Fused salt heat storage and solid oxide fuel cell variable load cooperative control method

Abstract

The invention discloses a fused salt heat storage and solid oxide fuel cell variable load cooperative control method, and relates to the field of new energy cooperative control. The method comprises the following steps: establishing a physical model of an integrated system consisting of a fused salt heat storage system and a solid oxide fuel cell system; respectively establishing heat flow models of the fused salt heat storage system and the solid oxide fuel cell system according to the physical model; further selecting an input quantity, a state quantity and an output quantity, and establishing a nonlinear state space model of the integrated system; observing the state quantity of the integrated system in real time by using the nonlinear state space model; and determining the state quantity meeting the real-time load demand, and regulating and controlling the operation states of the fused salt heat storage system and the solid oxide fuel cell system in the integrated system, so that the output power of the integrated system is equal to the real-time load demand. According to the application, the fused salt heat storage and the solid oxide fuel cell can be cooperatively controlled under the variable load operation condition, and the comprehensive utilization efficiency of the fused salt heat storage and the solid oxide fuel cell is improved.

Description

Technical Field

[0001] This application relates to the field of new energy collaborative control, and particularly to a variable load collaborative control method for molten salt thermal energy storage and solid oxide fuel cells. Background Art

[0002] Globally, the urgent need for energy structure transformation and environmental protection has promoted the rapid development of new energy technologies. Against this backdrop, molten salt thermal energy storage technology and solid oxide fuel cell (SOFC) technology have become research hotspots in the new energy field due to their high efficiency, environmental friendliness, and sustainability. Molten salt thermal energy storage technology utilizes the phase change characteristics of molten salts to store and release heat, while solid oxide fuel cells directly convert the chemical energy of fuels into electrical energy through electrochemical reactions.

[0003] Molten salt thermal energy storage technology, with its characteristics such as high energy density, wide temperature operating range, and long life cycle, has been widely applied in fields such as solar thermal power generation, industrial heat treatment, and cogeneration. This technology stores heat by melting salt substances at high temperatures and then releases the heat stored in the molten salts to meet heat energy demands when energy is needed. However, when the molten salt thermal energy storage system responds to load changes, there are problems such as complex heat management and fluctuating system efficiency, which limit its application in large-scale energy systems.

[0004] At the same time, as an efficient electrochemical energy conversion device, solid oxide fuel cells show great potential in fields such as distributed power generation and mobile power sources due to their high efficiency, low emissions, and fuel flexibility. However, when SOFC operates under variable loads, it is easily affected by unstable temperature and fuel supply, resulting in a decline in stack performance and a shortening of lifespan.

[0005] Therefore, how to overcome the limitations of molten salt thermal energy storage and solid oxide fuel cells when operating alone is a technical problem that urgently needs to be solved at present. Summary of the Invention

[0006] The purpose of this application is to provide a variable load collaborative control method for molten salt thermal energy storage and solid oxide fuel cells, which can collaboratively control molten salt thermal energy storage and solid oxide fuel cells under variable load operating conditions and improve the comprehensive utilization efficiency of molten salt thermal energy storage and solid oxide fuel cells.

[0007] To achieve the above purpose, this application provides the following solutions:

[0008] The present application provides a variable load cooperative control method for molten salt thermal energy storage and solid oxide fuel cells, including: establishing a physical model of an integrated system composed of a molten salt thermal energy storage system and a solid oxide fuel cell system; establishing a heat flow model of the molten salt thermal energy storage system according to the physical model; establishing a heat flow model of the solid oxide fuel cell system according to the physical model; selecting the fuel mass flow rate, air mass flow rate, and molten salt mass flow rate as input variables, the temperature state observation variables of different heat transfer surfaces in the integrated system as state variables, and the output power of the integrated system as the output variable, and establishing a nonlinear state space model of the integrated system according to the heat flow model of the molten salt thermal energy storage system and the heat flow model of the solid oxide fuel cell system; observing the state variables of the integrated system in real time by using the nonlinear state space model according to the initial input variables and the initially preset output variables; according to the real-time load demand, using the nonlinear state space model to determine the state variables that meet the real-time load demand, and regulating the operating states of the molten salt thermal energy storage system and the solid oxide fuel cell system in the integrated system according to the state variables that meet the real-time load demand, so that the output power of the integrated system is equal to the real-time load demand.

[0009] According to the specific embodiments provided by the present application, the present application has the following technical effects:

[0010] The present application provides a variable load cooperative control method for molten salt thermal energy storage and solid oxide fuel cells. Heat flow models are respectively established for the heat transfer processes of the molten salt thermal energy storage system and the solid oxide fuel cell system. The mass flows of air, hydrogen, and molten salt are selected as three input variables, the temperature state observation variables of different heat transfer surfaces in the integrated system are used as state variables, and the output power of the integrated system is used as the output variable. A nonlinear state space model of the integrated system is established. The nonlinear state space model can be used to observe in real time the temperature state observation variables such as the molten salt temperature in the heat storage heat exchanger and the waste heat flue gas temperature of the fuel cell. At the same time, according to the real-time load demand, the operating states of the molten salt thermal energy storage system and the solid oxide fuel cell system in the integrated system can be regulated, realizing the cooperative control of molten salt thermal energy storage and solid oxide fuel cells under variable load operating conditions, and improving the comprehensive utilization efficiency of molten salt thermal energy storage and solid oxide fuel cells. Description of the Drawings

[0011] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0012] Figure 1Schematic flow chart of a variable load coordinated control method for a molten salt thermal energy storage and solid oxide fuel cell provided in an embodiment of the present application;

[0013] Figure 2 Schematic diagram of the physical model of an integrated system provided in another embodiment of the present application;

[0014] Figure 3 Schematic diagram of the heat flow model of a molten salt thermal energy storage system provided in another embodiment of the present application;

[0015] Figure 4 Schematic diagram of the heat flow model of a solid oxide fuel cell system provided in another embodiment of the present application;

[0016] Figure 5 Simplified schematic flow chart of a variable load coordinated control method for a molten salt thermal energy storage and solid oxide fuel cell provided in an embodiment of the present application.

[0017] Reference numerals: First preheater - 1, second preheater - 2, stack - 3, tail gas combustion device - 4, electronic control unit - 5, molten salt thermal energy storage system model - 6. Detailed implementation manners

[0018] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0019] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0020] In an exemplary embodiment, as Figure 1 shown, a variable load coordinated control method for a molten salt thermal energy storage and solid oxide fuel cell is provided, including the following steps 101 to 106. Among them:

[0021] Step 101: Establish a physical model of an integrated system composed of a molten salt thermal energy storage system and a solid oxide fuel cell system.

