions over time. The actual operating state is divided into several typical operating conditions. Each typical operating condition is assigned a performance degradation rate and a corresponding number of cycles or operating time, and these are accumulated. The accumulated result is multiplied by an acceleration factor and used as the degradation index of the fuel cell stack FCS. d FC Degradation index of fuel cell stack FCS d FC As the denominator, the performance degradation threshold of the fuel cell stack (FCS) from its initial state to the end of its lifespan. As molecules, the lifespan model of the fuel cell stack (FCS) is obtained. T FC Lifetime model of fuel cell stack (FCS) T FC The reciprocal of the product, multiplied by the fuel cell stack price coefficient c FC To obtain the lifespan cost of the fuel cell stack .

[0008] Preferably, the capacity decay model of the battery energy storage system described in step S1 is based on the capacity of cyclic charge and discharge. A h Using the power-law relationship and the Arrhenius equation, the capacity loss of battery energy storage systems is constructed. The relationship is obtained by discretizing the capacity loss relationship of the battery energy storage system to obtain the capacity loss relationship at a certain charge / discharge stage. Capacity loss at each stage Accumulation is performed to achieve dynamic tracking of the capacity decay of the battery energy storage system; a unit capacity price coefficient for the battery energy storage system is introduced. The capacity loss is converted into the lifespan cost of the battery energy storage system. .

[0009] Further preferred, step S2 specifically includes: Modeling the intraday rolling optimization problem, making the overall objective function of the intraday rolling optimization layer... F RO The value is minimized, where the total objective function of the intraday rolling optimization layer is the smallest. F RO Hydrogen consumption cost, including the output power of the fuel cell stack at different times and for different fuels. Lifetime cost of fuel cell stacks Lifetime cost of battery energy storage systems and the cost of health consistency across multiple fuel cell stacks. Under the set constraints, rolling optimization is performed, and the solution is solved periodically in the rolling time domain. Each time, a new round of power output plan for fuel cell stack and battery energy storage system is generated using the updated load forecast and system state, so as to obtain the power reference trajectory of fuel cell stack and the state of charge reference trajectory of battery energy storage system. The constraints are as follows: 1) At each time step, the power of each fuel cell stack is multiplied by the efficiency of the DC / DC converter and then summed. The sum is then added to the charging and discharging power of the battery storage system, which equals the load power demand; 2) The... i The output power of a fuel cell stack is between its lower and upper limits; 3) at each moment, the state of charge of the battery energy storage system is between its lower and upper limits.

[0010] Furthermore, the hydrogen consumption cost is determined by the output power of the fuel cell stack. It is based on the sampling interval The corresponding hydrogen equivalent consumption multiplied by the unit price of hydrogen. The obtained hydrogen equivalent consumption includes the direct hydrogen consumption of the fuel cell stack. Equivalent hydrogen consumption of battery energy storage systems ; Multi-stack fuel cell health consistency cost It is through the coefficient of variation With weighting coefficients The coefficient of variation obtained after multiplication It is achieved by predicting the standard deviation of the remaining lifetime of the fuel cell stack. Divide by the average predicted remaining life of the fuel cell stack Obtained.

[0011] Furthermore, step S3 specifically includes: S31: Construct a discrete-time state-space model, separating the actual system equations containing disturbances into a nominal system and an error system; the nominal system contains nominal variables, and the state feedback gain matrix K is designed offline to keep the nominal system stable; calculate the minimum positive invariant set of the error system, and apply constraints to tighten the nominal system; acquire real-time sampling times. k s The corresponding nominal state and external load, the nominal state is derived from the nominal system; S32: Based on the power reference trajectory of the fuel cell stack and the state-of-charge reference trajectory of the battery energy storage system obtained in step S2, extract... N p The reference trajectory for each real-time sampling moment corresponds to a step size, and the reference trajectory includes a reference state sequence and a reference control sequence. N p The step size corresponding to each real-time sampling moment constitutes the prediction domain. S33: At each sampling moment of real-time rolling optimization, establish a nominal optimization problem. The decision variable of the optimization problem is the nominal trajectory, which includes the nominal state sequence and the nominal control sequence in the prediction domain. Under the given tightening constraints, minimize the deviation between the nominal trajectory and the reference trajectory to obtain the optimal nominal control input sequence. S34: After obtaining the optimal nominal control input sequence, select the first term of the optimal nominal control input sequence, combine it with the state feedback gain matrix K, and obtain the actual control law, thus obtaining the actual control input applied to the actual controlled object; S35: Update the real-time sampling time, return to step S31 to reacquire the nominal state and external load, and repeat steps S32-S34 until all real-time sampling times in the prediction domain have been traversed.

