Cooperative control method of solid oxide fuel cell system

Abstract

The invention relates to a cooperative control method of a solid oxide fuel cell system. According to the method, the output control quantity is cooperatively controlled and adjusted through double active disturbance rejection controllers (ADRC), controller optimization is carried out by adopting a Newton-Raphson intelligent optimization algorithm, and the working temperature of a battery is maintained in a high-efficiency operation range while it is ensured that the requirement for external power is met. And stable power output and temperature optimization control are realized by feeding back an error between a temperature and a power target value and an actual value. Results show that the stabilization time of SOFC working temperature control is about 10s, the maximum overshoot is controlled within 1%, the steady-state error is controlled within 0.01%, and the SOFC working temperature can be rapidly stabilized to a target value within about 2s under power interference; the stable time of power tracking is about 35 seconds, the overshoot and the steady-state error are both controlled within the range of 0.1%, the target value can be rapidly stabilized within about 20 seconds under the interference of the working temperature of the SOFC, and accurate power tracking is achieved.

Description

Technical Field

[0001] The present invention relates to the field of fuel cell control technology, and in particular to a coordinated control method for a solid oxide fuel cell system. Background Art

[0002] The cheap preparation and safe storage and transportation of hydrogen energy are important factors that hinder the development and promotion of fuel cells. Direct use of hydrogen as fuel has disadvantages such as poor safety performance, low storage efficiency, and high requirements for hydrogen storage devices. It is currently only applicable to high value-added industries such as hydrogen fuel cell vehicles. Therefore, fuel cell technology based on methane reforming came into being. Methane is gaseous at room temperature and pressure and can be transported through existing natural gas pipelines and infrastructure. In contrast, hydrogen needs to be stored at high pressure at room temperature, or must be liquefied for convenient storage and transportation. The low density and easy diffusion of hydrogen make its conventional storage and transportation face more challenges. The liquefaction temperature of methane is higher than that of hydrogen. Therefore, the storage density of methane after liquefaction is higher, and the storage and transportation efficiency is also better. The energy density of liquefied methane is higher than that of liquid hydrogen, which makes the transportation of methane in liquid form more economical and practical. Hydrogen is prepared by methane reforming reaction, and then introduced into the fuel cell for electrochemical reaction to convert hydrogen chemical energy into electrical energy. However, compared with directly using pure hydrogen as fuel for power generation, the process structure of the methane reforming SOFC system is relatively complex. During operation, the operating temperature of the SOFC cell is related to the system intake air flow rate, and this parameter directly affects the power generation of the SOFC. The coupling of the two makes the system control more difficult.

[0003] Although solid oxide fuel cell (SOFC) systems have shown great potential in the field of energy conversion and energy storage, their synergistic control research still faces some significant deficiencies. At present, the control of SOFC systems is mostly focused on the optimization of a single variable, such as independent control of power or temperature, and lacks comprehensive consideration of the complex interactions between the various variables in the system. Since the operating efficiency and stability of the SOFC system are highly dependent on the dynamic relationship between power and temperature, ignoring the synergistic effect between them often leads to problems such as slow system response, reduced efficiency or uneven temperature, which affects the long-term stability and performance of the fuel cell. Summary of the invention

[0004] Based on this, it is necessary to provide a coordinated control method for a solid oxide fuel cell system to address the above problems. While ensuring that the system meets the external variable load requirements, it overcomes the temperature control interference caused by fuel flow fluctuations and achieves rapid and accurate tracking and control of load power and SOFC operating temperature.

[0005] Therefore, it is particularly important to propose power-temperature coordinated control. This method not only considers the individual control of power and temperature, but also emphasizes the interaction between them. Through the coordinated control strategy, the overall performance of the system is optimized to ensure that the SOFC system maintains the best working state under various working conditions. The coordinated regulation of power and temperature can effectively reduce the instability caused by individual control and improve the system's adaptability to external disturbances.

[0006] In this context, the use of active disturbance rejection control (ADRC) technology becomes an ideal choice. ADRC has strong disturbance rejection capability and can estimate and compensate for external disturbances and internal uncertainties in the system in real time, especially when system parameters change greatly or environmental conditions fluctuate. Compared with traditional PID control, ADRC can more accurately control the power in the SOFC system, making it respond quickly and stabilize in the desired state, avoiding instability caused by control lag or parameter changes. Therefore, the power-temperature coordinated control based on Newton-Raphson dual ADRC provides a more reliable technical guarantee for the efficient and stable operation of the SOFC system.