[0022] Step 102: Establish a heat flow model of the molten salt thermal energy storage system according to the physical model.

[0023] Step 103: Establish a heat flow model of the solid oxide fuel cell system according to the physical model.

[0024] Step 104: According to the heat flow model of the molten salt thermal energy storage system and the heat flow model of the solid oxide fuel cell system, select the fuel mass flow rate, air mass flow rate, and molten salt mass flow rate as input variables, integrate the temperature state observables of different heat transfer surfaces in the integrated system as state variables, and integrate the output power of the integrated system as the output variable, and establish a nonlinear state space model of the integrated system.

[0025] Step 105: According to the initial input variables and the initially preset output variable, use the nonlinear state space model to observe the state variables of the integrated system in real time.

[0026] Step 106: According to the real-time load demand, use the nonlinear state space model to determine the state variables that meet the real-time load demand, and regulate the operating states of the molten salt thermal energy storage system and the solid oxide fuel cell system in the integrated system according to the state variables that meet the real-time load demand, so that the output power of the integrated system is equal to the real-time load demand.

[0027] Implementing the above Steps 101 to 106, a complete heat flow model of molten salt thermal energy storage and solid oxide fuel cells is established, which can observe and adjust the key parameters of the integrated system in real time, ensuring that the system power is adjusted to the maximum extent within the safety boundary of variable loads to meet the expected changes. At the same time, by observing in real time and using the waste heat temperature of the fuel cell exhaust gas in combination with molten salt energy storage, this collaborative control method can greatly improve the comprehensive utilization efficiency of solid oxide fuel cells and molten salt, reduce economic costs, and has extremely high application value.

[0028] In another exemplary embodiment of the present application, the overall heat transfer module of the molten salt thermal energy storage heat exchanger and the solid oxide fuel cell is analyzed, and a physical model of the integrated system is established by combining three heat transfer links, namely, the heat transfer link between the heat transfer surface and air and fuel, the reaction heat release link of fuel and air inside the stack, and the heat transfer link between the high-temperature waste heat flue gas and molten salt, as Figure 2 shown. The physical model includes: a molten salt thermal energy storage system model 6 and a solid oxide fuel cell system model. The solid oxide fuel cell system model includes: a first preheater 1, a second preheater 2, a stack 3, and a tail gas combustion device 4; air and fuel are preheated once by the first preheater 1 and then enter the second preheater 2 for secondary preheating; the air and fuel after secondary preheating enter the stack 3 to undergo a chemical reaction, and the tail gas after the chemical reaction is burned by the tail gas combustion device 4 to generate flue gas; the flue gas flows through the second preheater 2 and the first preheater 1 in sequence and then enters the molten salt thermal energy storage system model 6 to heat the cold molten salt into hot molten salt for storage, reducing energy loss. After the stack 3 undergoes a chemical reaction, combined heat and power generation can be carried out. Figure 2The electronic control unit 5 is also shown, and the electronic control unit 5 is used to maximize the power generation efficiency and the overall energy utilization rate of the system while ensuring the safety of the upper limits of the fuel cell stack temperature and the heat storage heat exchanger temperature according to the normal flow rates of the air flow rate, hydrogen flow rate, and molten salt flow rate.

[0029] In another exemplary embodiment of the present application, the molten salt heat storage system mainly consists of five major parts: a heat storage heat exchanger, a heat release heat exchanger, a cold molten salt tank, a hot molten salt tank, a heat storage medium, a pumping system, and a control system. Assuming that during the modeling process, the heat storage of the metal in the heat storage heat exchanger and the molten salt tank and the heat loss of the system pipeline equipment are ignored, and the inside of the heat storage heat exchanger is in a saturated state. Then the above step 102 can be replaced by the following steps 201 to 203:

[0030] Step 201: According to the physical model, establish the energy conservation equation of the molten salt heat storage system as:

[0031]

[0032] In the formula, M hse is the mass of the molten salt inside the heat storage heat exchanger in the molten salt heat storage system, kg; c p,sa is the specific heat capacity of the molten salt, kJ / (kg·°C); D hse is the molten salt flow rate flowing through the heat storage heat exchanger, kg / s; T hse,i , T hse,o are the inlet molten salt temperature and the outlet molten salt temperature of the heat storage heat exchanger, °C; Q hse is the heat exchange amount of the heat storage heat exchanger, kW; A hse is the heat exchange area of the heat storage heat exchanger, m 2 ; α hse is the heat transfer coefficient, kW / (m2·°C); T s is the saturated temperature of the heat storage heat exchanger, °C.

[0033] Step 202: According to the energy conservation equation of the molten salt heat storage system, establish the molten salt temperature state model of the heat storage heat exchanger in the molten salt heat storage system as:

[0034]

[0035] Step 203: According to the energy conservation equation of the molten salt heat storage system and the molten salt temperature state model, determine the heat flow model of the molten salt heat storage system.

[0036] The heat flow model of the molten salt heat storage system is as Figure 3 shown, and the overall process is briefly described as:

[0037] The first part - molten salt heat storage part: The main steam at the outlet of the superheater (i.e., economizer, steam-water separator) and the high-temperature waste heat flue gas flowing out of the first preheater in the solid oxide fuel cell are sent to the heat storage heat exchanger, where they are heat-exchanged with the cold molten salt pumped out of the cold tank. The low-temperature steam after heat exchange is sent to the inlet of the condenser and mixed with the exhaust steam of the last-stage steam turbine and then condensed into water. The low-temperature flue gas after heat exchange is sent into the heating pipeline to provide heating for enterprises and residential buildings, and then the heated molten salt is sent to the hot molten salt tank for storage.

[0038] The second part - molten salt heat release part: The hot molten salt pumped out of the hot molten salt tank is sent to the heat release heat exchanger to heat the pumped water from the outlet of the deaerator into high-pressure steam and send it to the boiler (i.e., economizer, steam-water separator, all in one). These high-pressure steam is efficiently converted into mechanical energy and the heat energy is regulated through the high-pressure cylinder, intermediate-pressure cylinder, and low-pressure cylinder, so as to be sent to the steam turbine generator for power generation most efficiently. Finally, the cooled molten salt is sent to the cold tank for storage, and the entire molten salt heat storage system forms a cycle.

[0039] In another exemplary embodiment of the present application, the above step 103 can be replaced by the following steps 301 to 304:

[0040] Step 301: According to the physical model, determine the heat release expression and radiation heat transfer expression of the internal chemical reaction in the stack of the solid oxide fuel cell system.