[0012] Preferably, step S31 specifically includes, The discrete-time state-space model is used to characterize the system dynamics, and the state vector is defined to include the real-time sampling time. k s The corresponding state of charge of the battery energy storage system , No. i A fuel cell stack at real-time sampling time k s and k s -1 power , ; The control input vector includes the battery energy storage system at real-time sampling time. k s The charging power and battery energy storage system at real-time sampling time k s The discharge power, the firsti A fuel cell stack at real-time sampling time k s The power change; let the predicted load for the first time scale be... Plus load forecasting error As an external load, the load forecasting error is processed by decomposing the load forecasting error into positive disturbance components. and the negative component of the disturbance By introducing binary variables and constants, mutual exclusion constraints are constructed to limit the effect of disturbances in a single direction, either positive or negative, at any given time. At the second timescale, construct the fuel cell stack at the real-time sampling time. k s The first-order integral model of power and the update formula of the state of charge of the battery energy storage system; The formula for updating the state of charge of the battery energy storage system is compared with the formula for updating the state of charge of the fuel cell stack at the real-time sampling time. k s By combining the first-order integral models of power, the actual system equations for a multi-fuel cell power generation system with disturbances are obtained. In the Tube-model predictive control, the actual system equations of a multi-stack fuel cell power generation system with disturbances are divided into a nominal system and an error system. The influence of the disturbance term is ignored in the nominal system. Computational error system minimum positive invariant set The nominal state is subject to tightening constraints.

[0013] Further preferred, step S32 specifically includes, A reference state sequence and a reference control sequence are constructed within the prediction domain. The reference state sequence includes several reference state vectors, and the reference control sequence includes several reference control vectors. The reference state vectors include the state-of-charge reference trajectory of the battery energy storage system in the intraday rolling optimization layer and the nominal reference output power of each fuel cell stack in the intraday rolling optimization layer at the prediction time. The reference control vectors include the reference charging power and reference discharging power of the battery energy storage system at the prediction time, as well as the reference power change of each fuel cell stack at the prediction time. The reference power change is obtained based on the difference between the nominal reference output power of the current fuel cell stack at adjacent prediction times.

[0014] Furthermore, step S33 specifically includes: Define the nominal state sequence and nominal control sequence within the prediction domain. The nominal state sequence includes several nominal state variables, and the nominal control sequence includes several nominal control variables. The nominal state variables include the values ​​from the real-time sampling time to the prediction time. k s + jThe state of charge of the battery energy storage system, from the real-time sampling time k s Predicted time k s + j -1 is the output power of each fuel cell stack; nominal control variables include those from the real-time sampling time. k s Predicted time k s + j The charging and discharging power of the battery energy storage system, and the data from real-time sampling time. k s Predicted time k s + j The power variation of each fuel cell stack; The nominal optimization problem is expressed as a mixed integer quadratic programming problem by introducing the decomposition of the charging and discharging power of the battery energy storage system and binary variables. The nominal optimization problem is to find the nominal control input sequence that minimizes the objective function in the prediction domain.

[0015] In a further preferred embodiment, step S34 specifically includes, After obtaining the nominal control input sequence that minimizes the objective function, the real-time sampling time will be... k s state vector Within the prediction domain k s The difference between the nominal state vectors at time 1 and 2 is multiplied by the feedback gain matrix K to form the feedback correction term, which is then added to the value in the prediction domain. k s The nominal control vector at time t is used as the actual control input.

[0016] The health management method for multi-stack fuel cell power generation systems based on hierarchical collaborative optimization provided by this invention has the following advantages compared to existing technologies: 1. By configuring a two-tiered coupled architecture of intraday rolling optimization layer and real-time rolling optimization layer, long-term economic efficiency and health planning are taken into account, as well as short-term disturbance suppression. The intraday rolling optimization layer takes hydrogen consumption cost, equipment life cost and multi-reactor health consistency cost as comprehensive optimization objectives. While meeting power requirements, it effectively balances operating economy, equipment durability and load balance of each reactor. The real-time rolling optimization layer constructs an invariant tubular set and tightens constraints through the Tube-MPC method. Combined with the feedback correction mechanism, it can effectively suppress uncertain disturbances such as load forecasting errors and ensure the robustness of the actual operating trajectory of the system.

[0017] 2. Degradation models based on typical operating conditions and capacity decay models based on electrochemical mechanisms are established for fuel cell stacks and battery energy storage systems, respectively. These models can dynamically track the degradation status of equipment, providing accurate basis for life cost quantification and health management. The health status consistency cost is introduced into the optimization model to promote the aging rate among fuel cell stacks to tend to be balanced, avoid premature degradation of individual stacks, and thus extend the overall service life of the multi-stack system.

[0018] 3. Based on a comprehensive consideration of various cost factors such as hydrogen consumption, consistency of health status among multiple stacks, and overall system health degradation, the system achieves optimal scheduling of total system cost and can better cope with load disturbances and maintain stable battery SOC, demonstrating advantages in terms of economy, equipment degradation delay, and stability. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of the health management method for multi-stack fuel cell power generation systems based on hierarchical collaborative optimization according to the present invention; Figure 2 This is a system architecture diagram of the health management method for multi-stack fuel cell power generation systems based on hierarchical collaborative optimization according to the present invention; Figure 3 This is a hierarchical collaborative optimization framework diagram of the health management method for multi-stack fuel cell power generation systems based on hierarchical collaborative optimization of the present invention; Figure 4 This is a flowchart of the intraday rolling optimization method for the health management method of multi-stack fuel cell power generation systems based on hierarchical collaborative optimization, as described in this invention. Figure 5 This is a flowchart of the real-time rolling optimization method for the health management method of multi-stack fuel cell power generation systems based on hierarchical collaborative optimization, as described in this invention. Detailed Implementation