[0007] Technical solution: A coordinated control method for a solid oxide fuel cell system, the method is based on ADRC control and ADRC control. The present invention is implemented by the following technical solution: A control method for a solid oxide fuel cell system with external methane reforming of the present invention, the solid oxide fuel cell system includes a SOFC stack, a reformer, a combustion chamber, a humidifier, a water pump, a heat exchanger, a fuel compressor, a first controller, a second controller, and an air compressor. It includes the following steps:

[0008] Step 1), constructing a stack temperature model, a system power model, a compressor model, a reformer model, a combustion chamber model, a humidifier model, a heat exchanger model, a water pump model, and a controller model;

[0009] Step 2), the first controller selects the air flow rate F of the air compressor air As a control variable, the solid oxide fuel cell stack operating temperature setting value T work,ref Feedback tracking; the second controller selects the fuel flow rate F of the fuel compressor fuel As a control variable, the output power setting value P of the solid oxide fuel cell system is realized system,ref Feedback tracking.

[0010] Step 3) Use external accessories to efficiently utilize the waste heat from the system exhaust to preheat the air entering the fuel cell stack.

[0011] Step 4), using the Newton-Raphson intelligent optimization algorithm to improve the ADRC to improve its control performance.

[0012] Preferably, in step 2), the first controller sets the operating temperature of the solid oxide fuel cell stack to a value T work,ref The feedback tracking method is as follows:

[0013] The first controller is based on the solid oxide fuel cell operating temperature T work The solid oxide fuel cell stack operating temperature setting value T work,ref The difference in value adjusts the air flow rate F of the air compressor air ;

[0014] The first controller is an ADRC controller, which is based on the solid oxide fuel cell operating temperature T work The solid oxide fuel cell stack operating temperature setting value T work,ref The difference in value adjusts the air flow rate F of the air compressor air , so that the solid oxide fuel cell operating temperature T work Approaching the set value T work,ref , achieving rapid and precise tracking and control of the operating temperature of solid oxide fuel cells.

[0015] Preferably, in step 2), the second controller sets the output power setting value P of the solid oxide fuel cell system. system,ref The feedback tracking method is as follows:

[0016] The second controller is based on the output power P of the solid oxide fuel cell system system The output power setting value P of the solid oxide fuel cell system system The difference in value adjusts the fuel flow rate F of the fuel compressor fuel .

[0017] The second controller is an ADRC controller. The second controller is based on the output power P of the solid oxide fuel cell system. system The output power setting value P of the solid oxide fuel cell system system,ref The difference in value adjusts the fuel flow rate F of the fuel compressor fuel , so that the system output power P system Approaching the set value P system,ref , realizing fast and accurate tracking and control of system output power.

[0018] Preferably, the method of improving the active disturbance rejection controller algorithm using the Newton-Raphson intelligent optimization algorithm in step 4) is as follows:

[0019] The two ADRC parameters wo, b0, kp, kd are taken as optimization objects, and the system output control performance such as control error, overshoot, time multiplied absolute error integral (ITAE) and other indicators are taken as optimization targets for optimization control.

[0020] As a preferred embodiment, the formula of the stack temperature model is as follows:

[0021]

[0022] Among them, C s is the stack gas heat capacity, T work is the operating temperature of the solid oxide fuel cell, W in,i is the molar flow rate of each component in the stack inlet, W out,i is the molar flow rate of each component at the stack outlet, h i is the enthalpy of the gas at the cathode and anode inlet and outlet of the battery, P SOFC is the stack output power, is the chemical reaction heat of the fuel cell; the calculation formula for the enthalpy value of each component is as follows:

[0023]

[0024] Among them, h i,0 is the standard production enthalpy of gas under standard conditions (298K, 101300Pa), T ref is the reference temperature (298K), C p,i is the constant pressure specific heat capacity of gas i. The calculation formula for the reaction heat is as follows:

[0025]

[0026] Among them, Q H2 is the chemical reaction heat, z is the hydrogen reaction rate, U f is the fuel utilization rate, W H2,in is the hydrogen inlet flow rate, hydrogen lower heating value LHV H2 ;

[0027] Preferably, the system power model is as follows:

[0028] P system =P SOFC -P compressor,air -P compressor,fuel -P pump (4)

[0029] Among them, P system is the system output power, P SOFC is the fuel cell stack power, P compressor,air , P compressor,fuel , P pump They are the power losses of the air compressor at the air end, the fuel compressor at the fuel end, and the water pump;

[0030] Among them, the fuel cell stack power model is as follows:

[0031] P SOFC =V·I (5)

[0032] Wherein, V is the stack output voltage, and I is the stack output current;

[0033] Preferably, the compressor model is as follows:

[0034]

[0035] P compressor,Pa =B·P in (8)

[0036] Among them, P compressor,Pa is the air compressor output pressure, P compressor is the power loss of the air compressor, T compressor,out is the air compressor outlet gas temperature, B is the pressure ratio, W1 is the molar flow rate, r1 is the gas adiabatic index;

[0037] Preferably, the reformer model is as follows:

[0038]

[0039] in, S CO are the reaction rates of methane and carbon monoxide, W CO,out , is the molar flow rate of each gas at the reformer outlet;

[0040] Preferably, the combustion chamber model is as follows:

[0041]

[0042] Among them, h in is the inlet gas enthalpy, Q CO，in Hydrogen, methane, and carbon monoxide carry energy. is the isentropic efficiency. i,out Molar flow rate of each substance after combustion, T B,out The combustion chamber outlet gas temperature, T0 is the standard temperature, C p,B,out is the specific heat capacity of the gas at the combustion chamber outlet, M fuel,in is the inlet fuel mass flow rate, is the combustion efficiency. B,out Combustion chamber outlet pressure, ω b is the pressure loss coefficient, P in is the combustion chamber inlet pressure.

