Solid oxide fuel cell carbon deposition-aware model predictive control method and system

Abstract

The present application belongs to the technical field of solid oxide fuel cell control and optimization, and particularly relates to a solid oxide fuel cell carbon deposition sensing model predictive control method and system. A six-dimensional measurement output vector of a system is collected in a sampling period, and algebraic loops in a measurement feedback channel are eliminated; thermal dynamic equations of each component of an auxiliary equipment system are embedded into a predictive trajectory linearized nonlinear model predictive control prediction model; an augmented cost function is constructed; and a burner exhaust temperature is taken as an input of a heat source side of each component of the auxiliary equipment system after being delayed by a second unit. The present application completely establishes MD / BR double-path carbon deposition dynamics and catalyst activity attenuation models, eliminates prediction deviation caused by neglecting BOP thermal inertia, and completely eliminates algebraic loops of the system by using a double-unit delay structure, thereby ensuring numerical stability of simulation and engineering implementation.

Description

Technical Field

[0001] This invention relates to the field of solid oxide fuel cell control and optimization technology, specifically to a predictive control method and system for carbon deposition sensing models in solid oxide fuel cells. Background Technology

[0002] Solid oxide fuel cells (SOFCs) are fourth-generation power generation technology, boasting advantages such as high power generation efficiency, all-solid-state structure, and wide fuel applicability, showing promising application prospects in large-scale power generation, distributed combined heat and power (CHP), and transportation. Methane direct internal reforming (DIR-SOFC) involves three parallel reactions at the anode: methane steam reforming (MSR), water-gas shift (WGS), and electrochemical oxidation, expanding the system state dimension from the existing 3-state hydrogen model to 11 states. When the anode water-to-carbon ratio (S / C) falls below the thermodynamic safety lower bound, both methane cracking (MD) and the Boudouard reverse reaction (BR) pathways will produce coke deposits on the Ni-YSZ anode catalyst surface, leading to irreversible degradation of catalyst activity. This is the core safety risk restricting the long-term reliable operation of SOFCs.

[0003] In practical engineering, the DIR-SOFC system includes a fuel preheater and a pre-reforming reactor (thermal time constant). The air heat exchanger and blower / compressor, among other BOP components, all exhibit thermal response lags ranging from several seconds to tens of seconds. Existing multi-model predictive control methods for SOFCs (such as CN107991881B and CN118380611A) are all designed for simplified hydrogen SOFCs. They neither establish a complete carbon deposition kinetic model for the methane 11-state system nor embed the thermal dynamics of each BOP component into the predictive equations, thus failing to achieve coordinated optimization of the carbon deposition sensing and BOP integrated system. The proposed NPLPT algorithm is only applicable to the single-input structure of 3-state hydrogen SOFC and does not have the ability to actively suppress carbon deposition. Summary of the Invention

[0004] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0005] To address the aforementioned technical problems, according to one aspect of the present invention, the present invention provides the following technical solution:

[0006] A carbon deposition sensing model predictive control method for solid oxide fuel cells is applied to a methane direct internal reforming power generation system containing a solid oxide fuel cell stack and auxiliary equipment system. The auxiliary equipment system includes a fuel preheater, a pre-reforming reactor, an air heat exchanger, a blower / compressor, and a burner. The method is as follows: A six-dimensional measurement output vector of the system is acquired during the sampling period, buffered with a first unit delay, and then fed into a linearized nonlinear model predictive control controller along the predicted trajectory to eliminate algebraic loops in the measurement feedback channel. The thermal dynamic equations of each component of the auxiliary equipment system are embedded into the predicted trajectory linearized nonlinear model predictive control prediction model, constructing a 17th-20th order BOP integrated extended prediction model based on the original 11-state stack ordinary differential equation system. The 11 states include the anode gas phase partial pressure. Temperature in Zone 3: The carbon deposit coverage Cc and catalyst activity a are used as the three-dimensional control inputs of fuel flow rate, steam flow rate and air flow rate. An augmented cost function is constructed, which includes output tracking cost, control smoothing penalty and four-level soft constraint penalty function. In the prediction time domain, the predictive control is linearized through the linearization of the nonlinear model of the prediction trajectory and iteratively linearized to transform it into a quadratic programming problem for rolling optimization. After the iteration converges, the first element of the optimal control sequence is applied to the system. The burner exhaust temperature is used as the heat source side input of each component of the stack auxiliary equipment system after a second unit delay. The algebraic loop in the heat recovery closed loop is eliminated and the cycle returns to the next rolling optimization.

[0007] As a preferred embodiment of the carbon deposition sensing model predictive control method for solid oxide fuel cells described in this invention, the six-dimensional measurement output vector is defined as follows:

[0008]

[0009] In the formula This is the DC output voltage of the fuel cell stack. For fuel utilization rate, The total carbon deposition rate per unit catalyst area. This is the lowest temperature of the fuel cell stack. The temperature difference between the inlet and outlet of the anode along the axial direction. The water-to-carbon ratio; the first unit delay sampling period The initial condition is taken as the steady-state measurement value under rated operating conditions; the second unit delay initial condition is taken as the rated exhaust temperature of the burner.

[0010] As a preferred embodiment of the carbon deposition sensing model predictive control method for solid oxide fuel cells described in this invention, the thermal hysteresis dynamics of the fuel preheater and the air heat exchanger are each described by the following first-order transfer function:

[0011]

[0012] In the formula For heat exchange efficiency, Let be the thermal time constant, and s be the Laplace operator; the above equation is discretized using the Tustin bilinear transform, and the discretization coefficients are:

[0013]

[0014] In the formula Sampling period; fuel preheater air heat exchanger The pre-reformer maintains its persistent thermal state using a lumped-parameter first-order ordinary differential equation, with a thermal time constant... The blower / compressor uses a linearized state-space equation to describe the flow-speed dynamics, with a thermal time constant. The burner calculates the exhaust temperature using quasi-steady-state algebraic equations; combining the above component equations with the original 11-state SOFC stack ODE system, the following extended state equations are formed:

[0015]

[0016] In the formula ∈ℝⁿ (n=17~20) is the extended state vector. For three-dimensional control input, This represents the external disturbance vector. To integrate extended nonlinear equations for BOP, This is the output equation.