[0021] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0022] Regarding energy management of fuel cell systems, existing technologies still have some shortcomings in practical applications. On the one hand, existing technologies are mostly concentrated in the transportation sector, focusing on dealing with dynamic operating conditions and short-term power fluctuations, which is difficult to meet the application requirements of long-term continuous operation and relatively stable load characteristics in grid-supported scenarios. On the other hand, although some existing technologies consider the stack degradation characteristics, there is a lack of research on long-term health management for the consistency of lifespan degradation among stacks, which limits the application effectiveness and life cycle value of multi-stack fuel cell power generation systems in grid-supported scenarios.

[0023] In view of this, such as Figure 1 and Figure 2 As shown, this invention provides a health management method for multi-stack fuel cell power generation systems based on hierarchical collaborative optimization, comprising the following steps: S1: Based on the operating parameters of the multi-stack fuel cell power generation system, establish a degradation model for the fuel cell stack and a capacity decay model for the battery energy storage system, and obtain the life cost of the fuel cell stack and the life cost of the battery energy storage system.

[0024] The degradation model of the fuel cell stack described in step S1 involves linearly degrading the performance of the fuel cell stack (FCS) under given operating conditions over time. This is achieved by breaking down the actual operating state into several typical operating conditions, including load variation cycles, start-stop cycles, idling conditions, and high-power load conditions, and assigning a performance degradation rate to each of these typical operating conditions. c 1. c 2. c 3. c 4. After summing the number of cycles or running time corresponding to the performance degradation rate, multiply the sum by the acceleration factor. K d Later used as a degradation indicator for fuel cell stacks (FCS) d FC , , n 1 and n 2 represents the number of cycles for the load change cycle and the start / stop cycle, respectively. t 1. t 2 represents the operating time under idling and high-power load conditions, respectively; the degradation index of the fuel cell stack FCS is used. d FC As the denominator, the performance degradation threshold of the fuel cell stack (FCS) from its initial state to the end of its lifespan. As molecules, the lifespan model of the fuel cell stack (FCS) is obtained. T FC , Lifetime model of fuel cell stack (FCS) T FC The reciprocal of the product, multiplied by the fuel cell stack price coefficient cFC To obtain the lifespan cost of the fuel cell stack , .

[0025] like Figure 2 As shown, the multi-fuel cell power generation system provided in this embodiment includes an Energy Management Controller (EMC), a hydrogen tank, a fuel cell stack (FCS), a DC / DC converter, a Battery Energy Storage System (BESS), and a DC / AC converter. The system receives the total power demand, the State of Health (SOH) of each fuel cell stack (FCS), and the State of Charge (SOC) of the BESS through the EMC, and issues power allocation commands to each FCS. Each FCS is connected to the DC bus via an independent DC / DC converter. The BESS provides energy buffering and rapid dynamic response, and is connected to the power grid via DC / AC, thereby achieving multi-source coordinated power supply.

[0026] In this embodiment, a degradation model of the fuel cell stack FCS is established based on the operating parameters of the multi-stack fuel cell power generation system, which can be used to quantify the lifetime consumption of the fuel cell stack FCS.

[0027] In some embodiments of this specification, the battery energy storage system BESS uses a lithium iron phosphate (LiFePO4) battery solution, and its capacity loss... This significantly impacts the equivalent lifetime cost. Due to time... t ,temperature T Key operating conditions such as depth of discharge and rate of discharge affect capacity loss. These factors have a significant impact, therefore a capacity loss relationship is constructed based on the above factors. Specifically, the capacity decay model of the battery energy storage system described in step S1 is based on the capacity of cyclic charge and discharge. A h Using the power-law relationship and the Arrhenius equation, the capacity loss of the battery energy storage system BESS is constructed. Relationship, ,in B As the pre-factor, E a For activation energy, R The gas constant is... T Absolute temperature A h For the capacity of charge and discharge cycles,z The power-law factor is used to discretize the capacity loss relationship of the battery energy storage system, thus obtaining the capacity loss relationship at a certain charge / discharge stage. , , For the newly added charge / discharge capacity in the current stage, the capacity loss in each stage. Accumulation is performed to achieve dynamic tracking of the capacity decay of the battery energy storage system; a unit capacity price coefficient for the battery energy storage system is introduced. The capacity loss is converted into the lifespan cost of the battery energy storage system. , , This is the capacity failure threshold.

[0028] Capacity loss of battery energy storage system (BESS) The relationship describes the long-term capacity degradation trend of a battery energy storage system (BESS) under a given temperature trajectory and charge / discharge behavior. Considering that capacity loss in actual operation is accumulated from multiple charge / discharge processes, the equation is discretized to obtain the incremental capacity loss at a certain charge / discharge stage. In this embodiment, a degradation model of the BESS is established based on the operating parameters of a multi-stack fuel cell power generation system, which can be used to quantify the lifetime consumption of the BESS.

