Dynamic cooperative control method of fuel cell system

Abstract

The invention discloses a dynamic cooperative control method for a fuel cell system, and the method comprises the following steps: constructing a multi-objective optimization function with the purposes of minimizing the fuel consumption cost and maximizing the service life of a fuel cell, solving the multi-objective optimization function according to the real-time state of the fuel cell, and obtaining an optimal power reference trajectory of the fuel cell; constructing a disturbance model based on the state of the fuel cell and the disturbance source, and compressing the multi-dimensional disturbance model into a polyhedral feasible region to obtain an action range of the disturbance source; calculating the pipe domain radius of the robust predictive control model according to the action range of the disturbance source, and shrinking the pipe domain radius according to a set safety margin; and taking the minimum power trajectory tracking error, the control quantity change penalty and the tube domain violation penalty as optimization targets of a robust prediction control model, constraining the robust prediction control model through the contracted tube domain radius, and outputting a current density instruction of the fuel cell by the robust prediction control model.

Description

Technical Field

[0001] The present invention belongs to the technical field of energy management, and in particular relates to a dynamic coordinated control method for a fuel cell system. Background Art

[0002] With the increasing penetration of highly volatile renewable energy sources such as wind power and photovoltaics, traditional peak-shaving technologies such as gas turbines and lithium batteries are struggling to meet the dynamic support needs of the power grid due to their limited response speed or lifespan. Proton exchange membrane fuel cells, with their millisecond-level power response, high energy density, and zero-emission characteristics, have become a key flexibility resource for building new power systems. However, under strong dynamic grid disturbances, the electrochemical-thermal coupling characteristics of fuel cells present unique challenges for state management, severely restricting their large-scale industrialization. These issues include the inability to directly measure key internal state parameters such as the water content of the proton exchange membrane and the activity of the catalyst, resulting in the inability to perceive and accurately assess the health status of the fuel cell in real time, which can lead to a series of safety hazards such as delayed warning of thermal runaway risks. Furthermore, the strong coupling between the grid's second-by-second frequency regulation requirements and the hour-by-hour aging process of the fuel cell stack means that single-objective optimization can accelerate performance degradation.

[0003] Currently, the fuel cell control field primarily utilizes rule-based control or fixed-weight multi-objective optimization methods. Rule-based control relies on empirical parameters and sets a series of rules to control the fuel cell's operating state. Fixed-weight multi-objective optimization, on the other hand, sets fixed weights between multiple objectives to achieve comprehensive optimization. While these methods can manage fuel cells to a certain extent, they are limited when dealing with complex dynamic operating conditions.

[0004] Rule-based control, due to its reliance on empirical parameters, ignores changes in the internal state of the fuel cell stack, potentially leading to membrane perforation risks under low-humidity conditions. Static weighted optimization, on the other hand, cannot adapt to multi-mode switching requirements such as grid frequency regulation and off-grid switching, resulting in significant deviations in lifespan predictions. Therefore, achieving widespread adoption of fuel cell-supported power grid systems urgently requires a method that can address the mutual constraints and difficulty of coordinated control of multiple objectives, ensuring coordinated optimal control and long-term performance under complex dynamic conditions. Summary of the Invention

[0005] The present invention proposes a dynamic coordinated control method for a fuel cell system, which solves the problem that the existing technology is difficult to achieve coordinated control of fuel cells under complex dynamic working conditions.

[0006] To solve the above technical problems, the present invention provides a dynamic coordinated control method for a fuel cell system, comprising the following steps: Step S1: constructing a multi-objective optimization function with the goal of minimizing fuel consumption cost and maximizing fuel cell life, solving the multi-objective optimization function according to the real-time state of the fuel cell, and obtaining the optimal power reference trajectory of the fuel cell; Step S2: constructing a disturbance model based on the state of the fuel cell and the disturbance source, compressing the multi-dimensional disturbance model into a polyhedron feasible domain, and obtaining the range of action of the disturbance source; Step S3: calculating the pipe domain radius of the robust predictive control model according to the action range of the disturbance source, and shrinking the pipe domain radius according to a set safety margin; Step S4: minimizing the power trajectory tracking error, the control quantity change penalty, and the pipe domain violation penalty is used as the optimization goal of the robust predictive control model, and the robust predictive control model is constrained by the shrunken pipe domain radius. The robust predictive control model outputs the current density instruction of the fuel cell.

[0007] Preferably, the expression of the multi-objective optimization function in step S1 is: ; ; ; ; In the above formula, is the fuel consumption cost function; is the life reliability function; T To optimize the total time step in the time domain; for Total system efficiency at time; for System hydrogen consumption at the moment; It is the low calorific value of hydrogen; is the weight coefficient; The health status of the fuel cell; The remaining service life of the fuel cell; 、 They are the upper and lower limits of the equivalent state of charge and the upper and lower limits of the temperature of the fuel cell respectively; is the equivalent state of charge of the fuel cell; is the temperature of the fuel cell; is the fuel cell power; is the peak power of the fuel cell.