[0017] As a preferred embodiment of the carbon deposition sensing model predictive control method for solid oxide fuel cells described in this invention, the augmented cost function is composed of an output tracking cost, a control increment smoothing penalty, and a four-level soft constraint penalty function, specifically in the following form:

[0018]

[0019] In the formula, J(k) is the sum of output tracking cost and control smoothing penalty. The penalty coefficient is the carbon deposition rate constraint coefficient. This is the safe upper limit for carbon deposition rate; This is the penalty coefficient for fuel utilization rate constraints. For fuel utilization rate, it is a two-sided slack variable; This is the axial thermal gradient constraint penalty coefficient. This is the upper limit of the thermal gradient safety limit; This is the minimum temperature constraint penalty coefficient. The lower limit of temperature safety; the four-level penalty coefficient meets the requirements. The levels differ by a factor of 10 to ensure that high-priority carbon security constraints are always satisfied when multiple constraints of NPLPT are activated simultaneously; the output tracking weight matrix adopts a Kronecker block diagonal structure. ,in For voltage tracking weights, Set a weight for the water-to-carbon ratio at a set point. For thermal gradient penalty weights, , , The corresponding weight is zero, and it is handled by the soft constraint penalty function.

[0020] As a preferred embodiment of the carbon deposition sensing model predictive control method for solid oxide fuel cells described in this invention, the linearization of the predictive trajectory nonlinear model predictive control optimization adopts a voltage setpoint that adaptively droops with the load:

[0021]

[0022] In the formula This is the voltage reference value under rated load; The droop factor is [V / A]; Inom is the rated load current. The voltage setpoint is set as the lower bound; when the load exceeds the rated load, the setpoint droops linearly with the load, making the predicted trajectory linearized. The nonlinear model predictive control optimization objective always lies within the thermodynamically feasible region of the auxiliary equipment system integration system, preventing the optimizer from using all control margin to chase unattainable voltage targets and systematically ignoring carbon safety constraints; after the quadratic programming solution is completed, the water-carbon ratio floor constraint is implemented using a hard projection method: when the steam flow rate obtained from the quadratic programming... At that time, with replace ,in This is the thermodynamic safety lower bound for the water-to-carbon ratio. The current molar flow rate of methane inlet; this hard projection is executed after the QP solution is completed, without changing the convexity of the QP problem itself, and together with the soft constraint carbon deposition rate constraint, it constitutes a dual guarantee mechanism for carbon deposition safety;

[0023] The air flow After integration with the auxiliary equipment system, the constant boundary conditions activate the independent control variables for predictive control of the linearized nonlinear model of the predicted trajectory. The augmented cost function is further expanded with an additional parasitic power consumption efficiency penalty term, resulting in:

[0024]

[0025] In the formula Parasitic power consumed by the blower / compressor This refers to the DC output power of the fuel cell stack. The efficiency penalty coefficient is dynamically adjusted based on the current carbon deposition rate margin: a larger value is used when the carbon deposition rate margin is sufficient to prioritize reducing parasitic power consumption, and a smaller value is used when the carbon deposition rate is close to the safety limit to prioritize ensuring carbon safety. The value range is [0.2, 0.4]; therefore, The variable has been upgraded from a single thermal management variable to a dual-objective game variable of efficiency and carbon security under the predictive control framework of a linearized nonlinear model for predictive trajectory.

[0026] As a preferred embodiment of the carbon deposition sensing model predictive control method for solid oxide fuel cells described in this invention, the specific solution method for the predictive trajectory linearization nonlinear model predictive control iterative linearization framework is as follows: Define a QP decision variable vector consisting of a three-dimensional control increment sequence within the Nu-step control time domain. ∈ Through the lower triangular all-one integral matrix The control increment sequence is converted into a control quantity sequence; the predicted trajectory is linearized using a nonlinear model. The first-order Taylor expansion of the predicted trajectory in the t-th iteration is performed around the predicted trajectory in the (t-1)-th iteration. The correction formula for the predicted output is:

[0027]

[0028] In the formula For the predicted output of the t-th iteration at step p, ∈ {6×3Nu} The numerical Jacobian matrix at the current iteration. Let be the integral matrix. The third term is the decision variable for the current iteration. The bias correction term is used for trajectory linearization; the Jacobian matrix is ​​calculated using the central difference numerical method. The ODE white-box prediction engine performs numerical integration of the physical equations in each prediction step to achieve accurate prediction of strongly nonlinear physical processes such as methane steam reforming nonlinearity, coking positive feedback, and catalyst activity decay; the convergence criterion for the predictive control iteration of the linearized nonlinear model is:

[0029]

[0030] In the formula The convergence threshold is denoted by ||·|2|, which represents the Euclidean norm; the maximum number of iterations is reached. The current result is output as the suboptimal solution, ensuring that within the sampling period... The calculation is completed within the system; after the augmented cost function is rearranged into the standard QP form, the solver is called to obtain the optimal control increment, and the final control command is output after hard projection through the water-carbon ratio floor constraint.

[0031] As a preferred embodiment of the carbon deposition sensing model predictive control method for solid oxide fuel cells described in this invention, the prediction coverage ratio is defined as follows: Quantitative criteria for the performance boundary of predictive control using linearized nonlinear models of predicted trajectory, among which... Let N be the thermal time constant of the pre-reforming reactor, and N be the number of time-domain steps in the predictive control of the linearized nonlinear model of the predicted trajectory; when At that time, the NPLPT prediction window could not fully cover the thermal response of the pre-reformer, and the carbon deposition rate constraint had the risk of being estimated non-conservatively; therefore, a proportional feedforward gain compensation instruction was superimposed on the QP solution results:

[0032]

[0033] In the formula For the current voltage error, As a feedforward gain, the compensation command is superimposed on the fuel flow optimal control command; The tuning principle is as follows: Under engineering constraints, ensure that the peak carbon deposition rate under typical step load conditions does not exceed the safe upper limit. Feedforward compensation and soft-constraint carbon deposition rate constraints together constitute Carbon security assurance strategies in scenario 1.