[0041] Exemplarily, determine the fuel inlet temperature T fuel,o and the air inlet temperatures T air,o , T aircell,o inside and outside the air supply pipe, and determine the initial mass flow rates m in,air , m in,fuel .

[0042] The heat release expression of the internal chemical reaction in the solid oxide fuel cell can be expressed as:

[0043] Q gen = Q chem - Q elec (5)

[0044] In the formula, Q gen is the heat release of the internal chemical reaction in the stack of the solid oxide fuel cell system, Q chem is the available work released by the chemical reaction, and Q elec is the output electric power of the fuel cell. The calculation formula of Q chem is:

[0045] Q chem = nΔH (6)

[0046] Among them, n is the number of stacks, and ΔH is the change in enthalpy value of the internal chemical reaction of the stack in the solid oxide fuel cell system.

[0047] Q elec is defined as:

[0048] Q elec = I·V out (7)

[0049] Among them, I is the load current on the user side, and V out is the output voltage of the stack.

[0050] Q rad is the radiative heat transfer amount between the battery and the AST (air supply duct), and is expressed as:

[0051]

[0052] In the formula, Q rad is the radiative heat transfer amount between the battery and the air supply duct in the stack, ε AST is the emissivity of the air supply duct, σ is the Stefan-Boltzmann constant, A AST,outer is the external area of the air supply duct, T cell is the battery temperature, T AST is the air supply duct temperature.

[0053] Step 302: Establish the transfer function of the preheater in the solid oxide fuel cell system.

[0054] Exemplarily, according to the heat exchange process between the high-temperature flue gas and the fuel pipeline in the preheater, R conv,bur,fueltube and R conv,fuel,tube are set as the two thermal resistances of the heat exchange process, Q conv,bur,fueltube and Q conv,fuel,tube are the heat exchange amounts of the two thermal resistances, which are driven by two linear temperature differences, namely T bur -T fuel,tube and T fuel,tube -T fuel , and the heat exchange process between the high-temperature flue gas and the air pipeline is the same and will not be elaborated. T bur is the flue gas outlet temperature of the first preheater.

[0055] The specific transfer function expression is as follows:

[0056] The heat exchange expression between the flue gas and the fuel pipeline in the preheater is:

[0057]

[0058] In the formula, R conv,bur,fueltube is the heat transfer resistance between the flue gas and the fuel pipeline, G bur is the heat flow of the flue gas, a bur,fuelis the first intermediate parameter, a bur,fuel =(KA) bur,fuel / G bur , (KA) bur,fuel is the product of the heat transfer coefficient and the heat transfer area in the heat exchange process between the fuel and the flue gas; Q conv,bur,fueltube is the heat transfer amount of the heat transfer resistance between the flue gas and the fuel pipeline, T fuel,tube is the wall temperature of the fuel pipeline.

[0059] The heat exchange expression between the fuel pipeline and the fuel in the preheater is:

[0060]

[0061] In the formula, R conv,fuel,tube is the heat transfer resistance between the fuel and the fuel pipeline, G fuel is the fuel heat flow, a fuel is the second intermediate parameter, a fuel =(KA) fuel / G fuel , (KA) fuel is the product of the heat transfer coefficient and the heat transfer area in the heat exchange process between the fuel pipeline and the fuel, Q conv,fuel,tube is the heat transfer amount of the heat transfer resistance between the fuel and the fuel pipeline, T fuel is the real-time temperature of the fuel.

[0062] Step 303: Determine the energy conservation equations of the stack and the air supply pipe in the solid oxide fuel cell system according to the heat release expression, the radiative heat transfer expression, and the transfer function; wherein, air enters the stack through the air supply pipe.

[0063] Exemplarily, the stack and the air supply pipe are the core structures of the solid oxide fuel cell and are crucial for adjusting the load change of the system. The simplified energy conservation equation of the stack is:

[0064]

[0065]

[0066] Wherein, C AST and C cell are the heat capacities of the AST and the battery. The differential equation describing the temperature change of each node is:

[0067]

[0068] Wherein, (mc) air , (mc) aircell and (mc) fuelIt is the product of the heat capacity and mass of different fluids. Taking the differential equation (15) as an example, the node temperature at this time is the instantaneous state quantity of the air temperature during the heat exchange process between the high-temperature flue gas and the low-temperature air.

[0069] Step 304: Determine the heat flow model of the solid oxide fuel cell system according to the energy conservation equations of the stack and the air supply pipe in the solid oxide fuel cell system.

[0070] The heat flow model of the solid oxide fuel cell system is as Figure 4 shown. The heat flow model of the solid oxide fuel cell system includes: a fuel preheating model, an air preheating model, a stack model, and a power generation model.

[0071] The fuel preheating model includes a first power supply, a second power supply, a third power supply, a first resistor, a second resistor, a third resistor, a fourth resistor, a first capacitor, and a second capacitor; the positive pole of the first power supply is respectively connected to one end of the first resistor and the negative pole of the second power supply; the other end of the first resistor is respectively connected to one end of the second resistor and one end of the first capacitor, the other end of the second resistor is connected to the negative pole of the third power supply, and the other end of the first capacitor is grounded; the positive pole of the second power supply is connected to one end of the third resistor, the other end of the third resistor is respectively connected to one end of the fourth resistor and one end of the second capacitor, and the other end of the second capacitor is grounded; wherein, the negative pole of the first power supply is used as the fuel inlet temperature T fuel,o , the negative pole of the second power supply is used as the fuel temperature T fuel1 at the stack inlet, the connection midpoint between the other end of the first resistor and one end of the second resistor is used as the first fuel pipeline wall temperature T fueltube1 , the negative pole of the third power supply is used as the flue gas inlet temperature T bur1 of the first preheater, the connection midpoint between the other end of the third resistor and one end of the fourth resistor is used as the second fuel pipeline wall temperature T fueltube2 , and both the positive pole of the third power supply and the other end of the fourth resistor are used as the flue gas inlet temperature T bur2 of the second preheater.

[0072] The air preheating model includes a fourth power supply, a fifth power supply, a sixth power supply, a fifth resistor, a sixth resistor, a seventh resistor, an eighth resistor, a third capacitor, and a fourth capacitor; the positive pole of the fourth power supply is respectively connected to one end of the fifth resistor and the negative pole of the fifth power supply; the other end of the fifth resistor is respectively connected to one end of the sixth resistor and one end of the third capacitor, the other end of the sixth resistor is connected to the negative pole of the sixth power supply, and the other end of the third capacitor is grounded; the positive pole of the fifth power supply is connected to one end of the seventh resistor, the other end of the seventh resistor is respectively connected to one end of the eighth resistor and one end of the fourth capacitor, and the other end of the fourth capacitor is grounded; wherein, the negative pole of the fourth power supply is used as the air inlet temperature T air,in , the negative pole of the fifth power supply is used as the air temperature T air1, the connection midpoint between the other end of the fifth resistor and one end of the sixth resistor serves as the temperature T of the first air duct wall airtube1 , the negative pole of the sixth power supply serves as the temperature T of the flue gas inlet of the first preheater bur1 , the connection midpoint between the other end of the seventh resistor and one end of the eighth resistor serves as the temperature T of the second air duct wall airtube2 , both the positive pole of the sixth power supply and the other end of the eighth resistor serve as the temperature T of the flue gas inlet of the second preheater bur2 .