[0008] Preferably, solving the multi-objective optimization function in step S1 includes the following steps: Step S11: using a fast elite multi-objective genetic algorithm NSGA-II to solve the multi-objective optimization function to obtain a Pareto solution set of the multi-objective optimization function; Step S12: calculating the data distribution discreteness of each optimization objective in the Pareto solution set, and dynamically adjusting the weight of each optimization objective in the multi-objective optimization function according to the data distribution discreteness; Step S13: Calculate the closeness of the solutions in the Pareto solution set according to the adjusted weights, and take the solution with the largest closeness as the optimal solution.

[0009] Preferably, in step S12, the expression for dynamically adjusting the weight of each optimization objective in the multi-objective optimization function according to the discreteness of the data distribution is: ; ; In the above formula, For the The weight of the optimization goal; For the The discreteness of the data distribution of the optimization objectives; is the number of solutions in the Pareto solution set; is the normalized Pareto solution set.

[0010] Preferably, the expression for calculating the closeness of the solutions in the Pareto solution set according to the adjusted weights in step S13 is: ; ; ; In the above formula, is the closeness of the solution; For the i A solution The weighted Euclidean distance of For the i A solution The weighted Euclidean distance of For the i The solution in j The original value of the optimization target; For the The optimal value of an optimization objective; For the The worst value of the optimization objective; For the The maximum solution of an optimization objective; For the The minimum solution of an optimization objective.

[0011] Preferably, the expression of the disturbance model in step S2 is: ; ; ; ; ; ; ; ; In the above formula, is the perturbation model; is the state matrix; is the input matrix; is the system state vector; Input for system status; is the perturbation coupling matrix; is the disturbance of the system; for The equivalent state of charge of the fuel cell at this moment; for The stack temperature at the moment; for The internal resistance of the battery stack at the moment; for The fuel cell current density at the time; for Load current fluctuation at each moment; for Internal resistance drift at any time; for The ambient temperature changes at all times; is the disturbance gain coefficient; The maximum charge that can be output sustainably in theory; is the sum of the specific heat capacities of the stack materials; is the thermal resistance; is the aging coefficient; is the Faraday efficiency; 、 are the rated power and voltage of the stack respectively; The fuel supply duration is determined by the hydrogen tank capacity; is the component quality; is the specific heat capacity.

[0012] Preferably, the expression for compressing the multi-dimensional disturbance model into a polyhedron feasible region in step S2 is: ; ; ; ; In the above formula, is the initial feasible region of the perturbation model; is the disturbance center; is the generator matrix of the disturbance direction and amplitude; It means element-by-element addition; represents the unit hypercube; is the disturbance mean; is the disturbance amplitude boundary; , representing three perturbations.

[0013] Preferably, in step S3, updating the pipe area radius according to the set safety margin includes the following steps: Step S31: determining a safety set and a maximum disturbance boundary according to the range of the disturbance source; Step S32: Calculating the control domain radius of the robust predictive control model according to the safety set and the maximum disturbance boundary; Step S33: Calculate the safety radius according to the set safety margin, determine whether the current pipe domain radius exceeds the safety radius, and if so, shrink the pipe domain radius according to the safety radius and update the pipe domain radius. The expression for updating the pipe domain radius is: ; ; ; ; ; In the above formula, is the updated pipe domain radius; is the attenuation factor; The weight coefficients representing the disturbance amplitude and safety constraints; is the radius of the pipe domain considering the influence of the disturbance amplitude; is the radius of the safety zone; is the decay rate; To control the cycle; is the current disturbance amplitude; is the maximum allowable disturbance amplitude; is the initial radius under the nominal system; is the current pipe domain radius; is the safety constraint violation amount; is the current temperature of the fuel cell; is the maximum temperature for safety constraints; For safety margin.

[0014] Preferably, step S31 includes the following steps: Step S311: Define the initial security set :If the system status , then for all perturbation amplitude boundaries and ,have ,in is the perturbation set, is the time variable; Step S312: Define the attenuation condition of the fuel cell system, substitute the attenuation condition into the disturbance model and convert it into a matrix form to obtain a linear matrix inequality, solve the linear matrix inequality, and obtain the initial safety set The boundary of and the maximum disturbance boundary of the disturbance source; Step S313: Verify the initial security set Whether it converges, if not, adjust dynamically Otherwise, output the safe set.

[0015] Preferably, the optimization objective and constraint conditions of the robust predictive control model in step S4 are expressed as follows: ; ; ; In the above formula, The cost function of the optimization objective of the robust predictive control model; To control the time domain length; For the system State variables at the moment; is the optimal power reference trajectory; is the state weight matrix; For the system Control increments of moments; Enter the weight matrix; is the pipe domain radius weight; is the current pipe domain radius; is a constraint condition; is the current temperature; 、 are the minimum and maximum values ​​of temperature respectively; is the control variable of the robust predictive control model; 、 are the minimum and maximum current densities of the fuel cell stack, respectively; is a state variable.