[0034] A carbon deposition sensing model predictive control system for solid oxide fuel cells includes:

[0035] BOP subsystem module: includes fuel preheater unit, pre-reform reactor unit, air heat exchanger unit, blower / compressor unit and burner unit, each unit is connected through heat recovery loop;

[0036] SOFC fuel cell stack module performs direct internal reforming of methane through electrochemical conversion, outputting DC output voltage Vdc and fuel utilization rate. Carbon deposition rate Axial temperature difference ΔT, minimum temperature S / C ratio (water to carbon);

[0037] Measurement convergence module, acquires six-dimensional measurement vectors ;

[0038] The first-generation loop elimination unit is set in the feedback channel between the measurement convergence module and the linearized nonlinear model predictive control module along the predicted trajectory. It includes a single-step unit delay and the initial condition is set to the rated steady-state measurement value.

[0039] The second-generation number loop elimination unit is located between the exhaust temperature output terminal of the burner unit and the input terminal of the BOP heat source side, and includes a single-step unit delay. The initial condition is the rated exhaust temperature of the burner.

[0040] Predictive trajectory linearization nonlinear model predictive control controller module, with six-dimensional measurement vector y and load current. Using the 17th to 20th order BOP ensemble extended prediction model as input, the augmented cost function containing four levels of soft constraint penalty functions (P1 to P4) is solved iteratively through an ordinary differential equation white-box prediction engine, numerical Jacobian matrix, and quadratic programming. Output fuel flow Steam flow rate and airflow Three-dimensional control commands;

[0041] The control command allocation module routes the three-dimensional control commands to the fuel channel, steam channel, and air channel, respectively.

[0042] As a preferred embodiment of the solid oxide fuel cell carbon deposition sensing model predictive control system described in this invention, the optimization solution of the predicted trajectory linearized nonlinear model predictive control controller module uses a 17th to 20th order extended state ODE white-box prediction engine to perform multi-step forward simulation in each sampling period, achieving accurate prediction of strongly nonlinear physical processes such as methane steam reforming nonlinearity, coking positive feedback, and catalyst activity decay; the sensitivity of the predicted output to the three-dimensional control increment is described by the central difference numerical Jacobian matrix, and the nonlinear effects are accurately captured by recalculating around the updated predicted trajectory in each iteration of the predicted trajectory linearized nonlinear model predictive control; a damped update strategy ensures the numerical stability of the iteration; the iteration termination is controlled by a convergence threshold and a maximum number of iterations; and the optimal control command is output after the solution result is hard-projected by the water-to-carbon ratio floor constraint.

[0043] As a preferred embodiment of the solid oxide fuel cell carbon deposition sensing model predictive control system described in this invention, the pre-reforming reactor unit is the single component with the largest thermal time constant in the BOP subsystem module, and its thermal time constant... ;when When the value is greater than 1, the predictive trajectory linearization nonlinear model predictive control module automatically activates the proportional feedforward gain. A compensation mechanism feeds forward the voltage error to the fuel flow control command to mitigate the risk of non-conservative estimation of carbon deposition rate constraints caused by the inability of the prediction window to fully cover the pre-reformer thermal response; the blower / compressor unit calculates parasitic power consumption in real time. The augmented cost function of the predictive control is predicted by linearizing the nonlinear model of the predicted trajectory. Medium efficiency penalty item With carbon deposition rate constraint The synergistic trade-offs constitute a closed loop of synergistic optimization for the dual objectives of efficiency and carbon security.

[0044] Compared with the prior art, the beneficial effects of this invention are: This invention, for the first time, extends the control object of methane DIR-SOFC to an 11-state physical white box ODE, fully establishes a dual-pathway carbon deposition kinetics and catalyst activity decay model for MD / BR, and achieves control over the coking rate within the MPC framework. Online sensing and active suppression; the thermal dynamics of each BOP component are embedded in the NPLPT prediction expansion using the Tustin discretized first-order transfer function and lumped parameter ODE, eliminating prediction bias caused by ignoring the thermal inertia of the BOP; the four-level soft constraint augmented cost function of P1 to P4 is... The hierarchical design ensures the absolute priority of carbon security constraints, while the addition of a parasitic power consumption efficiency penalty term upgrades airflow into a dual-objective game variable of efficiency and carbon security; a proposal is made... Predicting coverage ratio criterion, and in >1. Feedforward compensation ensures the effectiveness of carbon security constraints in the scenario; the dual-unit delay structure completely eliminates the algebraic loop in the system, ensuring the numerical stability of simulation and engineering implementation. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and detailed embodiments. 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. Wherein:

[0046] Figure 1 This is an overall structural block diagram of the DIR-SOFC closed-loop control system with BOP auxiliary equipment in one embodiment of the present invention;

[0047] Figure 2 This is a flowchart of the iterative solution algorithm for the MPC-NPLPT controller of the present invention in one embodiment;

[0048] Figure 3 The closed-loop simulation response curve of the DIR-SOFC system of the present invention under the S1 step load condition in one embodiment is shown. Detailed Implementation

[0049] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0050] Secondly, the present invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of the present invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of the present invention. In addition, actual fabrication should include three-dimensional spatial dimensions of length, width, and depth.

[0051] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0052] This invention provides a carbon deposition sensing model-predictive control (MPC) method for a solid oxide fuel cell (SOFC) stack auxiliary equipment system (Balance of Plant, BOP) integrated system. It is applied to a direct internal reforming (DIR) methane power generation system containing an SOFC stack and a BOP. The BOP includes a fuel preheater, a pre-reforming reactor, an air heat exchanger, a blower / compressor, and a burner. During the sampling period, a six-dimensional measurement output vector of the system is acquired, buffered with a first unit delay, and then fed into a nonlinear predictive control with linearization along predicted trajectory (NPLPT) controller to eliminate algebraic loops in the measurement feedback channel. The thermal dynamic equations of each BOP component are embedded into the NPLPT prediction model, within the original 11-state stack ordinary differential equations. Based on the Equation (ODE) system, an integrated extended prediction model of BOP of order 17-20 is constructed. Using three-dimensional control inputs of fuel flow, steam flow, and air flow, an augmented cost function is constructed, which includes output tracking cost, control smoothing penalty, and four-level soft constraint penalty function. In the prediction time domain, it is transformed into a quadratic programming (QP) problem through NPLPT iterative linearization and then solved by rolling optimization. After iterative convergence, the first element of the optimal control sequence is applied to the system. The burner exhaust temperature is used as the heat source input of each component of BOP after a second unit delay to eliminate the algebraic loop in the heat recovery closed loop and return to the next cycle for rolling optimization.