[0029] S2: On the first time scale, based on the hydrogen consumption cost, the life cost of the fuel cell stack, and the life cost of the battery energy storage system, the intraday rolling optimization problem is modeled, and intraday rolling optimization is performed under the set constraints to obtain the power reference trajectory of the fuel cell stack and the state of charge reference trajectory of the battery energy storage system.

[0030] like Figure 3 As shown, the hierarchical collaborative optimization framework provided in this embodiment of the invention is based on time-scale separation, dividing power scheduling into two levels: intraday rolling optimization and real-time rolling optimization. In the intraday rolling optimization stage at the first time scale, the system generates an output plan for the next few hours based on the total power demand, the SOH of each fuel cell stack, and the SOC of the battery energy storage system (BESS). This stage optimizes the optimal reference state trajectory of each fuel cell stack's FCS with hydrogen consumption, fuel cell stack FCS health consistency, and minimizing total system degradation as optimization objectives. Intraday planning ensures the health and friendliness of the overall operating direction while providing reference instructions for real-time control.

[0031] The specific content is as follows: like Figure 4 As shown, the modeling content of the intraday rolling optimization problem is: to make the intraday rolling optimization layer, the overall objective function is... F RO The value is minimized, where the intraday rolling optimization layer, also known as the upper layer's overall objective function, is located.F RO Hydrogen consumption cost, including the output power of the fuel cell stack at different times and for different fuels. Lifetime cost of fuel cell stacks Lifetime cost of battery energy storage systems and the cost of health consistency across multiple fuel cell stacks. Under constraints, rolling optimization is performed, and the solution is solved periodically in the rolling time domain. Each time, a new round of power output plan for fuel cell stacks and battery energy storage system is generated using updated load forecasts and system states. The power reference trajectory of fuel cell stacks and the state of charge reference trajectory of battery energy storage system are obtained. This not only takes into account hydrogen consumption and lifetime cost, but also effectively balances the load distribution of each fuel cell stack through health state consistency constraints. , , , , , , ; in, F RO The overall objective function for the intraday rolling optimization layer is... During the time period k r + j The cost of hydrogen consumption is determined by the output power of each fuel cell stack. It is the lifespan cost of the fuel cell stack. For the life-cycle cost of battery energy storage systems, For the cost of health consistency across multiple fuel cell stacks, j =1,2,..., N roll Indicates the time step at different sampling times, with subscripts. k r This indicates the start time corresponding to the rolling optimization. Indicates the first i A fuel cell stack at time Power at that time i =1,2,…, N FCS Indicates the sequence number of the fuel cell stack. For the efficiency of the DC / DC converter connected to the fuel cell stack, For battery energy storage systems at all times The synthesis of charging and discharging power, For a moment The load power demand, The lower and upper limits of the charging and discharging power of the battery energy storage system. For the first i The lower and upper limits of the output power of a fuel cell stack. These are the lower and upper limits of the state of charge (SOC) of a battery energy storage system, respectively. State of charge initialization for battery energy storage system , and Adjacent time points , The state of charge of the battery energy storage system; The rated energy capacity of the battery energy storage system. For battery energy storage systems at all times The charging and discharging efficiency is related to the charging and discharging process. , and These refer to the charging efficiency and discharging efficiency of the battery energy storage system, respectively. The sampling time interval; The constraints are defined in the formula following the overall objective function: 1) At each time step, the power of each fuel cell stack is multiplied by the efficiency of the DC / DC converter and then summed. The sum is then added to the charging and discharging power of the battery storage system, which equals the load power demand; 2) The... i The output power of a fuel cell stack is between its lower and upper limits; 3) at each moment, the state of charge of the battery energy storage system is between its lower and upper limits.

[0032] Wherein, the overall objective function F RO Hydrogen consumption cost determined by fuel cell stack output power It is based on the sampling interval The corresponding hydrogen equivalent consumption multiplied by the unit price of hydrogen. The obtained hydrogen equivalent consumption includes the direct hydrogen consumption of the fuel cell stack. Equivalent hydrogen consumption of battery energy storage systems , , The lower heating value of hydrogen. For equivalent electrical efficiency, Indicates the first i A fuel cell stack at time Power at that time; , For the battery energy storage system at time The charging power and discharging power.

[0033] The charging and discharging process of a battery energy storage system does not directly consume hydrogen, but it uses equivalent logic to link the energy conversion between electrical energy and hydrogen. The charging process of the battery energy storage system is regarded as "consuming hydrogen to store electrical energy", and the discharging process is regarded as "recovering the electrical energy corresponding to hydrogen".

[0034] Multi-stack fuel cell health consistency cost It is through the coefficient of variation With weighting coefficients The coefficient of variation obtained after multiplication It is achieved by predicting the standard deviation of the remaining lifetime of the fuel cell stack. Divide by the average predicted remaining life of the fuel cell stack What was obtained , , and The first i The predicted remaining lifetime of individual fuel cell stacks and the average predicted lifetime of all fuel cell stacks. , , and The first i The remaining health and decommissioning threshold health of each fuel cell stack. The decay rate per unit time is the first... i The total decay of a fuel cell stack within the current time window is divided by the total duration of the current time window.