[0016] The beneficial effects of the present invention include at least: 1. Construct a multi-objective optimization function based on the real-time status of the fuel cell to accurately reflect the actual operating status of the current fuel cell, so that the optimal power reference trajectory obtained is more in line with actual needs, thereby achieving precise control of the fuel cell and improving the overall performance of the system; 2. Construct a disturbance model based on the fuel cell system's state and disturbance sources, and compress the multi-dimensional disturbance model into a polyhedron feasible domain. This can clearly determine the scope of the disturbance source, provide an accurate basis for subsequent control strategy formulation, and facilitate accurate response to various disturbance factors. 3. Taking into account various factors such as system uncertainty and external disturbances, a robust predictive control model was constructed. This model can predict the future behavior of the system and formulate control strategies in advance in the presence of uncertainty and disturbance, thereby effectively responding to system uncertainty and external disturbances and ensuring the stable operation of the fuel cell. By calculating the pipe domain radius of the robust predictive control model and shrinking it according to the set safety margin, a clear safety boundary is set for the operation of the fuel cell, so that the fuel cell can always be within a safe and controllable range during operation, reducing risks such as thermal runaway and ensuring long-term stable operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Schematic diagram of a method flow in an embodiment of the present invention; Figure 2 A framework diagram of the control strategy of an embodiment of the present invention; Figure 3 Flowchart of the NSGA-II algorithm based on constraint tightening in an embodiment of the present invention; Figure 4 Schematic diagram of the construction process of a dynamic invariant set according to an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The following is a clear and complete description of the technical solutions in the embodiments of the present invention, in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0019] Existing fuel cell control methods cannot directly measure key parameters of proton exchange membrane fuel cells (PEMFCs), such as membrane moisture content and catalyst activity. This makes it difficult to perceive the battery's health status in real time, potentially leading to delayed warnings of thermal runaway risks. Furthermore, the grid's second-by-second frequency regulation requirements are strongly coupled with the hour-by-hour aging process of the fuel cell stack, leading to accelerated performance degradation from single-target optimization.

[0020] Furthermore, existing technologies typically employ static weighting methods with fixed coefficients, making them completely incapable of adapting to multi-mode switching requirements such as grid frequency regulation and off-grid switching. This results in either insufficient disturbance suppression capabilities or overly conservative control strategies. The phased approach to power trajectory optimization and health / safety constraints fragments the solution space and delays response during operating mode switching, which not only impacts system performance but also potentially leads to safety hazards such as thermal runaway. Furthermore, coupled modeling and dynamic suppression mechanisms for multi-source disturbances such as current ripple, temperature drift, and aging parameter drift are lacking.

[0021] The method of the embodiment of the present invention effectively addresses the limitations of single-objective optimization in existing technologies by overcoming the bottleneck of unmeasurable internal fuel cell states and other technical means. It also significantly solves the problem of energy efficiency and economic efficiency and life reliability under dynamic fuel cell operating conditions, which are mutually constrained and difficult to coordinate and control. Specifically, the method of the embodiment of the present invention can resolve multi-objective conflicts, eliminate the conservatism of static optimization, unify constraints, suppress strong random perturbations, and accurately model electrochemical-thermal coupling nonlinearities.

[0022] like Figure 1 and Figure 2 As shown, an embodiment of the present invention provides a dynamic coordinated control method for a fuel cell system, comprising the following steps: Step S1: Constructing a multi-objective optimization function with the goal of minimizing fuel consumption cost and maximizing fuel cell life, solving the multi-objective optimization function according to the real-time status of the fuel cell to obtain the optimal power reference trajectory of the fuel cell, including the following steps: Step S11: Based on the perceived information of the fuel cell's state of health (SOH), remaining useful life (RUL), and the output dynamic characteristics of the fuel cell's peak power (SOP), a multi-objective optimization model is constructed that considers both energy efficiency and life reliability.

[0023] Specifically, the battery state of health (SOH) is a key indicator that characterizes the degree of battery performance degradation. The SOH of a fuel cell needs to shift from capacity degradation to a composite indicator of performance degradation, and its expression is: ; Where, is the battery health status of the fuel cell; is the calibration coefficient; 、 、 is the weight coefficient; for The activation voltage decays at the moment; for The internal resistance increases at every moment; for Fuel utilization at the moment; 、 、 They are the initial activation voltage attenuation reference value, internal resistance growth reference value, and fuel utilization rate reference value under rated operating conditions.

[0024] The remaining useful life (RUL) of a fuel cell combines chemical decay and mechanical aging and is expressed as: ; Where, is the remaining useful life of the fuel cell; are the fitting parameters determined by accelerated aging experiments; is the activation energy; is the universal gas constant; is the battery temperature; The total number of data points of the current and temperature data sampled by the fuel cell on an hourly basis, that is, the total sampling hours; is the current fluctuation rate; is the temperature baud rate.

[0025] The model monitors fuel cell status parameters in real time and dynamically updates RUL prediction values, providing a forward-looking decision-making basis for battery management.

[0026] The expression of the limiting model of the maximum power (SOP) of the fuel cell is: ; Where, is the fuel cell peak power; is the fuel cell stack voltage; is the maximum current density of the proton exchange membrane; is the maximum allowable temperature of the fuel cell; is the current temperature of the fuel cell; is the thermal resistance.