[0053] Specifically, an eleven-state physical white box ODE system for methane DIR-SOFC was established to fully describe the strong nonlinear coupling between MSR / WGS chemical kinetics, MD / BR dual-path carbon deposition kinetics, and three-zone thermal dynamics. The thermal dynamic equations of each BOP component were embedded into the NPLPT prediction model in the form of first-order transfer functions or lumped parameter ODEs. An integrated extended prediction model of BOP was constructed from the 11th state to the 17th to 20th order. The algebraic loops in the heat recovery closed loop and the measurement feedback channel were eliminated by a dual-unit delay scheme.

[0054] The acquisition system uses a six-dimensional measurement output vector with fuel flow, steam flow and air flow as three-dimensional control inputs. It constructs an augmented cost function that includes output tracking cost, control smoothing penalty and four-level soft constraint penalty functions from P1 to P4. It also adopts a voltage setpoint mechanism that droops with load and a water-carbon ratio floor constraint hard projection to form a dual guarantee for carbon security.

[0055] The BOP ensemble extended prediction model is linearized at the trajectory level using the NPLPT iterative linearization framework. Closed-loop rolling optimization is achieved within each sampling period through the ODE white-box prediction engine, numerical Jacobian matrix, and quadratic programming (QP) solution. A prediction coverage ratio is proposed. As a quantitative criterion for the control performance boundary, a proportional feedforward gain compensation strategy was designed to address the engineering constraint that the prediction time domain is shorter than the thermal response time of the pre-reformer.

[0056] In application, this invention first establishes an 11-state physical white-box (ODE) model for the methane DIR-SOFC system, embedding the thermal dynamics of each component of the BOP into the NPLPT prediction model to form an extended prediction model of order 17-20; then, using three-dimensional control inputs, it constructs an augmented cost function with four levels of soft constraints. The optimization problem is transformed into a QP solution through NPLPT iterative linearization; finally, the carbon deposition rate is controlled by a dual constraint of adaptive droop voltage setpoint and water-to-carbon ratio floor. By keeping the constraints within the safety limits, the BOP integrated system-level control of the methane DIR-SOFC system is achieved.

[0057] The six-dimensional measurement output vector of the acquisition system is defined as follows:

[0058] (1)

[0059] In the formula, Vdc is the DC output voltage of the fuel cell stack [V]; For fuel utilization rate; The total carbon deposition rate per unit catalyst area [mol / (m²·s)]; The lowest temperature of the fuel cell stack [K]; The axial inlet and outlet temperature difference of the anode [K]; Water-to-carbon ratio; first unit delay sampling period The second unit delays the initial condition by taking the burner's rated exhaust temperature.

[0060] The method for constructing the BOP integrated extended prediction model is as follows: the thermal hysteresis dynamics of the fuel preheater and the air heat exchanger are each described by the following first-order transfer functions:

[0061] (2)

[0062] In the formula, ε is the heat transfer efficiency; τ is the thermal time constant [s]; s is the Laplace operator; fuel preheater air heat exchanger blower / compressor The pre-reformer maintains a persistent thermal state using a lumped-parameter first-order ODE, with a thermal time constant of [missing information]. This is the largest single dynamic lag in BOP;

[0063] Equation (2) is discretized using the Tustin bilinear transform, and the discretization coefficients are:

[0064] (3)

[0065] In the formula, Ts is the sampling period; by combining the equations of each BOP component with the original 11-state SOFC stack ODE system, the extended state equations are formed:

[0066] (4)

[0067] In the formula ∈ℝⁿ (n=17~20) is the extended state vector; u = [ , , ]ᵀ represents the three-dimensional control input; v represents the external disturbance vector; h represents the six-dimensional output equation.

[0068] The extended Nernst open-circuit voltage equation for mixed fuels in the ODE system is:

[0069] (5)

[0070] In the formula, N0 is the number of battery cells connected in series in the stack; E0 is the standard electromotive force; R and F are the universal gas constant and Faraday constant, respectively; , , , The partial pressures [atm] for H2, CO, H2O at the anode and O2 at the cathode are respectively; β is the electrochemical activity coefficient of CO relative to H2; the activation polarization loss adopts the Tafel approximation, the lumped equivalent internal resistance is used for ohmic polarization, and the limiting diffusion model is used for concentration polarization.

[0071] (6)

[0072] (7)

[0073] (8)

[0074] In the formula 0 is the Tafel intercept [V]; βT is the Tafel slope; If is the effective electrochemical reaction current density [A / m²]; r is the equivalent ohmic internal resistance [Ω]; IL is the limiting diffusion current density [A / m²]; and the stack output voltage is... The MPC prediction model incorporates estimation of unmeasured disturbances. Compensation is performed to ensure no steady-state tracking.

[0075] The system fuel utilization rate and water-to-carbon ratio are defined as follows:

[0076] (9)

[0077] (10)

[0078] In the formula Total load current [A]; , The molar flow rates of H2 and CO at the anode inlet are respectively [mol / s]. The molar flow rate of water vapor at the anode inlet is [mol / s]. The molar flow rate of imported methane [mol / s]; Subject to P2 soft constraint: ∈[0.72, 0.88]; the lower bound of the thermodynamic safety of S / C is taken as... =2.0, the transmission dynamics of the control input to the actual flow rate at the anode / cathode inlet are described using Tustin bilinear discretization:

[0079] (11)

[0080] In the formula Here are the Tustin discretization coefficients; K is the steady-state gain of each channel; These correspond to the effective current If and the molar flow rate of H2 at the anode inlet, respectively. Anode inlet water vapor molar flow rate .