[0043] Preferably, the humidifier model is as follows:

[0044]

[0045] in, is the humidification amount, Inlet water molar flow rate, fuel inlet specific heat capacity, M fuel,in Fuel inlet mass flow rate, T fuel,in Fuel inlet temperature, T ref Reference temperature, Specific heat capacity of gaseous water, Humidification water mass flow rate, Temperature of water after humidification and evaporation, C p,fuel,out Specific heat capacity of fuel after humidification, M fuel,out Fuel mass flow rate after humidification, is the outlet water molar flow rate, T fuel,out is the fuel outlet temperature.

[0046] Preferably, the heat exchanger model is as follows:

[0047] A1=M h ·C p,h (twenty four)

[0048] A2=M c ·C p,c (25)

[0049]

[0050] Q ex =C p,c ·M c ·(T c,out -T c,in ) (29)

[0051] Among them, A1, A2, A3 are heat transfer coefficients, K is the average heat transfer coefficient, S is the heat transfer area, M h 、M c is the mass flow rate of the hot and cold ends, C p,h , C p,c is the specific heat capacity of the hot and cold ends, T c,out 、T h,out is the outlet temperature of the cold end and the hot end, Q ex For heat exchange.

[0052] Preferably, the water pump model is as follows:

[0053]

[0054] Among them, P pump is power consumption, a is lift, M water is the mass flow rate of water, ω p is the power conversion factor, is the efficiency of the pump.

[0055] Preferably, the controller model is as follows:

[0056]

[0057] Where e is the control error, z1, z2, z3 are the observer states, kp and kd are the controller gains, wo is the observer bandwidth, ref is the target value, and y is the system output value.

[0058] Preferably, the Newton-Raphson intelligent optimization algorithm (NRBO) operates as follows:

[0059] The Newton-Raphson optimization algorithm is inspired by the Newton-Raphson solution method and uses two search rules: Newton-Raphson search rule (NRSR) and trap avoidance operator (TAO). NRSR uses the Newton-Raphson solution method to improve the search ability and convergence speed of the NRBO algorithm to obtain a better search space location. TAO helps NRBO avoid local optimal traps.

[0060] The first step is to define the objective function, which involves understanding the optimization goal, conducting a feasibility analysis, accumulating prior experience, establishing a suitable fitness function (as shown in the following formula), and formulating the optimization goal y along various constraints:

[0061]

[0062] Among them, dim is the algorithm optimization variable dimension, lb and ub are the upper and lower limits of the variables respectively, u1, u2, u3, and u4 are optimization evaluation indicators, among which u1 represents the convergence speed of power tracking control, u2 represents the steady-state error of control, u3 represents the overshoot, u4 is the controller evaluation parameter ITAE, and K, L, M, and N are the weights of each indicator.

[0063] In the second step, the parameters of NRBO optimization are as follows:

[0064]

[0065] ω is the parameter of the ADRC controller.

[0066] In the third step, the NRBO algorithm performs parameter initialization. NRBO starts searching for the optimal solution by generating an initial random population within the boundary of candidate solutions. Based on the existence of Np populations, each population consists of j-dimensional decision variables. Therefore, the random population is generated using the following equation.

[0067]

[0068] in represents the j-th dimension position of the n-th population, and rand represents a random number between (0, 1).

[0069] In the fourth step, the algorithm uses two search rules, NRSR and TAO, and runs the target number of iterations. NRSR is expressed as follows:

[0070]

[0071] Where randn represents a normally distributed random number with a mean of 0 and a variance of 1, and X w Indicates the worst position, X b represents the optimal position. The equation has a random parameter to improve the search ability of NRBO and better balance the development and exploration capabilities. The algorithm can be enhanced by applying an adaptive coefficient called δ.

[0072]

[0073] Where IT represents the current iteration and Max_IT represents the maximum number of iterations. In order to maintain the balance between the exploration phase and the exploitation phase, the parameter δ is adaptive during the iteration process. The utilization of the proposed NRBO is improved by introducing another parameter called ρ, which guides the population in the right direction. The expression of ρ is as follows.

[0074]

[0075] Where a and b are random numbers between (0, 1), and r1 and r2 are different integers randomly selected from the population. However, the values ​​of r1 and r2 are not equal. The vector X n IT The current position of has been updated by the following equation.