[0027] Establish energy efficiency and economic objective function with the goal of minimizing fuel consumption cost , establish the life reliability objective function with the goal of maximizing RUL and SOH , thus the expression of the multi-objective optimization function is: ; ; ; ; In the above formula, T To optimize the total time step in the time domain; for Total system efficiency at time; for System hydrogen consumption at the moment; It is the low calorific value of hydrogen; is the weight coefficient; The health status of the fuel cell; The remaining service life of the fuel cell; 、 They are the upper and lower limits of the equivalent state of charge and the upper and lower limits of the temperature of the fuel cell respectively; The equivalent charge state of the fuel cell is the ratio of the actual available charge to the theoretical maximum charge, reflecting the proportion of charge actually participating in the reaction; is the temperature of the fuel cell; is the fuel cell power.

[0028] Step S12: Considering fuel cell safety, a fast elite multi-objective genetic algorithm (NSGA-II) based on constraint tightening is used to solve the Pareto optimal solution set of the multi-objective optimization function, and the optimal compromise trajectory is screened according to the TOPSIS method based on entropy weight to achieve a balance between energy efficiency and life reliability maximization.

[0029] Specifically, we first use the NSGA-II algorithm based on constraint tightening to solve the multi-objective optimization function. By dynamically adjusting the improved fitness penalty function of NSGA-II, we achieve constraint tightening and prioritize safety margins. To effectively handle constraints, we introduce a penalty term as an independent objective, and then use a loosening strategy to ensure that the penalty term is zero. The new multi-objective optimization model is expressed as: ; ; In the above formula, For penalty items; is the penalty factor; is the number of constraint violations; For the i The amount of constraint violations.

[0030] like Figure 3 FIG. 4 is a flowchart of the NSGA-II algorithm based on constraint tightening, which involves a relaxation-tightening algorithm and a multi-sorting principle and specifically includes the following steps: Step S121: Population initialization: Randomly generate an initial solution set within the SOP dynamic boundary , where N is the number of individuals in the population. Each initial solution generated Pre-screening is required to satisfy the safety constraints, otherwise regeneration is performed, where TT represents the dimension of the decision vector.

[0031] Step S122: Non-dominated sorting: The expression of the improved fitness function is: ; In order to ensure the optimization direction while taking into account the objective function and constraint satisfaction, the solution set is layered according to the Pareto dominance relationship. The layering rules are: , ; Where, Indicates the the level of the solution; express The rank of the solution is equal to the solution that dominates it in the population The total number of .

[0032] The dominance relationship between the two different solutions is as follows: (1) If The corresponding penalty item Less than or equal to the relaxation factor ,and The corresponding penalty term is greater than the relaxation factor , then it is called ; (2) If The corresponding penalty item Greater than the relaxation factor ,and The corresponding penalty item Less than or equal to the relaxation factor , then it is called ; (3) If and The corresponding penalty item Both are greater than the relaxation factor , then proceed to the next step of comparison; if The penalty term is less than The penalty term is called ;if The penalty term is less than The penalty term is called ; (4) If and The corresponding penalty item Are less than or equal to the relaxation factor , then proceed to the next step of comparison.

[0033] Step S123: Calculate the crowding degree: measure the distribution of individuals on the Pareto frontier, and give priority to retaining individuals with sparse distribution. The calculation expression of crowding degree is: ; Where, For the The congestion degree of a solution; is the number of objective functions; For the An optimization objective function; 、 Respectively Hedi The optimization objective function value of a solution; 、 Respectively The maximum and minimum values ​​of the optimization objective function.

[0034] Step S124: Genetic operation: Generate high-quality and diverse offspring using the results of sorting and crowding calculations, and update the population.

[0035] After obtaining the Pareto frontier solution, the TOPSIS method based on entropy weight is further combined to make decisions and screen the optimal trajectory. First, the Pareto solution of the energy efficiency and life reliability objective functions is mapped to the [0,1] interval to eliminate the dimensional effect: .

[0036] In order to provide an objective basis for weight allocation, it is necessary to quantify the discreteness of the target parameters and calculate the discreteness of the data distribution of each optimization target in the Pareto solution set: ; Where, For the The discreteness of the data distribution of the optimization objectives; is the normalized Pareto solution set.

[0037] When all solutions are in the target When the upper values ​​are close, If a target The solution values ​​of are significantly different, then , indicating that the information entropy of the target is small, and the target weight should be higher. Therefore, the expression for weight distribution is defined as: ; Where, For the The weight of the optimization objective.

[0038] The logic of weight distribution is that if energy efficiency and economy The difference in the solution value is greater than the life reliability ,but .

[0039] The calculation expression of TOPSIS closeness is: ; ; ; In the above formula, is the closeness of the solution, represents the closest solution to the ideal solution, i.e. the optimal reference trajectory; For the i A solution The weighted Euclidean distance of For the i A solution The weighted Euclidean distance of For the i The solution in j The original value of the optimization target; For the The optimal value of an optimization objective; For the The worst value of the optimization objective; For the The maximum solution of an optimization objective; For the The minimum solution of an optimization objective.