[0073] The stack model includes a seventh power supply, an eighth power supply, a ninth power supply, a ninth resistor, a tenth resistor, an eleventh resistor, a twelfth resistor, a fifth capacitor, and a sixth capacitor; the negative pole of the seventh power supply is connected to the positive pole of the second power supply, the positive pole of the seventh power supply is connected to one end of the ninth resistor, the other end of the ninth resistor is respectively connected to one end of the tenth resistor and one end of the fifth capacitor, the other end of the tenth resistor is connected to the positive pole of the eighth power supply, the negative pole of the eighth power supply is connected to one end of the eleventh resistor, the other end of the eleventh resistor is respectively connected to one end of the twelfth resistor and one end of the sixth capacitor, the other end of the twelfth resistor is connected to the positive pole of the ninth power supply, the negative pole of the ninth power supply is connected to the positive pole of the fifth power supply, the other end of the fifth capacitor is connected to the input end of the power generation model, and the other end of the sixth capacitor is grounded; among them, the ninth resistor is the heat transfer resistance between the fuel and the battery, the tenth resistor is the heat transfer resistance between the air and the battery, the eleventh resistor is the heat transfer resistance of the air outside the air duct, and the twelfth resistor is the heat transfer resistance of the air inside the air duct; the negative pole of the seventh power supply serves as the initial temperature T of the fuel fuel,o , the positive pole of the seventh power supply serves as the temperature T of the fuel fuel , the connection midpoint between the other end of the ninth resistor and one end of the tenth resistor serves as the temperature T of the battery cell , the positive pole of the eighth power supply serves as the transient temperature T of the air inside the battery aircell,i , the negative pole of the eighth power supply serves as the temperature T of the air outlet of the air duct aircell,o , the connection midpoint between the other end of the eleventh resistor and one end of the twelfth resistor serves as the temperature T of the air duct AST , the positive pole of the ninth power supply serves as the real-time temperature T of the air on the cathode side of the fuel cell air , the negative pole of the ninth power supply serves as the initial temperature T of the air inside the air duct air,o .

[0074] Figure 4 Brief description of the overall process shown:

[0075] The first part: The preheater part - the white frame 1 and the white frame 2 are the above-mentioned 3.2 preheater energy flow part, T bur2 (The flue gas inlet temperature K of the second preheater 2) and T bur1(The flue gas inlet temperature K of the first preheater 1) exchanges convective heat with air and fuel hydrogen. First, it exchanges heat through the air pipeline R conv,air,tube1 and the fuel hydrogen pipeline R conv,bur,fueltube1 by convective heat transfer, and then exchanges heat with the corresponding air and hydrogen through the hot air pipeline and hydrogen pipeline to achieve the purpose of preheating and meet the temperature conditions for entering the fuel cell stack for chemical reactions. K is the Kelvin temperature.

[0076] The second part: The fuel cell stack part - the white frame 3 is the above-mentioned 3.1 fuel cell stack energy flow part. The preheated hydrogen and oxygen pass through the corresponding heat transfer resistances R conv,air (the heat transfer resistance between air and the cell) and R conv,fuel (the heat transfer resistance between fuel and the cell), and reach the anode and cathode of the electrochemical reaction respectively to carry out the chemical reaction, start to release heat and generate electricity.

[0077] The third part: The power generation part - the white frame 4. The electricity generated by the fuel cell stack is initially the open-circuit voltage during the electrochemical reaction process. After activation polarization V act , concentration polarization V conc and ohmic polarization V ohm , there are different degrees of voltage drop losses. The figure clearly shows the corresponding equivalent thermal resistances and the series-parallel relationship of the circuit. These losses will affect the overall resistance of the SOFC. Therefore, the actual output voltage of the fuel cell is lower than the open-circuit voltage of the cell. The actual output voltage of the SOFC can be expressed as: V cell = E cell - V act - V ohm - V conc .

[0078] In another exemplary embodiment of the present application, the above step 104 can be replaced by the following steps 401 to:

[0079] Step 401: According to the heat flow model of the molten salt thermal energy storage system and the heat flow model of the solid oxide fuel cell system, select the fuel mass flow rate, air mass flow rate, and molten salt mass flow rate as input quantities, integrate the temperature state observables of different heat transfer surfaces in the system as state quantities, and integrate the output power of the system as the output quantity.

[0080] Determine the temperature observation of key points inside the system according to the molten salt thermal energy storage system model and the solid oxide fuel cell heat flow model: the cell temperature T cell , the air duct temperature T AST , the flue gas outlet temperature T of the primary preheater (the first preheater 1) bur , the inlet and outlet molten salt temperatures T of the thermal energy storage heat exchanger hse,i , T hse,o and the key point temperatures inside the preheater: T airtube1 , T airtube2,T fueltube1 ,T fueltube2 , a total of nine temperature state observables are established to fully meet the purpose of real-time observation and control of the system, and to determine the initial mass flow rates of fuel and air O air ,O fuel and the initial mass flow rate Q of the heat storage heat exchanger hse .

[0081] Since some of the selected parameters use the given values under standard conditions, that is, the data at the stable operating conditions reached after the cold start of the battery are used to describe the model, and the research faces a wide range of loads and multiple operating conditions. To accurately present the parameter changes under different operating conditions, by selecting multiple state variables and finding the correlation function with the operating parameters, the target nonlinear state space equation is obtained to ensure the accuracy of the model.

[0082] For the established state space expression model, the fuel mass flow rate, air mass flow rate, and molten salt mass flow rate are selected as the input quantity u:

[0083] u = [O air ,O fuel ,O bse T .

[0084] The stack battery temperature T cell , the stack air supply pipe temperature T AST , the preheater air duct temperature T airube1 ,T airtube2 , the preheater fuel duct temperature T fueltube1 ,T fueltube2 , the flue gas outlet temperature T of the primary preheater bur , the inlet and outlet molten salt temperatures T of the heat storage heat exchanger hse,i ,T hse,o A total of 9 heat transfer surface temperatures, x, are used as state variables:

[0085] x = [T hse,o ,T hse,i ,T bur ,T AST ,T cell ,T airtube1 ,T airtube2 ,T fueltube1 ,T fueltube2 T .