[0035] S3: On the second time scale, an invariant tubular set is constructed using Tube-model predictive control and constraint tightening is applied. Based on the load prediction error, an actual control law is generated for real-time rolling optimization, and robust corrections are made to the power reference trajectory and the state of charge reference trajectory.

[0036] The specific content of step S3 is as follows: within the time range defined by the first time scale, real-time rolling optimization is performed according to the second time scale. The first time scale is the sampling time step of intraday rolling optimization, and the second time scale is the sampling time step of real-time rolling optimization. By selecting an appropriate prediction domain length for the second time scale, it is made to exactly cover the duration of the first time scale, thereby forming a time scale matching between the upper and lower layers.

[0037] Specifically, it includes the following: S31: Construct a discrete-time state-space model, separating the actual system equations containing disturbances into a nominal system and an error system; the nominal system contains nominal variables, and the state feedback gain matrix K is designed offline to keep the nominal system stable; calculate the minimum positive invariant set of the error system, and apply constraints to tighten the nominal system; acquire real-time sampling times. k sThe corresponding nominal state and external load, the nominal state is derived from the nominal system.

[0038] Specifically, a discrete-time state-space model is used to characterize the system dynamics, and the state vector is defined to include real-time sampling times. k s The corresponding state of charge of the battery energy storage system , No. i A fuel cell stack at real-time sampling time k s and k s -1 power , .

[0039] The control input vector includes the battery energy storage system at real-time sampling time. k s The charging power and battery energy storage system at real-time sampling time k s The discharge power, the first i A fuel cell stack at real-time sampling time k s The power change; let the predicted load for the first time scale be... Plus load forecasting error as an external load To process load forecasting errors, the load forecasting error is decomposed into positive disturbance components. and the negative component of the disturbance By introducing binary variables and constants, mutual exclusion constraints are constructed to limit the effect of disturbances in only a single direction, either positive or negative, at any given time.

[0040] At the second timescale, construct the fuel cell stack at the real-time sampling time. k s The first-order integral model of power, the update formula of the state of charge of the battery energy storage system; the first-order integral model of the fuel cell stack is... , For the first i A fuel cell stack at real-time sampling time k s The change in power relative to the power at the previous moment; the formula for updating the state of charge of the battery energy storage system is: , and Real-time sampling time k s and the next adjacent real-time sampling time k s +1 corresponds to the state of charge of the battery energy storage system. Ts The sampling interval is the second time scale. and These represent the battery energy storage system at real-time sampling times. k s The charging power and discharging power.

[0041] The formula for updating the state of charge of the battery energy storage system is compared with the formula for updating the state of charge of the fuel cell stack at the real-time sampling time. k s By combining the first-order integral models of the power, the actual system equations of the multi-stack fuel cell power generation system with disturbances are obtained. The state-space form of the actual system equations with disturbances is as follows: , The state transition matrix is ​​shown below. , is the identity matrix; input matrix , parameter matrix , , and Real-time sampling time k s and the next adjacent real-time sampling time k s +1 state vector, Real-time sampling time k s The control vector, , This is the set of state constraints for the equations of a real system containing disturbances. , This is the set of control constraints for the equations of a real system containing disturbances. and The disturbance term is used; Tube-model predictive control is employed to divide the actual system equations of the multi-stack fuel cell power generation system into a nominal system and an error system. The influence of the disturbance term is neglected in the nominal system, and the expression for the nominal system is: , and The nominal system at the real-time sampling time k s and the next adjacent real-time sampling time k s +1 state vector, The nominal system at the real-time sampling moment k s The control vector, which combines the state vector and control vector of the nominal system. , , As a nominal state; Here is the state transition matrix. The input matrix is ​​denoted as .

[0042] Define the error vector and the hierarchical control law; error vector Real-time sampling time k s The difference between the state vector and the undisturbed state vector. Control Law It is the received error vector and the real-time sampling time. k s The process of generating an undisturbed state vector and outputting the actual input vector. K is the feedback gain matrix; the control law Substituting into the equations of the actual system containing the disturbance, we obtain Combined with real-time sampling time k s The +1 error vector definition, Let the disturbance vector be denoted as , , ,gather It is based on the positive component of the disturbance. and the negative component of the disturbance The feasible region of load forecasting error constructed with its mutual exclusion constraints, and the expression for the error system. .

[0043] Computational error system minimum positive invariant set Tightening the constraints on the nominal state is to Given an initial set, the elements of subsequent sets are generated iteratively using the following formula: superscript and This corresponds to different iteration rounds. The Minkowski sum; iteration stops when the change in the set between two consecutive iterations is less than a preset threshold, and the set converges to the smallest positive invariant set. The expression for tightening the constraints of the nominal state is: , ,in Minkowski's difference.

[0044] Minimum positive invariant set This ensures that the actual system remains safe and feasible under all permissible disturbances, enabling robust real-time tracking control of the upper-level power plan.