[0081] The carbon deposition kinetic model includes two carbon deposition pathways, MD and BR, and its rate equation is as follows:

[0082] (12)

[0083] (13)

[0084] (14)

[0085] In the formula , These are the pre-path exponential factors for MD and BR, respectively; a(k)∈[0,1] represents the catalyst activity state variable; , The partial pressure of CH4 and CO at the anode [atm]; , The activation energies for each pathway reaction are [J / mol]. (k) is the direct monitoring quantity of the P1 soft constraint; in equation (9) Superlinear dependence is the mathematical root of the positive feedback phenomenon in coking; the dynamic equation for coking coverage Cc and catalyst activity a is:

[0086] (15)

[0087] (16)

[0088] In the formula The rate of decarbonization by steam oxidation; Carbon deposit coverage; Cc is the catalyst deactivation rate constant (Arrhenius type); Cc and a constitute the 10th and 11th ODE states of the system, and are recursively deduced by forward Euler discretization with Ts=1 s.

[0089] The augmented cost function consists of the output tracking cost, the control smoothing penalty, and a four-level soft constraint penalty function. The objective function is:

[0090] (17)

[0091] In the formula, E=R(k)−Ŷ(k) is the N-step tracking error stacking vector in the prediction time domain (∈ℝ^{6N}); To output the tracking weight matrix; Control the incremental smoothing weight matrix; , , , The penalty coefficients for the four levels, P1 to P4, are respectively satisfied. (The difference between each level is 10 times). This is the safe upper limit for carbon deposition rate; For fuel utilization rate, it is a two-sided slack variable; This is the upper limit of the thermal gradient safety limit; Temperature safety lower limit; airflow After activation as an independent control variable, a parasitic power efficiency penalty term is added. ,Will It has been upgraded to a dual-objective game variable of efficiency and carbon security.

[0092] NPLPT optimization employs a voltage setpoint that droops with load adaptation:

[0093] (18)

[0094] In the formula This is the voltage reference value under rated load; The droop factor is [V / A]; Inom is the rated load current. This serves as the lower bound of the voltage setpoint; when the load exceeds the rated capacity, the setpoint droops linearly with the load to prevent the optimizer from systematically ignoring carbon safety constraints; after QP is solved, a hard projection of the water-carbon ratio floor constraint is performed: when QP is obtained... When qH2O*(k), then Together with the P1 soft constraint, it constitutes a dual guarantee mechanism for carbon security.

[0095] The specific solution method for the NPLPT iterative linearization framework is as follows: In the t-th iteration of NPLPT, a first-order Taylor expansion is performed around the predicted trajectory of the (t-1)-th iteration, and the correction formula for the prediction output is:

[0096] (19)

[0097] In the formula This is the predicted output of the (t-1)th iteration at step k+p; ∈ The numerical Jacobian matrix at the current iteration is calculated using the central difference method: ; The matrix is ​​a lower triangular integral matrix of all 1s; the third term is the trajectory linearization bias correction term, which is the key structure for ensuring the nonlinear convergence of NPLPT; the optimal solution is obtained by solving the QP problem. The iterative convergence criterion is:

[0098] (20)

[0099] In the formula The convergence threshold; reaching the maximum number of iterations. The current result is output as the suboptimal solution; the augmented cost function is then rearranged into the standard QP form and called. The solver obtains the optimal control increment and outputs the final control command after hard projection through the water-carbon ratio floor constraint.

[0100] Define prediction coverage ratio This serves as a quantitative criterion for the control performance boundary of NPLPT, where... Let N be the thermal time constant of the pre-reforming reactor, and N be the prediction time-domain step number; when At that time, the prediction window could not fully cover the thermal response of the pre-reformer, and the carbon deposition rate constraint had the risk of being estimated non-conservatively; therefore, a proportional feedforward gain compensation instruction was superimposed on the QP solution results:

[0101] (twenty one)

[0102] In the formula The feedforward gain is used; the compensation command is superimposed on the optimal fuel flow control command. The tuning principle is as follows: Under constraints, under typical step load conditions Peak value not exceeding Feedforward compensation and P1 soft constraint together constitute Carbon security assurance strategies in scenario >1.

[0103] The present invention also provides a carbon deposition sensing model predictive control (MPC) system for an integrated system of a solid oxide fuel cell (SOFC) stack auxiliary equipment system (BOP), comprising:

[0104] The BOP subsystem module includes a fuel preheater unit, a pre-reforming reactor unit, an air heat exchanger unit, a blower / compressor unit, and a burner unit, all connected via a heat recovery loop; the SOFC stack module performs the electrochemical conversion of direct internal reforming (DIR) of methane, outputting DC output voltage Vdc and fuel utilization rate. Carbon deposition rate Axial temperature difference ΔT, minimum temperature Water-to-carbon ratio (S / C); measurement convergence module, acquiring six-dimensional measurement vectors. The first-generation number loop elimination unit is located in the feedback channel between the measurement convergence module and the linearized nonlinear model predictive control (NPLPT) controller module along the predicted trajectory. It includes a single-step unit delay, and the initial condition is set to the rated steady-state measurement value. The second-generation number loop elimination unit is located between the exhaust temperature output terminal of the burner unit and the input terminal of the BOP heat source side. It includes a single-step unit delay, and the initial condition is the rated exhaust temperature of the burner. The NPLPT controller module uses a six-dimensional measurement vector y and the load current. Using the 17th to 20th order BOP ensemble extended prediction model as input, the augmented cost function containing four levels of soft constraint penalty functions (P1 to P4) is solved iteratively through an ordinary differential equation (ODE) white-box prediction engine, numerical Jacobian matrix, and quadratic programming (QP). Output fuel flow Steam flow rate and airflow Three-dimensional control commands; control command allocation module, which routes the three-dimensional control commands to the fuel passage, steam passage and air passage respectively.

[0105] The optimization solution of the NPLPT controller module uses a 17-20 order extended state ODE white-box prediction engine to perform multi-step forward simulations in each sampling period, achieving accurate prediction of strongly nonlinear physical processes such as methane steam reforming (MSR) nonlinearity, coking positive feedback, and catalyst activity decay. The sensitivity of the predicted output to the three-dimensional control increment is described by the central difference numerical Jacobian matrix, and it is recalculated around the updated prediction trajectory in each NPLPT iteration to accurately capture nonlinear effects. A damped update strategy ensures the numerical stability of the NPLPT iteration. The iteration termination is controlled by a convergence threshold and a maximum number of iterations. The solution result is output as the optimal control command after being hard-projected by the water-to-carbon ratio floor constraint.