[0076]

[0077] in, By updating The new vector position is obtained. r1 and r2 represent random numbers between (0, 1). TAO is added to improve the effectiveness of NRBO in dealing with real-world problems. By using TAO, it can significantly change It combines the best position X b and the current vector position Produce enhanced quality If the value of rand is less than DF, the solution is generated by the following equation

[0078]

[0079] Where rand represents a uniform random number between (0, 1), θ1 and θ2 are uniform random numbers between (-1, 1) and (-0.5, 0.5), DF represents the determining factor controlling the performance of NRBO, and μ1 and μ2 are random numbers, which are respectively expressed by the following equations.

[0080]

[0081] Wherein, rand represents a random number between (0, 1), and Δ represents a number between (0, 1). The above equation is further simplified as follows.

[0082] μ1=β·3·rand+(1-β); μ2=β·rand+(1-β) (41)

[0083] Where β represents a binary number 1 or 0, and rand represents a random number. If the value of Δ is greater than or equal to 0.5, the value of β is 0; otherwise, the value is 1. Due to the randomness of the selection of parameters μ1 and μ2, the population becomes more diverse and escapes from the local optimal solution, which helps to improve its diversification.

[0084] The beneficial effect of the present invention is that when the fuel cell is operating under dynamic nonlinear conditions, quickly meeting external demands is the first priority. Therefore, a controller is used to control the fuel flow so that the output power of the fuel cell system meets the demand. However, the traditional control method has problems such as large overshoot, long adjustment time, and weak robustness, which makes it difficult to meet the control requirements. This study combines the fast global optimization capability, strong robustness, and NRSR-TAO search rule of the intelligent algorithm with the strong anti-interference and error dynamic observation capabilities of the self-anti-disturbance control. For the SOFC system, the Newton-Raphson algorithm is used to dynamically adjust the parameters wo, b0, kp, and kd of the ADRC controller. This method enables the controller to dynamically adjust the inlet fuel flow to respond to load demands and temperature disturbances based on external load demands, thereby ensuring that the system meets external load demands while overcoming the temperature control interference caused by fuel flow fluctuations, and realizing fast and accurate tracking and control of load power and SOFC operating temperature. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is a structural schematic diagram of this embodiment;

[0086] Figure 2 Optimize the structure diagram for the algorithm;

[0087] Figure 3 This is the effect diagram of the working temperature control of solid oxide fuel cells;

[0088] Figure 4 It is the control effect diagram of system power;

[0089] Figure 5 Figure 1. Temperature diagram for inlet air preheat. DETAILED DESCRIPTION

[0090] In order to facilitate the understanding of the present invention, the present invention will be described more fully below with reference to the relevant drawings. The preferred embodiments of the present invention are given in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thoroughly understood.

[0091] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used herein in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more related listed items.

[0092] Embodiment: A coordinated control method of a solid oxide fuel cell system in this embodiment, such as Figure 1 As shown, the solid oxide fuel cell system includes a SOFC stack 1, a reformer 2, a combustion chamber 3, a humidifier 4, a water pump 5, a heat exchanger 6, a fuel compressor 7, a first controller 8, a second controller 9, and an air compressor 10, and includes the following steps:

[0093] Step 1), constructing a stack temperature model, a system power model, a compressor model, a reformer model, a combustion chamber model, a humidifier model, a heat exchanger model, a water pump model, and a controller model;

[0094] The formula of the stack temperature model is as follows:

[0095]

[0096] Among them, C s is the stack gas heat capacity, T work is the operating temperature of the solid oxide fuel cell, W in,i is the molar flow rate of each component in the stack inlet, W out,i is the molar flow rate of each component at the stack outlet, h i is the enthalpy of the gas at the cathode and anode inlet and outlet of the battery, P SOFC is the stack output power, The heat of chemical reaction in fuel cells;

[0097] The calculation formula of the enthalpy value of each component is as follows:

[0098]

[0099] Among them, h i,0 is the standard production enthalpy of gas under standard conditions (298K, 101300Pa), T ref is the reference temperature (298K), C p,i is the constant-pressure specific heat capacity of gas i.

[0100] The calculation formula of reaction heat is as follows:

[0101]

[0102] Among them, Q H2 is the chemical reaction heat, z is the hydrogen reaction rate, U f is the fuel utilization rate, W H2,in is the hydrogen inlet flow rate, hydrogen lower heating value LHV H2 ;

[0103] The system power model is as follows:

[0104] P system =P SOFC -P compressor,air -P compressor,fuel -P pump (4)

[0105] Among them, P system is the system output power, P SOFC is the fuel cell stack power, P compressor,air , P compressor,fuel , P pump They are the power losses of the air compressor at the air end, the fuel compressor at the fuel end, and the water pump;

[0106] Among them, the fuel cell stack power model is as follows:

[0107] P SOFC =V·I (5)

[0108] Wherein, V is the stack output voltage, and I is the stack output current;

[0109] The compressor model is as follows:

[0110]

[0111] P compressor,Pa =B·P in (8)

[0112] Among them, P compressor,Pa is the air compressor output pressure, P compressor is the power loss of the air compressor, T compressor,out is the air compressor outlet gas temperature, B is the pressure ratio, W1 is the molar flow rate, r1 is the gas adiabatic index;