[0086] At the same time, the power P is selected as the output quantity y to explore the variable load flexibility regulation of the integrated system of molten salt heat storage and solid oxide fuel cell under different operating conditions, and to observe the heat storage capacity of the molten salt after the waste flue gas is fully utilized by the molten salt heat storage and the generated power through the steam turbine generator in the later stage, so as to accurately calculate the improvement range of the efficiency of the solid oxide fuel cell.​​

[0087] Step 402: Establish a non-linear state transition equation according to the selected state variables.

[0088] Exemplarily, based on the energy conservation equation, a non-linear state space model is initially obtained:

[0089]

[0090] where is used to evaluate the heat storage capacity of the heat transfer working medium and the battery heat transfer surface, the heat storage capacity of the molten salt in the heat storage heat exchanger, and the utilization amount of the waste heat of the battery flue gas. are the state matrix and the input matrix respectively. and describe the change of the output variable caused by the change of the input and the state variable. The matrix is usually a zero matrix. Due to the complexity of the parameters, the above matrix parameters are currently in a non-linear form. According to the heat flow model of the integrated system of molten salt heat storage and solid oxide fuel cell, the detailed expression of its non-linear state transition equation is obtained from the functional relationship of the temperature state variable x:

[0091]

[0092] In the formula, x is the state variable, t is the time, D hse is the molten salt flow rate through the heat storage heat exchanger, c p,sa is the specific heat capacity of the molten salt, M hse is the mass of the molten salt inside the heat storage heat exchanger in the molten salt heat storage system, C bur is the heat capacity of the flue gas, R conv,bur,airtube is the heat transfer resistance between the flue gas and the air pipeline, R conv,bur,fueltube is the heat transfer resistance between the flue gas and the fuel pipeline, C AST is the heat capacity of the air supply pipeline, R con,AST,outer is the heat transfer resistance of the air outside the air supply pipeline, R con,AST,inner is the heat transfer resistance of the air inside the air supply pipeline, C cell is the heat capacity of the battery, R conv,air is the heat transfer resistance between the air and the battery, R conv,fuel is the heat transfer resistance between the fuel and the battery, C airtube1 is the heat capacity of the first air pipeline, R conv,bur,airtube1 is the heat transfer resistance between the flue gas and the first air pipeline, R conv,air,tube1 is the heat transfer resistance between the air and the first air pipeline, C airtube2 is the heat capacity of the second air pipeline, C fueltube1 is the heat capacity of the first fuel pipeline, R conv,bur,fueltube1 is the heat transfer resistance between the flue gas and the first fuel pipeline, R conv,fuel,tube1 is the heat transfer resistance between the fuel and the first fuel pipeline, C fueltube2is the heat capacity of the second fuel pipeline, R conv,bur,fueltube2 is the heat transfer resistance between the flue gas and the second fuel pipeline, R conv,fuel,tube2 is the heat transfer resistance between the fuel and the second fuel pipeline; T hse,i 、T hse,o are the inlet molten salt temperature and the outlet molten salt temperature of the heat storage heat exchanger respectively, T AST is the temperature of the air supply pipe, T cell is the battery temperature, T airube1 is the temperature of the wall of the first air pipeline, T airtube2 is the temperature of the wall of the second air pipeline, T fueltube1 is the temperature of the wall of the first fuel pipeline, T fueltube2 is the temperature of the wall of the second fuel pipeline; T air,tube is the temperature of the air pipeline, T fuel,tube is the temperature of the fuel pipeline, Q rad is the radiative heat transfer amount between the battery and the air supply pipe in the stack, T aircell,i is the transient temperature of the air in the battery, T air,i is the transient temperature of the air in the air supply pipe, Q chem is the available work released by the chemical reaction, Q elec is the output electric power of the fuel cell, T fuel,i is the transient temperature of the fuel, T bur1 is the inlet flue gas temperature of the first preheater, T air1 is the air temperature at the inlet of the stack, T bur2 is the inlet flue gas temperature of the second preheater, T air,o is the initial temperature of the air in the air supply pipe, T fuel1 is the fuel temperature at the inlet of the stack, T fuel,o is the initial temperature of the fuel.

[0093] Step 403: Establish a non - linear output equation according to the selected input and output variables.

[0094] Exemplarily, place the selected output variable y and input variable u into the output equation to determine the dynamic characteristics of the integrated system of molten salt heat storage and solid oxide fuel cell in real - time. The following is the detailed expression for obtaining its non - linear output equation:

[0095]

[0096] In the formula, P is the output power of the integrated system, is the matrix describing the change of the output variable caused by the change of the input variable, is the matrix describing the change of the output variable caused by the change of the state variable; T hse,i 、T hse,o are the inlet molten salt temperature and the outlet molten salt temperature of the heat storage heat exchanger respectively, T AST is the temperature of the air supply pipe, Tcell is the battery temperature, T airtube1 is the first air duct wall temperature, T airtube2 is the wall temperature of the second air duct, T fueltube1 is the wall temperature of the first fuel pipeline, T fueltube2 is the wall temperature of the second fuel pipeline; air is the air input mass flow rate, O fuel is the fuel input mass flow rate, O hse is the molten salt flow rate of the heat storage heat exchanger.

[0097] Step 404: Simplify the nonlinear state transfer equation and the nonlinear output equation to: Where x is the state quantity, u is the input quantity, t is the time, f is the nonlinear state function describing the dynamic behavior of solid oxide fuel cells and molten salt heat storage, y is the output quantity, and g is the nonlinear output function.

[0098] An important reason for establishing the state-space expression is that it can accurately characterize the heat storage capacity of the key components of the molten salt heat storage system and the solid oxide fuel cell model at each stage, and make corrections based on the model data to obtain accurate heat exchange rates in real time, thereby establishing a control system model for the solid oxide fuel cell and molten salt heat storage system model that can accurately evaluate the heat exchange capacity.

[0099] Since the parameter matrix currently presented is in a nonlinear form, it is necessary to select the appropriate working point for data linearization to obtain a standard state space model, and use the model predictive control algorithm to perform real-time control and parameter adjustment on the integrated system.

[0100] This application establishes a complete molten salt heat storage and solid oxide fuel cell heat flow model and state space expression, which can observe and adjust the key parameters of the integrated system in real time, ensuring that the system can adjust the system power to the maximum extent within the safety boundary of variable load to meet the expected changes. At the same time, by real-time observation and utilization of the waste heat temperature of fuel cell waste flue gas combined with molten salt energy storage, this collaborative control method can greatly improve the comprehensive utilization efficiency of solid oxide fuel cells and molten salts, reduce economic costs, and has extremely high application value.