[0106] The pre-reformer reactor unit is the single component with the largest thermal time constant in the BOP subsystem module. ;when When the value is greater than 1, the NPLPT controller module automatically activates the proportional feedforward gain. A compensation mechanism feeds forward voltage errors to fuel flow control commands to mitigate the risk of non-conservative estimation of carbon deposition rate constraints caused by the inability of the prediction window to fully cover the pre-reformer thermal response; the blower / compressor unit calculates parasitic power consumption in real time. augmented cost function through NPLPT Medium efficiency penalty item With carbon deposition rate constraint The synergistic trade-offs constitute a closed loop of synergistic optimization for the dual objectives of efficiency and carbon security.

[0107] Example 1

[0108] refer to Figures 1-2 This embodiment introduces a carbon deposition sensing model predictive control method for a solid oxide fuel cell BOP integrated system, including:

[0109] Establish a methane DIR-SOFC eleven-state physical white-box ODE system, where the states include the anolyte gas phase partial pressure (ODE). ), three-zone temperature ( The thermal dynamic equations of each BOP component are embedded into the NPLPT prediction model to construct an integrated extended prediction model of BOP of order 17 to 20, with double-unit delay to eliminate algebraic rings.

[0110] With three-dimensional control input An augmented cost function containing four levels of soft constraint penalty functions from P1 to P4 is constructed, and carbon security is ensured by a voltage setpoint that droops with load adaptation and a water-carbon ratio floor constraint.

[0111] The NPLPT iterative linearization framework achieves closed-loop rolling optimization through the ODE white-box prediction engine, numerical Jacobian matrix, and QP solution. After iterative convergence, the first element of the optimal control sequence is applied to the system to ensure that the carbon deposition rate is continuously constrained within the safe upper limit under variable load conditions and that the output voltage quickly and accurately tracks the adaptive setpoint.

[0112] Example 2

[0113] Based on Example 1, this example also incorporates the following design:

[0114] The system's six-dimensional measurement output vector is shown in equation (1); the first unit delay sampling period The initial conditions are taken as the steady-state measurement values ​​under rated operating conditions: The second unit delay initial condition is taken as the burner's rated exhaust temperature of 1173 K.

[0115] The BOP integrated extended prediction model is shown in equations (2) to (4). Substituting the parameters of each component into equation (3) yields the Tustin discretization coefficient: fuel preheater ( =9 s, ε=0.95): =0.895, =0.050; Air heat exchanger ( =11 s, ε=0.92): =0.913, =0.040; Blower / Compressor ( =8 s): =0.882, =0.059; the pre-reformation reactor is described by the lumped parameter ODE ( =25 s); after the ODE of the 11-state stack is combined, the extended state dimension n=18, as shown in equation (4).

[0116] The Nernst open-circuit voltage is shown in equation (5). In this embodiment, N0 = 90, E0,ref = 1.18 V. =2.304×10 -4 V / K, β=0.62; the three types of polarization losses are shown in equations (6) to (8), r=0.126 Ω, IL=800 A / m²; after introducing disturbance compensation d(k) into the MPC prediction model, the steady-state deviation under each simulation condition is | - |<0.5 V.

[0117] Fuel utilization rate and water-carbon ratio are shown in equations (9) to (10) in this embodiment. ∈[0.72, 0.88] (corresponding to P2 soft constraint), S / C floor constraint =2.0; Effective current path ( =0.8 s): ae=0.231, be=0.385; fuel flow channel ( =5 s, =4): =0.818, =0.210; Steam flow channel (after BOP integration) ): =0.875, =0.059.

[0118] The carbon deposition rate is shown in equations (12) to (13). In this embodiment, the MD path is: =2.1×10 -3 mol / (m²·s·atm), =9.6×10 4 J / mol; BR pathway: =3.4×10 -5 mol / (m²·s·atm²), =1.1×10 5 J / mol; =5×10 -8 mol / (m²·s); the equations for coking and deactivation are shown in equation (16), kdeact,0 = 1.2 × 10⁻ 6 s⁻¹, n=2, initial conditions Cc(0)=0, a(0)=1.

[0119] The augmentation cost function is shown in equation (17). In this embodiment, the weight parameters are taken as follows: =5, =150, =10; The penalty coefficients for the four levels are as follows: ;satisfy T, with each level differing by a factor of 10; =80 K, =1023 K; The efficiency penalty coefficient ρeff is 0.40 when the carbon deposition rate margin is sufficient, and 0.20 when it is close to the safety limit.

[0120] The adaptive droop voltage setpoint is shown in equation (18). In this embodiment, =130 V, =0.06 V / A, , =300 A / m²; Substitute into 400 A / m² load for verification:

[0121]

[0122] That is, under a load of 400 A / m², the setpoint automatically drops to 124 V, which is within the thermodynamically feasible region of the BOP integrated system.

[0123] The NPLPT iterative formula is shown in equation (19). In this embodiment, the prediction time domain N = 30 steps and the control time domain Nu = 7 steps. =6, =1×10 -4 Central difference step size Under warm start, convergence typically takes t≤4 steps, with each sampling period taking approximately 600 ms to compute, satisfying the real-time requirement of Ts=1 s.

[0124] The predicted coverage ratio criterion and feedforward compensation are shown in Equation (21). In this embodiment... N=30 steps:

[0125]

[0126] The predicted time domain can fully cover the thermal response of the pre-reformer, and the feedforward compensation is in standby mode; if computational resources are limited, N=15 steps are used ( If =1.67>1), then feedforward compensation is activated. Adjusted according to typical step operating conditions Peak value not exceeding .

[0127] refer to Figure 3 Under the above parameter settings, and with the MPC-NPLPT controller in operation, the output voltage Vdc can quickly and accurately track the adaptive droop setpoint of 124 V after the load jumps from 300 A / m² to 400 A / m²; carbon deposition rate Always constrained Within this range, the water-to-carbon ratio (S / C) remains constant throughout the variable load process. =2.0 or higher, fuel utilization rate It consistently maintains a safe range [0.72, 0.88], demonstrating good control performance.