[0040] Step S2: Construct a disturbance model based on the state of the fuel cell system and the disturbance source, compress the multi-dimensional disturbance model into a polyhedron feasible domain, and obtain the scope of the disturbance source. Figure 4 As shown, the following steps are included: Step S21: A unified disturbance model including operating condition fluctuation, aging drift and environmental disturbance is established based on stochastic differential equations, and the coupling range of multi-source disturbances is characterized by using the Qino polyhedron zonotope method.

[0041] First, a unified perturbation model of the stochastic differential equation of the system state is established, which includes operating condition fluctuations, i.e. load changes, aging drift, i.e. internal resistance growth, and environmental disturbances, i.e. temperature changes: ; ; ; ; ; ; ; ; ; ; In the above formula, is the perturbation model; is the state matrix; is the input matrix; is the system state vector; Input for system status; is the perturbation coupling matrix; is the disturbance of the system; for The internal resistance of the battery stack at the moment; for The fuel cell current density at the time; for Load current fluctuation at each moment; for Internal resistance drift at any time; for The ambient temperature changes at all times; is the disturbance gain coefficient; The maximum charge that can be output sustainably in theory; is the sum of the specific heat capacities of the stack materials; is the thermal resistance; is the aging coefficient; is the Faraday efficiency; 、 are the rated power and voltage of the stack respectively; The fuel supply duration is determined by the hydrogen tank capacity; is the component quality; is the specific heat capacity.

[0042] Multi-source disturbance The feasible domain of is expressed as the zonotope generating matrix: ; ; ; ; In the above formula, is the initial feasible region of the perturbation model; is the disturbance center; is the generator matrix of the disturbance direction and amplitude; It means element-by-element addition; represents the unit hypercube; is the disturbance mean; is the disturbance amplitude boundary; , representing three perturbations.

[0043] Step S22: construct a dynamic perturbation invariant set through robust positive invariant set theory, and analyze the maximum allowable perturbation boundary of the perturbation model in combination with Lyapunov stability.

[0044] Robust positive invariant set means that the system state always remains within a certain set within the disturbance range, that is, Lyapunov analysis is performed by constructing a quadratic energy function , ensuring that the system is stable under disturbances, and using linear matrix inequality (LMI) to solve the maximum allowable disturbance amplitude boundary The specific steps include: Step S221: Derive the dynamic equation of the closed-loop system according to the unified disturbance model: .

[0045] Define robust positive invariant set :If the system status , then for all and ,have ,in is the perturbation set, represents the time variable, The value of starts from the initial moment and extends continuously to any future moment. It emphasizes that the robust invariance of the set R must hold at any time.

[0046] Define robust positive invariant set Boundary size: ; Where, is the system state variable; is the Lyapunov matrix obtained by the LMI solver; is the range of the invariant set.

[0047] The judgment conditions are: ; Where, represents the Frobenius norm; is the threshold for the algorithm to converge.

[0048] Step S222: Calculate the Lyapunov stability condition.

[0049] Select the quadratic Lyapunov function ( ), requiring the closed-loop system to meet the attenuation condition: ; ; In the above formula, 、 are the attenuation rate of controlling convergence speed and the gain of disturbance suppression capability, respectively, and ; is the system disturbance; is the system state quantity.

[0050] Substituting the above formula into the closed-loop system dynamic equation, we get: ; Expand the above formula to get: ; Combined with the attenuation condition, we can get: .

[0051] Step S223: solving the maximum disturbance boundary.

[0052] The robustness is ensured by linear matrix inequality (LMI) constraints. and The conditions for establishment are: ; ; ; In the above formula, Represents the elements of the Lyapunov matrix P obtained by the LMI solver. The subscripts represent the rows and columns of the matrix, and P is defined as a three-dimensional matrix.

[0053] Among them, P, 、 They are the Lyapunov matrix obtained by the LMI solver, the attenuation rate that controls the convergence speed, and the gain of the disturbance suppression capability.

[0054] According to the attenuation condition, we can get: .

[0055] Taking the worst case, the maximum allowable disturbance amplitude is conservatively estimated to be: ; Where, is the Lyapunov matrix The minimum eigenvalue of .

[0056] Step S224: Update the zonotope generation matrix G And adjust the perturbation set W , verify the robust positive invariant set Whether the Lyapunov stability condition is met, if so, the robust positive invariant set is output R as a perturbation invariant set.

[0057] Step S3: Calculate the pipe domain radius of the robust predictive control model according to the action range of the disturbance source, and update the pipe domain radius according to the set safety margin.

[0058] Specifically, the embodiment of the present invention adopts the robust predictive control model Tube-MPC based on dynamic invariant sets to realize dynamic collaborative control of fuel cells. First, the tube domain radius is dynamically adjusted according to the current disturbance amplitude and safety constraints, and the tracking error and robustness cost function are rolling optimized. The optimal control quantity is output to make the system state converge to the robust tube domain.