[0101] The method of the present application can be simplified as follows: Figure 5The process shown includes steps 1 to 4. Step 1: Analyze the overall heat exchange module of the molten salt thermal energy storage heat exchanger and the solid oxide fuel cell. Combine the heat exchange links between the heat exchange surface and air and fuel, the reaction heat release link of fuel and air inside the stack, and the heat exchange link between the high-temperature waste heat flue gas and molten salt to establish an overall physical model for a total of three heat exchange links. Step 2: According to the physical model of the overall heat exchange module of the molten salt thermal energy storage heat exchanger and the solid oxide fuel cell established above, establish dynamic heat flow models for the heat exchange modules of the molten salt thermal energy storage system and the solid oxide fuel cell system respectively. Step 3: Based on the above two dynamic heat flow models and extract the key temperature state variables therein to determine the state space model of the integrated system of the molten salt thermal energy storage heat exchanger and the solid oxide fuel cell. Step 4: Use the state space model to determine various dynamic characteristics of the integrated system of the heat storage heat exchanger and the solid oxide fuel cell in real time under the disturbance of variable load and on the premise of ensuring the safety boundary, and continuously improve the cogeneration efficiency of the integrated system.

[0102] To overcome the limitations when the molten salt thermal energy storage and the solid oxide fuel cell operate separately, this application combines the two and realizes variable load coordinated control. This coordinated control can achieve the following technical advantages by intelligently regulating the operating states of the molten salt thermal energy storage and the SOFC:

[0103] First of all, the coordinated control can dynamically adjust the heat storage and release of the molten salt thermal energy storage system according to the real-time load demand, thereby balancing the power output of the SOFC and improving the stability and response speed of the entire energy system. Secondly, by optimizing the operation and control strategies of the molten salt thermal energy storage and the SOFC, the energy utilization rate can be maximized, energy waste can be reduced, and the overall economic benefits of the system can be improved. In addition, the coordinated control can also effectively utilize the remaining heat energy of the SOFC under partial load and recover it through the molten salt thermal energy storage system to further improve the energy utilization efficiency.

[0104] In terms of environmental protection, the synergistic effect of the molten salt thermal energy storage and the SOFC not only reduces the consumption of fossil fuels but also reduces the emissions of greenhouse gases and other pollutants, contributing to the goal of sustainable development. At the same time, this coordinated control also has good scalability and can be combined with renewable energy sources such as wind energy and solar energy to form a more efficient and environmentally friendly energy supply system.

[0105] In short, the variable load coordinated control method of the molten salt thermal energy storage and the solid oxide fuel cell combines the advantages of the two technologies. It can not only improve the energy conversion efficiency, enhance the system stability, but also promote the utilization of renewable energy and reduce environmental pollution, having broad application prospects and important social and economic value.

[0106] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0107] In this article, specific examples are used to elaborate on the principles and implementation manners of the present application. The descriptions of the above embodiments are only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation on the present application.

Claims

1. A method for coordinated control of molten salt heat storage and solid oxide fuel cells with variable load, characterized in that: include: Establish a physical model of the integrated system consisting of a molten salt thermal energy storage system and a solid oxide fuel cell system; According to the physical model, a heat flow model of the molten salt heat storage system is established; According to the physical model, a heat flow model of a solid oxide fuel cell system is established; According to the heat flow model of molten salt heat storage system and the heat flow model of solid oxide fuel cell system, the fuel mass flow rate, air mass flow rate and molten salt mass flow rate are selected as input quantities, the temperature state observations of different heat exchange surfaces in the integrated system are taken as state quantities, and the output power of the integrated system is taken as output quantity, and a nonlinear state space model of the integrated system is established; According to the initial input quantity and the initial preset output quantity, using the nonlinear state space model, the state quantity of the integrated system is observed in real time; According to the real-time load demand, the nonlinear state space model is used to determine the state quantity that meets the real-time load demand, and the operating state of the molten salt heat storage system and the operating state of the solid oxide fuel cell system in the integrated system are regulated according to the state quantity that meets the real-time load demand, so that the output power of the integrated system is equal to the real-time load demand.

2. The variable load coordinated control method of molten salt heat storage and solid oxide fuel cell according to claim 1 is characterized in that: The physical model includes: a molten salt heat storage system model and a solid oxide fuel cell system model; the solid oxide fuel cell system model includes: a first preheater, a second preheater, a fuel cell stack and a tail gas combustion device; After the air and fuel are preheated once in the first preheater, they enter the second preheater for secondary preheating; The air and fuel after secondary preheating enter the fuel cell stack to undergo a chemical reaction. The tail gas after the chemical reaction is burned in the tail gas combustion device to produce flue gas. After the flue gas flows through the second preheater and the first preheater in sequence, it enters the molten salt heat storage system model to heat the cold molten salt into hot molten salt for storage.

3. The variable load coordinated control method of molten salt heat storage and solid oxide fuel cell according to claim 1 is characterized in that: According to the physical model, a heat flow model of the molten salt heat storage system is established, which specifically includes: According to the physical model, the energy conservation equation of the molten salt heat storage system is established as: and Where M hse is the mass of molten salt inside the heat exchanger in the molten salt heat storage system, c p,sa is the specific heat capacity of molten salt, D hse is the molten salt flow rate flowing through the heat storage heat exchanger, T hse,i 、T hse,o are the inlet and outlet molten salt temperatures of the heat storage heat exchanger, Q hse is the heat transfer capacity of the heat storage heat exchanger, A hse is the heat transfer area of ​​the heat storage heat exchanger, α hse is the heat transfer coefficient, T s is the saturation temperature of the heat storage heat exchanger; According to the energy conservation equation of the molten salt heat storage system, the molten salt temperature state model of the heat storage heat exchanger in the molten salt heat storage system is established as follows: and According to the energy conservation equation of the molten salt heat storage system and the molten salt temperature state model, a heat flow model of the molten salt heat storage system is determined.

4. The variable load coordinated control method of molten salt heat storage and solid oxide fuel cell according to claim 1 is characterized in that: According to the physical model, a heat flow model of a solid oxide fuel cell system is established, which specifically includes: According to the physical model, determining the heat release expression and radiation heat transfer expression of the internal chemical reaction of the stack in the solid oxide fuel cell system; Establish the transfer function of the preheater in a solid oxide fuel cell system; According to the heat release expression, the radiation heat transfer expression and the transfer function, the energy conservation equation of the stack and the air supply pipe in the solid oxide fuel cell system is determined; wherein the air enters the stack through the air supply pipe; According to the energy conservation equation of the stack and the air supply pipe in the solid oxide fuel cell system, the heat flow model of the solid oxide fuel cell system is determined.