[0113] The reformer model is as follows:

[0114]

[0115] in, S CO are the reaction rates of methane and carbon monoxide, W CO,out , is the molar flow rate of each gas at the reformer outlet;

[0116] The combustion chamber model is as follows:

[0117]

[0118] P B,out =P in ·ω b (twenty one)

[0119] Among them, h in is the inlet gas enthalpy, Q CO，in Hydrogen, methane, and carbon monoxide carry energy. is the isentropic efficiency. i,out Molar flow rate of each substance after combustion, T B,out The combustion chamber outlet gas temperature, T0 is the standard temperature, C p,B,out is the specific heat capacity of the gas at the combustion chamber outlet, M fuel,in is the inlet fuel mass flow rate, is the combustion efficiency. B,out Combustion chamber outlet pressure, ω b is the pressure loss coefficient, P in is the combustion chamber inlet pressure.

[0120] The humidifier model is as follows:

[0121]

[0122] in, is the humidification amount, Inlet water molar flow rate, fuel inlet specific heat capacity, M fuel,in Fuel inlet mass flow rate, T fuel,in Fuel inlet temperature, T ref Reference temperature, Specific heat capacity of gaseous water, Humidification water mass flow rate, Temperature of water after humidification and evaporation, C p,fuel,out Specific heat capacity of fuel after humidification, M fuel,out Fuel mass flow rate after humidification, is the outlet water molar flow rate, T fuel,out is the fuel outlet temperature.

[0123] The heat exchanger model is as follows:

[0124] A1=M h ·C p,h (twenty four)

[0125] A2=M c ·C p,c (25)

[0126]

[0127] Q ex =C p,c ·M c ·(T c,out -T c,in ) (29)

[0128] Among them, A1, A2, A3 are heat transfer coefficients, K is the average heat transfer coefficient, S is the heat transfer area, M h 、M c is the mass flow rate of the hot and cold ends, C p,h , C p,c is the specific heat capacity of the hot and cold ends, T c,out 、T h,out is the outlet temperature of the cold end and the hot end, Q ex For heat exchange.

[0129] The water pump model is as follows:

[0130]

[0131] Among them, P pump is power consumption, a is lift, M water is the mass flow rate of water, ω p is the power conversion factor, is the efficiency of the pump.

[0132] The controller model is as follows:

[0133]

[0134] Where e is the control error, z1, z2, z3 are the observer states, kp and kd are the controller gains, wo is the observer bandwidth, ref is the target value, and y is the system output value.

[0135] Step 2), the first controller selects the air flow rate F of the air compressor air As a control variable, the solid oxide fuel cell stack operating temperature setting value T work,refFeedback tracking; the second controller selects the fuel flow rate F of the fuel compressor fuel As a control variable, the output power setting value P of the solid oxide fuel cell system is realized system,ref Feedback tracking.

[0136] In step 2), the first controller sets the operating temperature of the solid oxide fuel cell stack to a value T work,ref The feedback tracking method is as follows:

[0137] The first controller is based on the solid oxide fuel cell operating temperature T work The solid oxide fuel cell stack operating temperature setting value T work,ref The difference in value adjusts the air flow rate F of the air compressor air ;

[0138] In step 2), the second controller sets the output power value P of the solid oxide fuel cell system. system,ref The feedback tracking method is as follows:

[0139] The second controller is based on the output power P of the solid oxide fuel cell system system The output power setting value P of the solid oxide fuel cell system system,ref The difference in value adjusts the fuel flow rate F of the fuel compressor fuel .

[0140] In this solution, the first controller is an ADRC controller, which is based on the solid oxide fuel cell operating temperature T work The solid oxide fuel cell stack operating temperature setting value T work,ref The difference in value adjusts the air flow rate F of the air compressor air , so that the solid oxide fuel cell operating temperature T work Approaching the set value T work,ref , achieving rapid and precise tracking and control of the operating temperature of solid oxide fuel cells.

[0141] The second controller is an ADRC controller. The second controller is based on the output power P of the solid oxide fuel cell system. system The output power setting value P of the solid oxide fuel cell system system,ref The difference in value adjusts the fuel flow rate F of the fuel compressor fuel , so that the system output power P system Approaching the set value P system,ref , realizing fast and accurate tracking and control of system output power.

[0142] Step 3) Use external accessories to efficiently utilize the waste heat from the system exhaust to preheat the air entering the fuel cell stack.

[0143] By establishing the above model, the waste heat of the system exhaust gas can be efficiently utilized and the air entering the fuel cell stack can be preheated.

[0144] Step 4), using the Newton-Raphson intelligent optimization algorithm to improve the ADRC to improve its control performance.

[0145] The method of improving the ADRC algorithm by the Newton-Raphson intelligent optimization algorithm in step 4) is as follows:

[0146] The two ADRC parameters wo, b0, kp, kd are taken as optimization objects, and the system output control performance such as control error, overshoot, time multiplied absolute error integral (ITAE) and other indicators are taken as optimization targets for optimization control.