[0128] Although the present invention has been described above with reference to embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, as long as there is no structural conflict, the features in the disclosed embodiments can be combined with each other in any manner. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A predictive control method for carbon deposition sensing model in solid oxide fuel cells, characterized in that, A direct internal reforming methane power generation system is applied to a solid oxide fuel cell stack and auxiliary equipment system. The auxiliary equipment system includes a fuel preheater, a pre-reforming reactor, an air heat exchanger, a blower / compressor, and a burner. The method is as follows: A six-dimensional measurement output vector of the system is acquired during a sampling period, buffered with a first unit delay, and then fed into a linearized nonlinear model predictive control controller along a predicted trajectory to eliminate algebraic loops in the measurement feedback channel. The thermal dynamic equations of each component of the auxiliary equipment system are embedded into the predicted trajectory linearized nonlinear model predictive control model. Based on the original 11-state stack ordinary differential equation system, a 17th to 20th order BOP integrated extended predictive model is constructed. The 11 states include the anode gas phase partial pressure. Temperature in Zone 3: Coke coverage (Cc) and catalyst activity (a); Using three-dimensional control inputs—fuel flow, steam flow, and air flow—an augmented cost function is constructed, comprising output tracking cost, control smoothing penalty, and a four-level soft constraint penalty function. In the prediction time domain, the predictive control is iteratively linearized using a linearized nonlinear model of the predicted trajectory, transforming the problem into a quadratic programming problem for rolling optimization. After iterative convergence, the first element of the optimal control sequence is applied to the system. The burner exhaust temperature, after a second unit delay, is used as the heat source input for each component of the fuel cell stack auxiliary equipment system, eliminating algebraic loops in the heat recovery closed loop, and returning to the next cycle for rolling optimization. The six-dimensional measurement output vector is defined as follows: In the formula This is the DC output voltage of the fuel cell stack. For fuel utilization rate, The total carbon deposition rate per unit catalyst area. This is the lowest temperature of the fuel cell stack. The temperature difference between the inlet and outlet of the anode along the axial direction. The water-to-carbon ratio; the first unit delay sampling period The initial condition is taken as the steady-state measurement value under rated operating conditions; the second unit delay initial condition is taken as the rated exhaust temperature of the burner. The thermal hysteresis dynamics of the fuel preheater and the air heat exchanger are each described by the following first-order transfer function: In the formula For heat exchange efficiency, Let be the thermal time constant, and s be the Laplace operator; the above equation is discretized using the Tustin bilinear transform, and the discretization coefficients are: In the formula Sampling period; fuel preheater air heat exchanger The pre-reformer maintains its persistent thermal state using a lumped-parameter first-order ordinary differential equation, with a thermal time constant. The blower / compressor uses a linearized state-space equation to describe the flow-speed dynamics, with a thermal time constant. The burner calculates the exhaust temperature using quasi-steady-state algebraic equations; combining the equations of the above components with the original 11-state SOFC stack ODE system, the following extended state equations are formed: In the formula ∈ℝⁿ (n=17~20) is the extended state vector. For three-dimensional control input, This represents the external disturbance vector. To integrate extended nonlinear equations for BOP, Output the equation; The augmented cost function consists of the output tracking cost, the control increment smoothing penalty, and a four-level soft constraint penalty function, specifically in the following form: In the formula, J(k) is the sum of output tracking cost and control smoothing penalty. The penalty coefficient is the carbon deposition rate constraint coefficient. This is the safe upper limit for carbon deposition rate; This is the penalty coefficient for fuel utilization rate constraints. For fuel utilization rate, it is a two-sided slack variable; This is the penalty coefficient for axial thermal gradient constraints. This is the upper limit of the thermal gradient safety limit; This is the minimum temperature constraint penalty coefficient. The lower limit of safe temperature; The four-level penalty coefficients satisfy The levels differ by a factor of 10 to ensure that high-priority carbon security constraints are always satisfied when multiple constraints of NPLPT are activated simultaneously; the output tracking weight matrix adopts a Kronecker block diagonal structure. ,in For voltage tracking weights, Set a weight for the water-to-carbon ratio at a set point. For thermal gradient penalty weights, , , The corresponding weight is zero, and it is handled by the soft constraint penalty function.

2. The solid oxide fuel cell carbon deposition sensing model predictive control method according to claim 1, characterized in that, The predicted trajectory linearization nonlinear model predictive control optimization adopts a voltage setpoint that adaptively droops with the load: In the formula This is the voltage reference value under rated load; The droop factor is [V / A]; Innom is the rated load current. This is the lower bound of the voltage setpoint; When the load exceeds the rated load, the setpoint droops linearly with the load, making the predicted trajectory linearized. The nonlinear model predictive control optimization objective always lies within the thermodynamically feasible region of the auxiliary equipment system integration system, preventing the optimizer from using all control margin to catch up with unreachable voltage targets and systematically ignoring carbon safety constraints. After the quadratic programming solution is completed, the water-carbon ratio floor constraint is applied using a hard projection method: when the steam flow rate obtained from the quadratic programming... At that time, with replace ,in This is the thermodynamic safety lower bound for the water-to-carbon ratio. The current molar flow rate of methane inlet; this hard projection is executed after the QP solution is completed, without changing the convexity of the QP problem itself, and together with the soft constraint carbon deposition rate constraint, it constitutes a dual guarantee mechanism for carbon deposition safety; The air flow After integration with the auxiliary equipment system, the constant boundary conditions activate the independent control variables for predictive control of the linearized nonlinear model of the predicted trajectory. The augmented cost function is further expanded with an additional parasitic power consumption efficiency penalty term, resulting in: In the formula Parasitic power consumed by the blower / compressor This refers to the DC output power of the fuel cell stack. The efficiency penalty coefficient is dynamically adjusted based on the current carbon deposition rate margin: a larger value is used when the carbon deposition rate margin is sufficient to prioritize reducing parasitic power consumption, and a smaller value is used when the carbon deposition rate is close to the safety limit to prioritize ensuring carbon safety. The value range is [0.2, 0.4]; therefore, The variable has been upgraded from a single thermal management variable to a dual-objective game variable of efficiency and carbon security under the predictive control framework of a linearized nonlinear model for predictive trajectory.