[0059] The core basis for dynamic adjustment of the pipe radius is the robust positive invariant set R and the maximum allowable disturbance amplitude ,in R Defines the security boundaries of the state, The dynamic adjustment of the pipe domain radius includes the following steps: Step S31: Consider the influence of the disturbance amplitude: ; in, is the current disturbance amplitude; is the initial radius under the nominal system, if , then the radius of the tube domain is expanded to accommodate the disturbance.

[0060] Step S32: Detect whether the system state is close to the safety boundary: ; Where, is the current temperature of the fuel cell; is the maximum temperature for safety constraints; For safety margin.

[0061] like , shrink the tube radius and force the system state to return to the safe zone: ; Where, is the current pipe domain radius.

[0062] Step S33: Update the pipe domain radius: ; ; In the above formula, is the attenuation factor, which is determined by the Lyapunov attenuation rate and control cycle Decide; is the weight coefficient of disturbance amplitude and safety constraint.

[0063] Step S4: Minimizing the trajectory tracking error, the control quantity change penalty, and the pipe domain violation penalty is used as the optimization goal of the robust predictive control model. The robust predictive control model is constrained by the updated pipe domain radius, and the robust predictive control model outputs the current density instruction of the fuel cell.

[0064] Specifically, the cost function of the optimization problem is J It consists of three parts, corresponding to different requirements, including state tracking item, control cost item and management domain penalty item.

[0065] The optimal power reference trajectory is defined as , The optimal power reference trajectory obtained by entropy weight-TOPSIS screening ,and It is a state quantity based on a unified disturbance model. Therefore, it is necessary to convert SOC / temperature / internal resistance into equivalent power through state-power mapping. According to the battery dynamic equation, the relationship between state quantity and power is established: ; ; In the above formula, Indicates equivalent output power; 、 、 They are the SOC, temperature, and internal resistance of the fuel cell at the current moment; represents the state-power mapping function, which is a nonlinear function that converts state variables into power; is the stack voltage corresponding to the current SOC; is the stack current density corresponding to the current SOC; Current temperature T The internal resistance of the battery stack.

[0066] Cost function of the optimization problem The expression is: ; ; ; In the above formula, To control the time domain length; For the system State variables at the moment; is the state weight matrix; For the system Control increments of moments; is the input weight matrix; is the pipe domain radius weight; is the current pipe domain radius; For joint power trajectory optimization and safety constraints, a robust invariant control domain centered around the optimal power reference trajectory is proposed; is the current temperature; 、 are the minimum and maximum values ​​of temperature respectively; is the control variable of the robust predictive control model; 、 are the minimum and maximum current densities of the fuel cell stack, respectively; Represents any state variable, and the deviation from the reference trajectory must not exceed the tube domain radius.

[0067] definition u As the decision vector, the following quadratic programming optimization problem is obtained: ; ; ; In the above formula, is the quadratic coefficient matrix of the objective function; is the coefficient vector of the first-order term of the objective function; is the coefficient matrix of the linear inequality constraints; is the constant term on the right side of the linear inequality constraint.

[0068] The actual output control quantity is: ; ; Where, Contains feedforward optimization and status feedback items .

[0069] The above formula is the optimal solution to the traditional QP optimization problem, providing the global optimal benchmark control quantity, and directly reflecting the Pareto trade-off between energy efficiency and life reliability. Dynamically correct the deficiencies of the feedforward, where R is the input weight matrix; B is the coefficient matrix of the unified perturbation model of the system state stochastic differential equation; and P is the Lyapunov matrix obtained by the LMI solver.

[0070] In summary, compared to traditional optimization problem formulations, the introduction of a closed-loop correction mechanism based on state errors and a pipe-domain penalty term effectively enhances system robustness. This achieves the dual guarantees of optimized prediction and dynamic feedback in fuel cell management, balancing accuracy and stability, making optimization a viable option.

[0071] Compared with the prior art, the method of the embodiment of the present invention has significant technical advantages and beneficial effects: the topological structure of the embodiment of the present invention consists of three parts, a multi-objective optimization module, a dynamic disturbance modeling module, and a Tube-MPC controller. The multi-objective optimization module is based on the basic parameter modeling of the electrochemical working mechanism and the system-level energy conversion characteristics, and constructs a multi-objective optimization function based on the real-time perception data of SOH, RUL, and SOP. It adopts the reference trajectory optimization method based on the constraint tightening NSGA-II combined with the entropy weight-TOPSIS to screen the Pareto optimal solution set and reference trajectory of energy efficiency and life reliability; the dynamic disturbance modeling module constructs the dynamic disturbance invariant set through the robust positive invariant set theory, and determines the maximum allowable disturbance boundary based on the disturbance feasible domain represented by Zonotope combined with Lyapunov stability analysis; the Tube-MPC controller generates a safe feasible domain of the reference trajectory based on the disturbance invariant set and the maximum allowable disturbance boundary, realizes the dynamic contraction of the tube domain radius, and outputs the optimal control quantity to make the system state converge to the robust tube domain. The coordinated optimal control of the multi-objective optimization problem of energy efficiency, economy and life reliability of batteries under complex dynamic conditions is achieved, which improves the overall performance and life reliability of the fuel cell system.