5. The variable load coordinated control method of molten salt heat storage and solid oxide fuel cell according to claim 4 is characterized in that: The heat release expression is: Q gen =Q chem -Q elec ; Q chem =nΔH; Q elec =I·V out ; In the formula, Q gen Q is the heat released by the chemical reaction inside the stack in the solid oxide fuel cell system, chem is the available work released by the chemical reaction, Q elec is the output power of the fuel cell, n is the number of stacks, ΔH is the enthalpy change of the chemical reaction inside the stack in the solid oxide fuel cell system, I is the user side load current, V out is the stack output voltage; The radiation heat transfer expression is: In the formula, Q rad is the radiation heat transfer between the battery and the air supply pipe in the battery stack, ε AST is the emissivity of the air supply duct, σ is the Stefan-Boltzmann constant, T AST,outer is the external area of ​​the air supply duct, T cell is the battery temperature, T AST is the air supply duct temperature.

6. The variable load coordinated control method of molten salt heat storage and solid oxide fuel cell according to claim 4 is characterized in that: The transfer function includes: a heat exchange expression between the flue gas in the preheater and the fuel pipeline, and a heat exchange expression between the fuel pipeline in the preheater and the fuel; The heat exchange expression between the flue gas and the fuel pipeline in the preheater is: In the formula, R conv,bur,fueltube is the heat transfer resistance between flue gas and fuel pipeline, G bur is the flue gas heat flow, a bur,fuel is the first intermediate parameter, a bur,fuel =(KA) bur,fuel / G bur , (KA) bur,fuel It is the product of the heat transfer coefficient and the heat transfer area in the heat exchange process between fuel and flue gas; Q conv,bur,fueltube is the heat transfer resistance between the flue gas and fuel pipeline, T bur is the preheater flue gas inlet temperature, T fuel,tube is the fuel pipeline wall temperature; The heat exchange expression between the fuel pipeline and the fuel in the preheater is: In the formula, R conv,fuel,tube is the heat transfer resistance between fuel and fuel pipeline, G fuel is the fuel heat flow, a fuel is the second intermediate parameter, a fuel =(KA) fuel / G fuel , (KA) fuel It is the product of the heat transfer coefficient and the heat transfer area of ​​the heat exchange process between the fuel pipeline and the fuel. conv,fuel,tube is the heat transfer resistance between the fuel and the fuel pipeline, T fuel The real-time fuel temperature.

7. The variable load coordinated control method of molten salt heat storage and solid oxide fuel cell according to claim 4 is characterized in that: The energy conservation equation for the stack and air supply pipe in the solid oxide fuel cell system is: In the formula, C AST is the heat capacity of the air supply pipe, T AST is the air supply pipe temperature, Q rad is the radiation heat transfer between the battery and the air supply pipe in the battery stack, T aircell,o is the air outlet temperature of the air supply duct, T air,i is the transient temperature of the air in the battery, R conv,AST,outer is the heat transfer resistance of air outside the air supply duct, R conv,AST,inner is the heat transfer resistance of air in the air supply duct; C cell is the battery thermal capacity, T cell is the battery temperature, Q chem is the available work released by the chemical reaction, Q elec is the output power of the fuel cell, T aircell,i is the transient temperature of the air in the battery, T fuel,i is the transient temperature of the fuel, R conv,air is the thermal resistance between air and battery, R conv,fuel Thermal resistance for heat exchange between fuel and battery.

8. The variable load coordinated control method of molten salt heat storage and solid oxide fuel cell according to claim 1 is characterized in that: The heat flow model of the solid oxide fuel cell system includes: a fuel preheating model, an air preheating model, a fuel cell stack model and a power generation model; The fuel preheating model includes a first power supply, a second power supply, a third power supply, a first resistor, a second resistor, a third resistor, a fourth resistor, a first capacitor and a second capacitor; the positive electrode of the first power supply is respectively connected to one end of the first resistor and the negative electrode of the second power supply; the other end of the first resistor is respectively connected to one end of the second resistor and one end of the first capacitor, the other end of the second resistor is connected to the negative electrode of the third power supply, and the other end of the first capacitor is grounded; the positive electrode of the second power supply is connected to one end of the third resistor, the other end of the third resistor is respectively connected to one end of the fourth resistor and one end of the second capacitor, and the other end of the second capacitor is grounded; wherein the negative electrode of the first power supply is used as the fuel inlet temperature, the negative electrode of the second power supply is used as the fuel temperature at the inlet of the fuel cell stack, the midpoint of the connection between the other end of the first resistor and one end of the second resistor is used as the first fuel pipeline wall temperature, the negative electrode of the third power supply is used as the first preheater flue gas inlet temperature, the midpoint of the connection between the other end of the third resistor and one end of the fourth resistor is used as the second fuel pipeline wall temperature, and the positive electrode of the third power supply and the other end of the fourth resistor are both used as the second preheater flue gas inlet temperature; The air preheating model includes a fourth power supply, a fifth power supply, a sixth power supply, a fifth resistor, a sixth resistor, a seventh resistor, an eighth resistor, a third capacitor and a fourth capacitor; the positive electrode of the fourth power supply is respectively connected to one end of the fifth resistor and the negative electrode of the fifth power supply; the other end of the fifth resistor is respectively connected to one end of the sixth resistor and one end of the third capacitor, the other end of the sixth resistor is connected to the negative electrode of the sixth power supply, and the other end of the third capacitor is grounded; the positive electrode of the fifth power supply is connected to one end of the seventh resistor, the other end of the seventh resistor is respectively connected to one end of the eighth resistor and one end of the fourth capacitor, and the other end of the fourth capacitor is grounded; wherein the negative electrode of the fourth power supply is used as the air inlet temperature, the negative electrode of the fifth power supply is used as the air temperature at the inlet of the battery stack, the midpoint of the connection between the other end of the fifth resistor and one end of the sixth resistor is used as the first air duct wall temperature, the negative electrode of the sixth power supply is used as the first preheater flue gas inlet temperature, the midpoint of the connection between the other end of the seventh resistor and one end of the eighth resistor is used as the second air duct wall temperature, and the positive electrode of the sixth power supply and the other end of the eighth resistor are both used as the second preheater flue gas inlet temperature; The battery stack model includes a seventh power supply, an eighth power supply, a ninth power supply, a ninth resistor, a tenth resistor, an eleventh resistor, a twelfth resistor, a fifth capacitor and a sixth capacitor; the negative electrode of the seventh power supply is connected to the positive electrode of the second power supply, the positive electrode of the seventh power supply is connected to one end of the ninth resistor, the other end of the ninth resistor is respectively connected to one end of the tenth resistor and one end of the fifth capacitor, the other end of the tenth resistor is connected to the positive electrode of the eighth power supply, the negative electrode of the eighth power supply is connected to one end of the eleventh resistor, the other end of the eleventh resistor is respectively connected to one end of the twelfth resistor and one end of the sixth capacitor, the other end of the twelfth resistor is connected to the positive electrode of the ninth power supply, the negative electrode of the ninth power supply is connected to the positive electrode of the fifth power supply, the other end of the fifth capacitor is connected to the input end of the power generation model, and the sixth capacitor the other end of the resistor is grounded; wherein the ninth resistor is the heat exchange resistance between the fuel and the battery, the tenth resistor is the heat exchange resistance between the air and the battery, the eleventh resistor is the heat exchange resistance of the air outside the air supply duct, and the twelfth resistor is the heat exchange resistance of the air inside the air supply duct; the negative electrode of the seventh power supply is used as the initial temperature of the fuel, the positive electrode of the seventh power supply is used as the temperature of the fuel, the midpoint of the connection between the other end of the ninth resistor and one end of the tenth resistor is used as the battery temperature, the positive electrode of the eighth power supply is used as the transient temperature of the air in the battery, the negative electrode of the eighth power supply is used as the air outlet temperature of the air supply duct, the midpoint of the connection between the other end of the eleventh resistor and one end of the twelfth resistor is used as the air supply duct temperature, the positive electrode of the ninth power supply is used as the real-time temperature of the air on the cathode side of the fuel cell, and the negative electrode of the ninth power supply is used as the initial temperature of the air in the air supply duct.