[0147] The operation process of the Newton-Raphson intelligent optimization algorithm (NRBO) is as follows:

[0148] The Newton-Raphson optimization algorithm is inspired by the Newton-Raphson solution method and uses two search rules: Newton-Raphson search rule (NRSR) and trap avoidance operator (TAO). NRSR uses the Newton-Raphson solution method to improve the search ability and convergence speed of the NRBO algorithm to obtain a better search space location. TAO helps NRBO avoid local optimal traps.

[0149] The first step is to define the objective function, which involves understanding the optimization goal, conducting a feasibility analysis, accumulating prior experience, establishing a suitable fitness function (as shown in the following formula), and formulating the optimization goal y along various constraints:

[0150]

[0151] Among them, dim is the algorithm optimization variable dimension, lb and ub are the upper and lower limits of the variables respectively, u1, u2, u3, and u4 are optimization evaluation indicators, among which u1 represents the convergence speed of power tracking control, u2 represents the steady-state error of control, u3 represents the overshoot, u4 is the controller evaluation parameter ITAE, and K, L, M, and N are the weights of each indicator.

[0152] In the second step, the parameters of NRBO optimization are as follows:

[0153]

[0154] ω is the parameter of the ADRC controller.

[0155] In the third step, the NRBO algorithm performs parameter initialization. NRBO starts searching for the optimal solution by generating an initial random population within the boundary of candidate solutions. Based on the existence of Np populations, each population consists of j-dimensional decision variables. Therefore, the random population is generated using the following equation.

[0156]

[0157] in represents the j-th dimension position of the n-th population, and rand represents a random number between (0, 1).

[0158] In the fourth step, the algorithm uses two search rules, NRSR and TAO, and runs the target number of iterations. NRSR is expressed as follows:

[0159]

[0160] Where randn represents a normally distributed random number with a mean of 0 and a variance of 1, and X w Indicates the worst position, X b represents the optimal position. The equation has a random parameter to improve the search ability of NRBO and better balance the development and exploration capabilities. The algorithm can be enhanced by applying an adaptive coefficient called δ.

[0161]

[0162] Where IT represents the current iteration and Max_IT represents the maximum number of iterations. In order to maintain the balance between the exploration phase and the exploitation phase, the parameter δ is adaptive during the iteration process. The utilization of the proposed NRBO is improved by introducing another parameter called ρ, which guides the population in the right direction. The expression of ρ is as follows.

[0163]

[0164] Where a and b are random numbers between (0, 1), and r1 and r2 are different integers randomly selected from the population. However, the values ​​of r1 and r2 are not equal. The vector X n IT The current position of has been updated by the following equation.

[0165]

[0166] in, By updating The new vector position is obtained. r1 and r2 represent random numbers between (0, 1). TAO is added to improve the effectiveness of NRBO in dealing with real-world problems. By using TAO, it can significantly change It combines the best position Xb and the current vector position Produce enhanced quality If the value of rand is less than DF, the solution is generated by the following equation

[0167]

[0168] Where rand represents a uniform random number between (0, 1), θ1 and θ2 are uniform random numbers between (-1, 1) and (-0.5, 0.5), DF represents the determining factor controlling the performance of NRBO, and μ1 and μ2 are random numbers, which are respectively expressed by the following equations.

[0169]

[0170] Wherein, rand represents a random number between (0, 1), and Δ represents a number between (0, 1). The above equation is further simplified as follows.

[0171] μ1=β·3·rand+(1-β); μ2=β·rand+(1-β) (41)

[0172] Where β represents a binary number 1 or 0, and rand represents a random number. If the value of Δ is greater than or equal to 0.5, the value of β is 0; otherwise, the value is 1. Due to the randomness of the selection of parameters μ1 and μ2, the population becomes more diverse and escapes from the local optimal solution, which helps to improve its diversification.

[0173] The system load power reference value is set to change between 60kW and 90kW, with a change interval of 100s and a duration of 500s. The target operating temperature of the SOFC is set to change between 1040K and 1100K, with a change interval of 50s and a duration of 500s. The solid oxide fuel cell operating temperature control effect diagram under the control method of this scheme is as follows: Figure 3 As shown in the figure, the control effect diagram of the system power is as follows: Figure 4 As shown. Figure 3 , Figure 4It can be seen that during the rapid step change of the load reference value, the system's output power and the operating temperature of the fuel cell can quickly achieve error-free tracking of the target reference value. Among them, the stabilization time of the SOFC operating temperature control is about 10s, the maximum overshoot is controlled within 1%, and does not exceed the safe operating temperature range of the SOFC battery. The steady-state error is controlled within 0.01%, and it can respond quickly under power disturbance and stabilize at the target value within about 2s; the stabilization time of power tracking is about 35s, the overshoot and steady-state error are controlled within 0.1%, and it can respond quickly under SOFC operating temperature disturbance and stabilize at the target value within about 20s, achieving accurate tracking of the target value. Figure 5 The temperature result diagram of the exhaust waste heat utilization for external accessories and preheating the air entering the fuel cell stack shows that this method can effectively preheat the air and ensure the efficient and long-term operation of the fuel cell stack.