[0072] The method of this embodiment establishes a multi-objective optimization model based on fuel cell SOH, RUL, and SOP perception information, combines it with a dynamic safety constraint mechanism, and updates all constraint parameters online to construct a time-varying safety feasible domain. This ensures that the optimization strategy always operates within the battery safety boundary, achieving a dynamic balance between performance and safety.

[0073] Compared to the traditional NSGA-II algorithm, the constraint-tightening NSGA-II algorithm introduces constraint-related penalty terms into the fitness function calculation as a separate objective. This technique reduces redundant computations, making the NSGA-II multi-objective optimization process time-efficient. The entropy-weighted TOPSIS method is then used to select the optimal compromise trajectory, ultimately achieving a balance between energy efficiency and lifespan reliability. This improves the efficiency of solving complex constraint problems and reduces redundant computations.

[0074] Based on stochastic differential equations, a unified disturbance model for operating condition fluctuations, aging drift, and environmental disturbances is established. This quantifies multi-source disturbances into a zonotope three-dimensional feasible domain, simplifying the optimization problem of multi-dimensional disturbances. This reduces redundant calculations, improves the system's anti-interference capability, and ensures efficient response speed and stability.

[0075] By constructing a dynamic perturbation invariant set based on robust positive invariant set theory, the feasible domain of multi-source perturbations quantified by zonotopes is combined with Lyapunov theory to calculate the perturbation bounds online, reducing the conservatism of robust control. This reduction in robust control conservatism also enables dynamic quantification of the multi-source perturbation coupling range.

[0076] The Tube-MPC framework is designed to be a robust, invariant domain centered around the optimal power trajectory. By combining control variables with a dual mechanism of optimized prediction and dynamic feedback, the framework ensures that the system remains within its bounds under scenarios such as renewable energy fluctuations and sudden load changes. This reduces the risk of state constraint violations under dynamic conditions, mitigates system failures caused by model accuracy issues, and addresses the challenge of coordinating multiple control objectives.

[0077] In summary, through technical means such as multi-objective collaborative control, dynamic balance of fuel cell intelligent state perception, constraint tightening-based NSGA-II algorithm, zonotope representation of multi-source disturbances, robust control of dynamic disturbance invariant sets, and precise modeling of electrochemical-thermal coupled nonlinear systems, the method of the embodiment of the present invention realizes collaborative optimal control of batteries under complex working conditions, ensures that the system state always converges to the robust invariant domain centered on the optimal reference trajectory, improves the comprehensive performance and life reliability of the fuel cell system, and has important practical application value.

[0078] The technical features of the above embodiments may be combined in any manner. To simplify the description, not all possible combinations of the technical features in the above embodiments are described. Only preferred embodiments of the present invention are presented. While the description is relatively specific and detailed, it should not be construed as limiting the scope of the present invention. As long as there are no conflicts in the combination of these technical features, they should be considered to be within the scope of this specification.

[0079] It should be noted that, for those skilled in the art, various modifications and improvements can be made without departing from the scope of the present invention, and these modifications and improvements fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A dynamic coordinated control method for a fuel cell system, characterized in that: The following steps are involved: Step S1: constructing a multi-objective optimization function with the goal of minimizing fuel consumption cost and maximizing fuel cell life, solving the multi-objective optimization function according to the real-time state of the fuel cell, and obtaining the optimal power reference trajectory of the fuel cell; Step S2: constructing a disturbance model based on the state of the fuel cell and the disturbance source, compressing the multi-dimensional disturbance model into a polyhedron feasible domain, and obtaining the range of action of the disturbance source; Step S3: calculating the pipe domain radius of the robust predictive control model according to the action range of the disturbance source, and shrinking the pipe domain radius according to a set safety margin; Step S4: minimizing the power trajectory tracking error, the control quantity change penalty, and the pipe domain violation penalty is used as the optimization goal of the robust predictive control model, and the robust predictive control model is constrained by the shrunken pipe domain radius. The robust predictive control model outputs the current density instruction of the fuel cell.

2. The dynamic coordinated control method of a fuel cell system according to claim 1, characterized in that: The expression of the multi-objective optimization function in step S1 is: ； ； ； ； In the above formula, is the fuel consumption cost function; is the life reliability function; T To optimize the total time step in the time domain; for Total system efficiency at the time; for System hydrogen consumption at the moment; It is the low calorific value of hydrogen; is the weight coefficient; The health status of the fuel cell; The remaining service life of the fuel cell; 、 They are the upper and lower limits of the equivalent state of charge and the upper and lower limits of the temperature of the fuel cell respectively; is the equivalent state of charge of the fuel cell; is the temperature of the fuel cell; is the fuel cell power; is the peak power of the fuel cell.

3. The dynamic coordinated control method of a fuel cell system according to claim 2, characterized in that: Solving the multi-objective optimization function in step S1 includes the following steps: Step S11: using a fast elite multi-objective genetic algorithm NSGA-II to solve the multi-objective optimization function to obtain a Pareto solution set of the multi-objective optimization function; Step S12: calculating the data distribution discreteness of each optimization objective in the Pareto solution set, and dynamically adjusting the weight of each optimization objective in the multi-objective optimization function according to the data distribution discreteness; Step S13: Calculate the closeness of the solutions in the Pareto solution set according to the adjusted weights, and take the solution with the largest closeness as the optimal solution.