[0045] S32: Based on the power reference trajectory of the fuel cell stack and the state-of-charge reference trajectory of the battery energy storage system obtained in step S2, extract... N pThe reference trajectory for each real-time sampling moment corresponds to a step size, and the reference trajectory includes a reference state sequence and a reference control sequence. N p The step size corresponding to each real-time sampling moment constitutes the prediction domain.

[0046] Specifically, let the reference state sequence and the reference control sequence in the prediction domain be respectively , Reference state vector Reference control vector In the reference state vector This serves as a reference trajectory for the state of charge (SOC) of the battery energy storage system within the intraday rolling optimization layer. For each fuel cell stack in the intraday rolling optimization layer at the predicted time k s + j -1 nominal reference output power; in the reference control vector For battery energy storage systems at predicted times k s + j -1 reference charging power and reference discharging power, This indicates the predicted time for each fuel cell stack. k s + j -1 represents the reference power change, which is based on the current fuel cell stack's predicted value at adjacent time points. k s + j -1 and k s + j The difference is obtained from the nominal reference output power.

[0047] S33: At each sampling moment of real-time rolling optimization, establish a nominal optimization problem. The decision variable of the optimization problem is the nominal trajectory, which includes the nominal state sequence and the nominal control sequence in the prediction domain. Under the given tightening constraints, minimize the deviation between the nominal trajectory and the reference trajectory to obtain the optimal nominal control input sequence.

[0048] Specifically, let the nominal state sequence and nominal control sequence in the prediction domain be respectively , Nominal state variables Nominal control variables , Indicates from the real-time sampling time k s Predicted time k s + j The state of charge of the battery energy storage system, Indicates from the real-time sampling time k s Predicted time k s + j The output power of each fuel cell stack is -1. and Indicates from the real-time sampling time k s Predicted time k s + j The charging and discharging power of the battery energy storage system Indicates from the real-time sampling time k s Predicted time k s + j The power variation of each fuel cell stack.

[0049] The nominal optimization problem, by introducing the decomposition of the charging and discharging power of the battery energy storage system and binary variables, is expressed as a mixed-integer quadratic programming problem. The nominal optimization problem is to find the nominal control input sequence that minimizes the objective function within the prediction domain. The expression for the objective function of the nominal optimization problem is: , , , , , , , , , ,in For a moment k s + j The control input vector is Q, where Q is the error weight matrix of the nominal state variables. To calculate the second-order norm operation, P is the error weight matrix of the nominal control variables. , These are the nominal state vectors at different times within the prediction domain. , These are the nominal control vectors at different times within the prediction domain. As the reference state vector, As a reference control vector, , , , , , For the first i A fuel cell stack at time k s + j-1 output power, battery energy storage system at any time k s + j -1 reference discharge power, battery energy storage system at time k s + j -1 reference charging power, time given in the first time scale k s + j -1 is the predicted load value, the binary variable of the charging state of the battery energy storage system, and the binary variable of the discharging state of the battery energy storage system.

[0050] In some embodiments described herein, binary variables are introduced to transform the charging and discharging state switching of the battery energy storage system (BESS) into quantifiable integer constraints, thereby avoiding state conflicts and power overruns during the charging and discharging process of the BESS. Furthermore, in conjunction with the mutual exclusion constraints of the positive and negative components of the disturbance, the entire real-time optimization problem becomes a mixed integer quadratic programming problem, ensuring real-time rolling optimization, i.e., the solution speed of the lower-level optimization problem.

[0051] S34: After obtaining the optimal nominal control input sequence, select the first term of the optimal nominal control input sequence and combine it with the state feedback gain matrix K to obtain the actual control law, thus obtaining the actual control input applied to the actual controlled object.

[0052] Specifically, after obtaining the nominal control input sequence that minimizes the objective function, the sampling time will be... k s state vector Within the prediction domain k s nominal state vector at time t The difference is multiplied by the feedback gain matrix K to form the feedback correction term, which is then added to the prediction domain. k s nominal control vector at time step As actual control input , .

[0053] The nominal control plus feedback correction yields the actual control law, which can counteract the impact of disturbances on the system and achieve robust feasibility and dynamic tracking.

[0054] S35: Update the real-time sampling time, return to step S31 to reacquire the nominal state and external load, and repeat steps S32-S34 until all real-time sampling times in the prediction domain have been traversed.

[0055] This embodiment employs a real-time rolling optimization layer, where the lower layer uses the Tube-MPC method to make local adjustments based on intraday planning. This reduces the likelihood that the reference trajectory will not directly meet operational constraints due to load disturbances, environmental changes, and reactor performance fluctuations, improving robustness to disturbances and enabling safe and implementable power corrections at the minute level. Real-time optimization ensures that each reactor can stably track the target power under dynamic conditions and avoids unsafe operation caused by differences in health status.

[0056] In this embodiment, through two-level coupling, the intraday rolling optimization layer is responsible for long-term overall optimization, while the real-time rolling optimization layer is responsible for disturbance rejection correction. The synergistic effect of the two enables the multi-reactor system to meet the grid requirements while taking into account health and economy, providing a systematic control structure for improving the overall system performance, operational stability and lifespan.