[0174] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0175] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A coordinated control method for a solid oxide fuel cell system, characterized in that: The output control quantity is adjusted by the coordinated control of the dual anti-disturbance controllers, and the controller is optimized by the Newton-Raphson intelligent optimization algorithm. The stable power output and temperature optimization control are achieved by feeding back the error between the temperature and power target value and the actual value, including the following steps: Step 1), constructing a stack temperature model, a system power model, a compressor model, a reformer model, a combustion chamber model, a humidifier model, a heat exchanger model, a water pump model, and a controller model; Step 2), the first controller selects the air flow rate F of the air compressor air As a control variable, the solid oxide fuel cell stack operating temperature setting value T work,ref Feedback tracking; the second controller selects the fuel flow rate F of the fuel compressor fuel As a control variable, the output power setting value P of the solid oxide fuel cell system is realized. system,ref Feedback tracking; Step 3), using external accessories to efficiently utilize the waste heat of the system exhaust gas to preheat the air entering the fuel cell stack; Step 4), using the Newton-Raphson intelligent optimization algorithm to improve the ADRC to improve its control performance.

2. A method according to claim 1, characterized in that In step 2), the first controller sets the operating temperature of the solid oxide fuel cell stack to a value T work,ref The feedback tracking method is as follows: The first controller is based on the solid oxide fuel cell operating temperature T work The solid oxide fuel cell stack operating temperature setting value T work,ref The difference in value adjusts the air flow rate F of the air compressor air ; In step 2), the second controller sets the output power of the solid oxide fuel cell system to a value P system,ref The feedback tracking method is as follows: The second controller is based on the output power P of the solid oxide fuel cell system system The output power setting value P of the solid oxide fuel cell system system,ref The difference in value adjusts the fuel flow rate F of the fuel compressor fuel .

3. A method according to claim 1, characterized in that The method of improving the active disturbance rejection controller algorithm using the Newton-Raphson intelligent optimization algorithm in step 4) is as follows: The two ADRC parameters wo, b0, kp, kd are taken as optimization objects, and the system output control performance such as control error, overshoot, time multiplied absolute error integral (ITAE) and other indicators are taken as optimization targets for optimization control.

4. A method according to claim 1, characterized in that The formula of the stack temperature model is as follows: Among them, C s is the stack gas heat capacity, T work is the operating temperature of the solid oxide fuel cell, W in,i is the molar flow rate of each component in the stack inlet, W out,i is the molar flow rate of each component at the stack outlet, h i is the enthalpy of the gas at the cathode and anode inlet and outlet of the battery, P SOFC is the stack output power, The heat of chemical reaction in fuel cells; The calculation formula of the enthalpy value of each component is as follows: Among them, h i,0 is the standard production enthalpy of gas under standard conditions (298K, 101300Pa), T ref is the reference temperature (298K), C p,i is the constant-pressure specific heat capacity of gas i; The calculation formula of reaction heat is as follows: in, is the chemical reaction heat, z is the hydrogen reaction rate, U f is the fuel utilization rate, is the hydrogen inlet flow rate, hydrogen lower heating value 5. A method according to claim 1, characterized in that The system power model is as follows: P system =P SOFC -P compressor,air -P compressor,fuel -P pump Among them, P system is the system output power, P SOFC is the fuel cell stack power, P compressor,air , P compressor,fuel , P pump They are the power losses of the air compressor at the air end, the fuel compressor at the fuel end, and the water pump; Among them, the fuel cell stack power model is as follows: P SOFC =V·I Wherein, V is the stack output voltage, and I is the stack output current; The compressor model is as follows: Among them, P compressor,Pa is the air compressor output pressure, P compressor is the power loss of the air compressor, T compressor,out is the air compressor outlet gas temperature, B is the pressure ratio, W1 is the molar flow rate, and r1 is the gas adiabatic index.