4. The dynamic coordinated control method of a fuel cell system according to claim 3, characterized in that: In step S12, the expression for dynamically adjusting the weight of each optimization objective in the multi-objective optimization function according to the discreteness of the data distribution is: ； ； In the above formula, For the The weight of the optimization goal; For the The discreteness of the data distribution of the optimization objectives; is the number of solutions in the Pareto solution set; is the normalized Pareto solution set.

5. The dynamic coordinated control method of a fuel cell system according to claim 4, characterized in that: The expression for calculating the closeness of the solutions in the Pareto solution set according to the adjusted weights in step S13 is: ； ； ； In the above formula, is the closeness of the solution; For the i A solution The weighted Euclidean distance of For the i A solution The weighted Euclidean distance of For the i The solution in j The original value of the optimization target; For the The optimal value of an optimization objective; For the The worst value of the optimization objective; For the The maximum solution of an optimization objective; For the The minimum solution of an optimization objective.

6. The dynamic coordinated control method of a fuel cell system according to claim 1, characterized in that: The expression of the disturbance model in step S2 is: ； ； ； ； ； ； ； ； ； In the above formula, is the perturbation model; is the state matrix; is the input matrix; is the system state vector; Input for system status; is the perturbation coupling matrix; is the disturbance of the system; for The equivalent state of charge of the fuel cell at this moment; for The stack temperature at the moment; for The internal resistance of the battery stack at the moment; for The fuel cell current density at the time; for Load current fluctuation at each moment; for Internal resistance drift at any time; for Ambient temperature changes at all times; is the disturbance gain coefficient; The maximum charge that can be output sustainably in theory; is the sum of the specific heat capacities of the stack materials; is the thermal resistance; is the aging coefficient; is the Faraday efficiency; 、 are the rated power and voltage of the stack respectively; The fuel supply duration is determined by the hydrogen tank capacity; is the component quality; is the specific heat capacity.

7. The dynamic coordinated control method of a fuel cell system according to claim 6, characterized in that: The expression for compressing the multi-dimensional perturbation model into a polyhedron feasible region in step S2 is: ； ； ； ； In the above formula, is the initial feasible region of the perturbation model; is the disturbance center; is the generator matrix of the disturbance direction and amplitude; It means element-by-element addition; represents the unit hypercube; is the disturbance mean; is the disturbance amplitude boundary; , representing three perturbations.

8. The dynamic coordinated control method of a fuel cell system according to claim 1, characterized in that: In step S3, the pipe region radius is contracted according to the set safety margin, including the following steps: Step S31: determining a safety set and a maximum disturbance boundary according to the range of the disturbance source; Step S32: Calculating the control domain radius of the robust predictive control model according to the safety set and the maximum disturbance boundary; Step S33: Calculate the safety radius according to the set safety margin, determine whether the current pipe domain radius exceeds the safety radius, and if so, shrink the pipe domain radius according to the safety radius and update the pipe domain radius. The expression for updating the pipe domain radius is: ； ； ； ； ； In the above formula, is the updated pipe domain radius; is the attenuation factor; The weight coefficients representing the disturbance amplitude and safety constraints; is the radius of the pipe domain considering the influence of the disturbance amplitude; is the radius of the safety zone; is the decay rate; To control the cycle; is the current disturbance amplitude; is the maximum allowable disturbance amplitude; is the initial radius under the nominal system; is the current pipe domain radius; is the safety constraint violation amount; is the current temperature of the fuel cell; is the maximum temperature for safety constraints; For safety margin.

9. The dynamic coordinated control method of a fuel cell system according to claim 8, characterized in that: Step S31 The following steps are involved: Step S311: Define the initial security set :If the system status , then for all perturbation amplitude boundaries and ,have ,in is the perturbation set, is the time variable; Step S312: Define the attenuation condition of the fuel cell system, substitute the attenuation condition into the disturbance model and convert it into a matrix form to obtain a linear matrix inequality, solve the linear matrix inequality, and obtain the initial safety set The boundary of and the maximum disturbance boundary of the disturbance source; Step S313: Verify the initial security set Whether it converges, if not, adjust dynamically Otherwise, output the safe set.

10. The dynamic coordinated control method of a fuel cell system according to claim 1, characterized in that: The optimization objective and constraint expressions of the robust predictive control model in step S4 are: ； ； ； In the above formula, The cost function of the optimization objective of the robust predictive control model; To control the time domain length; For the system State variables at the moment; is the optimal power reference trajectory; is the state weight matrix; For the system Control increments of moments; Enter the weight matrix; is the pipe domain radius weight; is the current pipe domain radius; is a constraint condition; is the current temperature; 、 are the minimum and maximum values ​​of temperature respectively; is the control variable of the robust predictive control model; 、 are the minimum and maximum current densities of the fuel cell stack, respectively; is a state variable.

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