[0057] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A health management method for multi-stack fuel cell power generation systems based on hierarchical collaborative optimization, characterized in that, Includes the following steps: S1: Based on the operating parameters of the multi-stack fuel cell power generation system, establish a degradation model for the fuel cell stack and a capacity decay model for the battery energy storage system, and obtain the life cost of the fuel cell stack and the life cost of the battery energy storage system. S2: On the first time scale, based on the hydrogen consumption cost, the life cost of the fuel cell stack, and the life cost of the battery energy storage system, the intraday rolling optimization problem is modeled, and intraday rolling optimization is performed under the set constraints to obtain the power reference trajectory of the fuel cell stack and the state of charge reference trajectory of the battery energy storage system. S3: On the second time scale, an invariant tubular set is constructed using Tube-model predictive control and constraint tightening is applied. Based on the load prediction error, an actual control law is generated for real-time rolling optimization, and robust corrections are made to the power reference trajectory and the state of charge reference trajectory.

2. The health management method for a multi-stack fuel cell power generation system based on hierarchical collaborative optimization according to claim 1, characterized in that, The degradation model of the fuel cell stack described in step S1 involves linearly degrading the performance of the fuel cell stack (FCS) under given operating conditions over time. The actual operating state is divided into several typical operating conditions, each assigned a performance degradation rate. A corresponding number of cycles or operating time is assigned to each degradation rate, and these rates are accumulated. The accumulated result is multiplied by an acceleration factor and used as the degradation index of the fuel cell stack (FCS). d FC Degradation index of fuel cell stack FCS d FC As the denominator, the performance degradation threshold of the fuel cell stack (FCS) from its initial state to the end of its lifespan. As molecules, the lifespan model of the fuel cell stack (FCS) is obtained. T FC Lifetime model of fuel cell stack (FCS) T FC The reciprocal of the product, multiplied by the fuel cell stack price coefficient c FC To obtain the lifespan cost of the fuel cell stack .

3. The health management method for a multi-stack fuel cell power generation system based on hierarchical collaborative optimization according to claim 2, characterized in that, The capacity decay model of the battery energy storage system described in step S1 is based on the capacity of cyclic charge and discharge. A h Using the power-law relationship and the Arrhenius equation, the capacity loss of battery energy storage systems is constructed. The relationship is obtained by discretizing the capacity loss relationship of the battery energy storage system to obtain the capacity loss relationship at a certain charge / discharge stage. Capacity loss at each stage Accumulation is performed to achieve dynamic tracking of the capacity decay of the battery energy storage system; a unit capacity price coefficient for the battery energy storage system is introduced. The capacity loss is converted into the lifespan cost of the battery energy storage system. .

4. The health management method for a multi-stack fuel cell power generation system based on hierarchical collaborative optimization according to claim 3, characterized in that, Step S2 specifically includes: Modeling the intraday rolling optimization problem, making the overall objective function of the intraday rolling optimization layer... F RO The value is minimized, where the total objective function of the intraday rolling optimization layer is the smallest. F RO The cost of hydrogen consumption is determined by the output power of each fuel cell stack at different times. Lifetime cost of fuel cell stacks Lifetime cost of battery energy storage systems and the cost of health consistency across multiple fuel cell stacks. Under the set constraints, rolling optimization is performed, and the solution is solved periodically in the rolling time domain. Each time, a new round of power output plan for fuel cell stack and battery energy storage system is generated using the updated load forecast and system state, so as to obtain the power reference trajectory of fuel cell stack and the state of charge reference trajectory of battery energy storage system. The constraints are as follows: 1) At each time step, the power of each fuel cell stack is multiplied by the efficiency of the DC / DC converter and then summed. The sum is then added to the charging and discharging power of the battery storage system, which equals the load power demand; 2) The... i The output power of a fuel cell stack is between its lower and upper limits; 3) at each moment, the state of charge of the battery energy storage system is between its lower and upper limits.

5. The health management method for a multi-stack fuel cell power generation system based on hierarchical collaborative optimization according to claim 4, characterized in that, Hydrogen consumption cost determined by fuel cell stack output power It is based on the sampling interval The corresponding hydrogen equivalent consumption multiplied by the unit price of hydrogen. The obtained hydrogen equivalent consumption includes the direct hydrogen consumption of the fuel cell stack. Equivalent hydrogen consumption of battery energy storage systems ; Multi-stack fuel cell health consistency cost It is through the coefficient of variation With weighting coefficients The coefficient of variation obtained after multiplication It is achieved by predicting the standard deviation of the remaining lifetime of the fuel cell stack. Divide by the average predicted remaining life of the fuel cell stack Obtained.