6. A method according to claim 3, characterized in that The reformer model is as follows: in, S CO are the reaction rates of methane and carbon monoxide, W CO,out , is the molar flow rate of each gas at the reformer outlet; The combustion chamber model is as follows: P B,out =P in ·oh b Among them, h in is the inlet gas enthalpy, Q CO，in Hydrogen, methane, and carbon monoxide carry energy. is the isentropic efficiency; W i,out Molar flow rate of each substance after combustion, T B,out The combustion chamber outlet gas temperature, T0 is the standard temperature, C p,B,out is the specific heat capacity of the gas at the combustion chamber outlet, M fuel,in is the inlet fuel mass flow rate, is the combustion efficiency; P B,out Combustion chamber outlet pressure, ω b is the pressure loss coefficient, P in is the combustion chamber inlet pressure; The humidifier model is as follows: in, is the humidification amount, Inlet water molar flow rate, fuel inlet specific heat capacity, M fuel,in Fuel inlet mass flow rate, T fuel,in Fuel inlet temperature, T ref Reference temperature, Specific heat capacity of gaseous water, Humidification water mass flow rate, Temperature of water after humidification and evaporation, C p,fuel,out Specific heat capacity of fuel after humidification, M fuel,out Fuel mass flow rate after humidification, is the outlet water molar flow rate, T fuel,out is the fuel outlet temperature; The heat exchanger model is as follows: A1=M h ·C p,h A2=M c ·C p,c Q ex =C p,c ·M c ·(T c,out -T c,in ) Among them, A1, A2, A3 are heat transfer coefficients, K is the average heat transfer coefficient, S is the heat transfer area, M h 、M c is the mass flow rate of the hot and cold ends, C p,h , C p,c is the specific heat capacity of the hot and cold ends, T c,out 、T h,out is the outlet temperature of the cold end and the hot end, Q ex For heat exchange; The water pump model is as follows: Among them, P pump is power consumption, a is lift, M water is the mass flow rate of water, ω p is the power conversion factor, is the efficiency of the pump; The controller model is as follows: Where e is the control error, z1, z2, z3 are the observer states, kp and kd are the controller gains, wo is the observer bandwidth, ref is the target value, and y is the system output value.

7. A method according to claim 1, characterized in that The operation process of the Newton-Raphson intelligent optimization algorithm (NRBO) is as follows: The Newton-Raphson optimization algorithm is inspired by the Newton-Raphson solution method and adopts two search rules: Newton-Raphson search rule (NRSR) and trap avoidance operator (TAO); NRSR adopts the Newton-Raphson solution method to improve the search ability and convergence speed of the NRBO algorithm to obtain a better search space position; TAO helps NRBO avoid local optimal traps.

8. A method according to claim 5, characterized in that The first step is to define the objective function, which involves understanding the optimization goal, conducting a feasibility analysis, accumulating prior experience, establishing a suitable fitness function (as shown in the following formula), and formulating the optimization goal y along various constraints: Wherein, dim is the dimension of algorithm optimization variable, lb and ub are the upper and lower limits of the variable respectively, u1, u2, u3 and u4 are optimization evaluation indicators, where u1 represents the convergence speed of power tracking control, u2 represents the steady-state error of control, u3 represents the overshoot, u4 is the controller evaluation parameter ITAE, and K, L, M and N are the weights of each indicator; In the second step, the parameters of NRBO optimization are as follows: ω is the parameter of ADRC controller; In the third step, the NRBO algorithm performs parameter initialization; the NRBO algorithm starts searching for the optimal solution by generating an initial random population within the boundary of candidate solutions; based on the existence of Np populations, each population consists of j-dimensional decision variables; therefore, the random population is generated using the following equation; in represents the j-th dimension position of the n-th population, and rand represents a random number between (0, 1); In the fourth step, the algorithm uses two search rules, NRSR and TAO, and runs the target number of iterations; NRSR is expressed as follows: Where randn represents a normally distributed random number with a mean of 0 and a variance of 1, and X w Indicates the worst position, X b represents the optimal position. The equation has a random parameter to improve the search ability of NRBO and better balance the development and exploration capabilities; the algorithm can be enhanced by applying an adaptive coefficient called δ; Where IT represents the current iteration and Max_IT represents the maximum number of iterations. To maintain the balance between the exploration phase and the exploitation phase, the parameter δ is adaptive during the iteration. The utilization of the proposed NRBO is improved by introducing another parameter called ρ, which guides the population in the right direction. The expression of ρ is as follows: Where a and b are random numbers between (0, 1), r1 and r2 are different integers randomly selected from the population; however, the values ​​of r1 and r2 are not equal; the vector X n IT The current position of has been updated by the following equation; in, By updating The new vector position obtained; r1, r2 represent random numbers between (0, 1); TAO is added to improve the effectiveness of NRBO in dealing with real-world problems. By using TAO, it can significantly change position; it combines the best position X b and the current vector position Produce enhanced quality If the value of rand is less than DF, the solution is generated by the following equation Where rand represents a uniform random number between (0, 1), θ1 and θ2 are uniform random numbers between (-1, 1) and (-0.5, 0.5), DF represents the determining factor controlling the performance of NRBO, μ1 and μ2 are random numbers, which are respectively expressed by the following equations; Where rand represents a random number between (0, 1), and Δ represents a number between (0, 1); the above equation is further simplified as follows; μ1=β·3·rand+(1-β); μ2=β·rand+(1-β) Among them, β represents a binary number 1 or 0, and rand represents a random number; if the value of Δ is greater than or equal to 0.5, the value of β is 0; otherwise, the value is 1; due to the randomness of the selection of parameters μ1 and μ2, the population becomes more diverse and escapes from the local optimal solution, which helps to improve its diversity.

Images