9. The variable load coordinated control method of molten salt heat storage and solid oxide fuel cell according to claim 1 is characterized in that: According to the heat flow model of molten salt heat storage system and the heat flow model of solid oxide fuel cell system, the fuel mass flow rate, air mass flow rate and molten salt mass flow rate are selected as input quantities, the temperature state observations of different heat exchange surfaces in the integrated system are taken as state quantities, and the output power of the integrated system is taken as output quantity. The nonlinear state space model of the integrated system is established, which specifically includes: According to the heat flow model of molten salt heat storage system and the heat flow model of solid oxide fuel cell system, the fuel mass flow rate, air mass flow rate and molten salt mass flow rate are selected as input quantities, the temperature state observations of different heat exchange surfaces in the integrated system are taken as state quantities, and the output power of the integrated system is taken as output quantity; According to the selected state quantity, a nonlinear state transfer equation is established; According to the selected input and output quantities, a nonlinear output equation is established; The nonlinear state transfer equation and the nonlinear output equation are simplified as follows: Where x is the state quantity, u is the input quantity, t is the time, f is the nonlinear state function describing the dynamic behavior of solid oxide fuel cells and molten salt heat storage, y is the output quantity, and g is the nonlinear output function.

10. The load-variable coordinated control method of molten salt heat storage and solid oxide fuel cell according to claim 9, characterized in that: The nonlinear state transfer equation is: In the formula, x is the state quantity, t is the time, D hse is the molten salt flow rate flowing through the heat storage heat exchanger, c p,sa is the specific heat capacity of molten salt, M hse is the mass of molten salt inside the heat exchanger in the molten salt heat storage system, C bur is the heat capacity of flue gas, R conv,bur,airtube is the heat transfer resistance between flue gas and air duct, R conv,bur,fueltube is the heat transfer resistance between flue gas and fuel pipeline, C AST is the heat capacity of the air supply pipe, R con,AST,outer is the heat transfer resistance of air outside the air supply duct, R con,AST,inner is the heat transfer resistance of air in the air supply duct, C cell is the battery heat capacity, R conv,air is the thermal resistance between air and battery, R conv,fuel is the thermal resistance between fuel and battery, C airtube1 is the heat capacity of the first air duct, R conv,bur,airtube1 is the heat exchange resistance between flue gas and the first air duct, R conv,air,tube1 is the heat exchange resistance between air and the first air duct, C airtube2 is the heat capacity of the second air duct, C fueltube1 is the heat capacity of the first fuel pipeline, R conv,bur,fueltube1 is the heat transfer resistance between flue gas and the first fuel pipeline, R conv,fuel,tube1 is the heat transfer resistance between the fuel and the first fuel pipeline, C fueltube2 is the heat capacity of the second fuel pipeline, R conv,bur,fueltube2 is the heat transfer resistance between the flue gas and the second fuel pipeline, R conv,fuel,tube2 is the heat exchange resistance between the fuel and the second fuel pipeline; T hse,i , T hse,o are the inlet and outlet molten salt temperatures of the heat storage heat exchanger, T bur is the flue gas outlet temperature of the first preheater, T AST is the air supply pipe temperature, T cell is the battery temperature, T airtube1 is the first air duct wall temperature, T airtube2 is the wall temperature of the second air duct, T fueltube1 is the wall temperature of the first fuel pipeline, T fueltube2 is the wall temperature of the second fuel pipeline; T air,tube is the air duct temperature, T fuel,tube is the fuel pipeline temperature, Q rad is the radiation heat transfer between the battery and the air supply pipe in the battery stack, T aircell,i is the transient temperature of the air in the battery, T air,i is the transient temperature of the air in the air supply duct, Q chem is the available work released by the chemical reaction, Q elec is the output power of the fuel cell, T fuel,i is the transient temperature of the fuel, T bur1 is the flue gas inlet temperature of the first preheater, T air1 is the air temperature at the stack inlet, T bur2 is the flue gas inlet temperature of the second preheater, T air,o is the initial temperature of the air in the air supply duct, T fuel1 is the fuel temperature at the stack inlet, T fuel,o is the initial temperature of the fuel; The nonlinear output equation is: Where P is the output power of the integrated system, is a matrix describing the change in output caused by the change in input. is the matrix describing the output change caused by the state change; T hse,i , T hse,o are the inlet and outlet molten salt temperatures of the heat storage heat exchanger, T bur is the flue gas outlet temperature of the first preheater, T AST is the air supply pipe temperature, T cell is the battery temperature, T airtube1 is the first air duct wall temperature, T airtube2 is the wall temperature of the second air duct, T fueltube1 is the wall temperature of the first fuel pipeline, T fueltube2 is the wall temperature of the second fuel pipeline; air is the air input mass flow rate, O fuel is the fuel input mass flow rate, O hse is the molten salt flow rate of the heat storage heat exchanger.

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