6. The health management method for a multi-stack fuel cell power generation system based on hierarchical collaborative optimization according to claim 4, characterized in that, Step S3 specifically includes: S31: Construct a discrete-time state-space model, separating the actual system equations containing disturbances into a nominal system and an error system; the nominal system contains nominal variables, and the state feedback gain matrix K is designed offline to keep the nominal system stable; calculate the minimum positive invariant set of the error system, and apply constraints to tighten the nominal system; acquire real-time sampling times. k s The corresponding nominal state and external load, the nominal state is derived from the nominal system; S32: Based on the power reference trajectory of the fuel cell stack and the state-of-charge reference trajectory of the battery energy storage system obtained in step S2, extract... N p The reference trajectory for each real-time sampling moment corresponds to a step size, and the reference trajectory includes a reference state sequence and a reference control sequence. N p The step size corresponding to each real-time sampling moment constitutes the prediction domain. S33: At each sampling moment of real-time rolling optimization, establish a nominal optimization problem. The decision variable of the optimization problem is the nominal trajectory, which includes the nominal state sequence and the nominal control sequence in the prediction domain. Under the given tightening constraints, minimize the deviation between the nominal trajectory and the reference trajectory to obtain the optimal nominal control input sequence. S34: After obtaining the optimal nominal control input sequence, select the first term of the optimal nominal control input sequence, combine it with the state feedback gain matrix K, and obtain the actual control law, thus obtaining the actual control input applied to the actual controlled object; S35: Update the real-time sampling time, return to step S31 to reacquire the nominal state and external load, and repeat steps S32-S34 until all real-time sampling times in the prediction domain have been traversed.

7. A health management method for a multi-stack fuel cell power generation system based on hierarchical collaborative optimization according to claim 6, characterized in that, Step S31 specifically includes: The discrete-time state-space model is used to characterize the system dynamics, and the state vector is defined to include the real-time sampling time. k s The corresponding state of charge of the battery energy storage system , No. i A fuel cell stack at real-time sampling time k s and k s -1 power , ; The control input vector includes the battery energy storage system at real-time sampling time. k s The charging power and battery energy storage system at real-time sampling time k s The discharge power, the first i A fuel cell stack at real-time sampling time k s The power change; let the predicted load for the first time scale be... Plus load forecasting error As an external load, the load forecasting error is processed by decomposing the load forecasting error into positive disturbance components. and the negative component of the disturbance By introducing binary variables and constants, mutual exclusion constraints are constructed to limit the effect of disturbances in a single direction, either positive or negative, at any given time. At the second timescale, construct the fuel cell stack at the real-time sampling time. k s The first-order integral model of power and the update formula of the state of charge of the battery energy storage system; The formula for updating the state of charge of the battery energy storage system is compared with the formula for updating the state of charge of the fuel cell stack at the real-time sampling time. k s By combining the first-order integral models of the power, the actual system equations of the multi-stack fuel cell power generation system with disturbances are obtained; In the Tube-model predictive control, the actual system equations of a multi-stack fuel cell power generation system with disturbances are divided into a nominal system and an error system. The influence of the disturbance term is ignored in the nominal system. Computational error system minimum positive invariant set The nominal state is subject to tightening constraints.

8. The health management method for a multi-stack fuel cell power generation system based on hierarchical collaborative optimization according to claim 7, characterized in that, Step S32 specifically includes: A reference state sequence and a reference control sequence are constructed within the prediction domain. The reference state sequence includes several reference state vectors, and the reference control sequence includes several reference control vectors. The reference state vectors include the state-of-charge reference trajectory of the battery energy storage system in the intraday rolling optimization layer and the nominal reference output power of each fuel cell stack in the intraday rolling optimization layer at the prediction time. The reference control vectors include the reference charging power and reference discharging power of the battery energy storage system at the prediction time, as well as the reference power change of each fuel cell stack at the prediction time. The reference power change is obtained based on the difference in nominal reference output power of the current fuel cell stack at adjacent prediction times.

9. A health management method for a multi-stack fuel cell power generation system based on hierarchical collaborative optimization according to claim 8, characterized in that, Step S33 specifically includes: Define the nominal state sequence and nominal control sequence within the prediction domain. The nominal state sequence includes several nominal state variables, and the nominal control sequence includes several nominal control variables. The nominal state variables include the values ​​from the real-time sampling time to the prediction time. k s + j The state of charge of the battery energy storage system, and the data from the real-time sampling time. k s Predicted time k s + j -1 is the output power of each fuel cell stack; nominal control variables include those from the real-time sampling time. k s Predicted time k s + j The charging and discharging power of the battery energy storage system, and the data from real-time sampling time. k s Predicted time k s + j The power variation of each fuel cell stack; The nominal optimization problem is expressed as a mixed integer quadratic programming problem by introducing the decomposition of the charging and discharging power of the battery energy storage system and binary variables. The nominal optimization problem is to find the nominal control input sequence that minimizes the objective function in the prediction domain.

10. A health management method for a multi-stack fuel cell power generation system based on hierarchical collaborative optimization according to claim 9, characterized in that, Step S34 specifically includes: After obtaining the nominal control input sequence that minimizes the objective function, the real-time sampling time will be... k s state vector Within the prediction domain k s The difference between the nominal state vectors at time 1 and 2 is multiplied by the feedback gain matrix K to form the feedback correction term, which is then added to the value in the prediction domain. k s The nominal control vector at time t is used as the actual control input.

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