3. The solid oxide fuel cell carbon deposition sensing model predictive control method according to claim 1, characterized in that, The specific solution method for the linearized nonlinear model predictive control iterative linearization framework of the predicted trajectory is as follows: Define a QP decision variable vector consisting of a three-dimensional control increment sequence within the Nu-step control time domain. ∈ Through the lower triangular all-one integral matrix The control increment sequence is converted into a control quantity sequence; the predicted trajectory is linearized using a nonlinear model. The first-order Taylor expansion of the predicted trajectory in the t-th iteration is performed around the predicted trajectory in the (t-1)-th iteration. The correction formula for the predicted output is: In the formula For the predicted output of the t-th iteration at step p, ∈ {6×3Nu} The numerical Jacobian matrix at the current iteration. Let be an integral matrix. The third term is the decision variable for the current iteration. The bias correction term is used for trajectory linearization; the Jacobian matrix is ​​calculated using the central difference numerical method. The ODE white-box prediction engine performs numerical integration of the physical equations in each prediction step to achieve accurate prediction of strongly nonlinear physical processes such as methane steam reforming nonlinearity, coking positive feedback, and catalyst activity decay; the convergence criterion for the predictive control iteration of the linearized nonlinear model is: In the formula The convergence threshold is denoted by ||·|2|, which represents the Euclidean norm; the maximum number of iterations is reached. The current result is output as the suboptimal solution, ensuring that within the sampling period... The calculation is completed within the time limit; after the augmented cost function is rearranged into the standard QP form, the solver is called to obtain the optimal control increment, and the final control command is output after hard projection through the water-carbon ratio floor constraint.

4. The solid oxide fuel cell carbon deposition sensing model predictive control method according to claim 1, characterized in that, Define prediction coverage ratio A quantitative criterion for the performance boundary of predictive control using a linearized nonlinear model of the predicted trajectory, wherein... Let N be the thermal time constant of the pre-reforming reactor, and N be the number of time-domain steps in the predictive control of the linearized nonlinear model of the predicted trajectory; when At that time, the NPLPT prediction window could not fully cover the thermal response of the pre-reformer, and the carbon deposition rate constraint had the risk of being estimated non-conservatively; therefore, a proportional feedforward gain compensation instruction was superimposed on the QP solution results: In the formula For the current voltage error, As a feedforward gain, the compensation command is superimposed on the fuel flow optimal control command; The tuning principle is as follows: Under engineering constraints, ensure that the peak carbon deposition rate under typical step load conditions does not exceed the safe upper limit. Feedforward compensation and soft-constraint carbon deposition rate constraints together constitute Carbon security assurance strategies in scenario 1.

5. A solid oxide fuel cell carbon deposition sensing model predictive control system, used to implement the solid oxide fuel cell carbon deposition sensing model predictive control method according to any one of claims 1-4, characterized in that, include: BOP subsystem module: includes fuel preheater unit, pre-reform reactor unit, air heat exchanger unit, blower / compressor unit and burner unit, each unit is connected through heat recovery loop; SOFC fuel cell stack module performs direct internal reforming of methane through electrochemical conversion, outputting DC output voltage Vdc and fuel utilization rate. Carbon deposition rate Axial temperature difference ΔT, minimum temperature S / C ratio (water to carbon); Measurement convergence module, acquires six-dimensional measurement vectors ; The first-generation loop elimination unit is set in the feedback channel between the measurement convergence module and the linearized nonlinear model predictive control module along the predicted trajectory. It includes a single-step unit delay and the initial condition is set to the rated steady-state measurement value. The second-generation number loop elimination unit is located between the exhaust temperature output terminal of the burner unit and the input terminal of the BOP heat source side, and includes a single-step unit delay. The initial condition is the rated exhaust temperature of the burner. Predictive trajectory linearization nonlinear model predictive control controller module, with six-dimensional measurement vector y and load current. Using the 17th to 20th order BOP ensemble extended prediction model as input, the augmented cost function containing four levels of soft constraint penalty functions (P1 to P4) is solved iteratively through an ordinary differential equation white-box prediction engine, numerical Jacobian matrix, and quadratic programming. Output fuel flow Steam flow rate and airflow Three-dimensional control commands; The control command allocation module routes the three-dimensional control commands to the fuel channel, steam channel, and air channel, respectively.

6. The solid oxide fuel cell carbon deposition sensing model predictive control system according to claim 5, characterized in that, The optimization solution of the linearized nonlinear model predictive control controller module of the predicted trajectory is performed by a 17-20 order extended state ODE white box prediction engine to perform multi-step forward simulation in each sampling period, so as to achieve accurate prediction of strong nonlinear physical processes such as nonlinearity of methane steam reforming, positive feedback of coking, and catalyst activity decay. The sensitivity of the predicted output to the three-dimensional control increment is described by the central difference numerical Jacobian matrix. In each iteration of the predictive control of the linearized nonlinear model of the predicted trajectory, the prediction is recalculated around the updated predicted trajectory to accurately capture the nonlinear effects. A damped update strategy is used to ensure the numerical stability of the iteration; The iteration termination is controlled by two conditions: the convergence threshold and the maximum number of iterations. The solution is output as the optimal control command after being hard-projected by the water-carbon ratio floor constraint.

7. The solid oxide fuel cell carbon deposition sensing model predictive control system according to claim 5, characterized in that, The pre-reform reactor unit is the single component with the largest thermal time constant in the BOP subsystem module. ;when When the value is greater than 1, the predictive trajectory linearization nonlinear model predictive control module automatically activates the proportional feedforward gain. A compensation mechanism feeds forward the voltage error to the fuel flow control command to mitigate the risk of non-conservative estimation of carbon deposition rate constraints caused by the inability of the prediction window to fully cover the pre-reformer thermal response; the blower / compressor unit calculates parasitic power consumption in real time. The augmented cost function of the predictive control is obtained by linearizing the predicted trajectory using a nonlinear model. Medium efficiency penalty item With carbon deposition rate constraint The synergistic trade-offs constitute a closed loop of synergistic optimization for the dual objectives of efficiency and carbon security.

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