Solid Oxide Fuel Cell System Model and Testing Method

Abstract

The present invention discloses a solid oxide fuel cell system model and a testing method. The model includes a heat exchanger model, a stack model, and a combustion chamber model. Among them, the heat exchanger is progressively divided into a plurality of heat exchange nodes with gradually shortening lengths from the input end to the output end, the stack is progressively divided into a plurality of stack nodes with gradually shortening lengths from the input end to the output end, the front part of the combustion chamber from the input end to the output end is progressively divided into a plurality of combustion nodes with gradually shortening lengths, and the rear part is divided into a plurality of combustion nodes with gradually increasing lengths in a gradually distant manner. Different system components are formed by connecting the node models inside them in series. According to the parameter change trends inside different components, the components are divided into a plurality of nodes with different lengths, which can improve the accuracy of performance parameters while reducing the model complexity and calculation amount.

Description

Technical Field

[0001] The present invention belongs to the technical field of solid oxide fuel cells, and more specifically, relates to a solid oxide fuel cell system model and a testing method. Background Art

[0002] The basic principle of a solid oxide fuel cell (SOFC) is very simple and involves the electrochemical process of hydrogen and oxygen. Solid oxide fuel cells have the advantages of high efficiency, convenience, low noise, and no pollution. The benefit of low noise is that it can be used without any restrictions even in densely populated areas such as big cities. Since countries around the world attach great importance to environmental protection today, no pollution is very important for the commercial promotion of SOFC, which can greatly reduce the impact and pressure on the urban environment and climate.

[0003] A solid oxide fuel cell system is a complex system with multiple variables and multiple couplings. However, because the experimental cost of the SOFC system is relatively high and it requires an environment of pure hydrogen and high temperature, there are certain risks, which to a certain extent hinder the large-scale popularization and development of solid oxide fuel cells. In order to accurately perform dynamic and static analysis on solid oxide fuel cells and find the optimal operating point, etc., researchers have established various simulation models. A model with excellent performance and capable of accurately reflecting the inherent characteristics of SOFC is also the basis for our various simulation studies. Currently, the modeling of solid oxide fuel cell systems mainly focuses on holistic modeling and uniform nodalization modeling. Holistic-based modeling directly establishes a parameter model for the input and output ports of a component, but such a modeling method cannot satisfactorily reflect the internal parameter changes of the component. The modeling idea based on uniform nodalization is to evenly divide a component into several nodes. Although such a modeling method improves the accuracy of the model to a certain extent compared with holistic modeling, it still cannot accurately reflect the actual operation of the system. Because the reaction degrees at different positions within the same system component are different, the more intense the reaction, the greater the parameter change, and the more gentle the reaction, the smaller the parameter change. If the parameters are evenly divided, if the division distance is too large, the accuracy of the calculated interval parameters is not high, and if the division distance is too small, it will greatly increase the complexity and calculation amount of the model. Summary of the Invention

[0004] In view of the above defects or improvement requirements of the prior art, the present invention provides a solid oxide fuel cell system model and a testing method, aiming to improve the accuracy of performance parameters while reducing the complexity and calculation amount of the model.

[0005] To achieve the above object, according to one aspect of the present invention, there is provided a solid oxide fuel cell system model, including: a heat exchanger model, a stack model, and a combustion chamber model, wherein,

[0006] The heat exchanger model includes a plurality of heat exchange node models connected in series from the input end to the output end of the heat exchanger. Among them, the heat exchanger is gradually divided from the input end to the output end into a plurality of heat exchange nodes with gradually decreasing lengths, and each heat exchange node establishes a corresponding heat exchange node model based on the divided internal structure;

[0007] The stack model includes a plurality of stack node models connected in series from the input end to the output end of the stack. Among them, the stack is gradually divided from the input end to the output end into a plurality of stack nodes with gradually decreasing lengths, and each stack node establishes a corresponding stack node model based on the divided internal structure;

[0008] The combustion chamber model includes a plurality of combustion node models connected in series from the input end to the output end of the combustion chamber. Among them, the front part of the combustion chamber from the input end to the output end is gradually divided into a plurality of combustion nodes with gradually decreasing lengths, and the rear part is divided into a plurality of combustion nodes with gradually increasing lengths in a gradually distant manner, and each combustion node establishes a corresponding combustion node model based on the divided internal structure;

[0009] Among them, the output parameter of each node represents the entire node parameter, and the output parameter of the previous node is the input parameter of the next node.

[0010] In one embodiment, a gas supply system lag model is further included, which simplifies the dynamic response process of gas flow regulation in the solid oxide fuel cell system into a first-order inertia link with delay. The transfer function of the gas supply system lag model is where τ is the

[0011] delay time and T is the inertia time constant.

[0012] In one embodiment, the heat exchanger has a reaction gas channel, an exhaust gas channel, and a heat conduction solid medium. During the input of the reaction gas through the reaction gas channel in the heat exchanger to the stack, the exhaust gas of the combustion chamber is input into the exhaust gas channel and heats the reaction gas in the reaction gas channel through the heat conduction medium. The reaction gas includes an oxidant and a fuel. After being heated, the oxidant and the fuel are sent to the cathode and anode of the stack and undergo an electrochemical reaction in the solid oxide layer in the stack. The unreacted oxidant and fuel in the stack enter the combustion chamber for combustion, and the exhaust gas generated by the combustion is sent into the exhaust gas channel in the heat exchanger to heat the reaction gas in the heat exchanger;

[0013] Among them, each of the heat exchange node models includes a solid temperature calculation sub-model for calculating the temperature of the heat conduction solid medium inside the heat exchange node and a fluid temperature calculation sub-model for calculating the temperature of the fluid inside the heat exchange node respectively;

[0014] The fuel cell stack node model includes a solid temperature calculation sub-model for calculating the temperature of the solid oxide layer inside the fuel cell stack node, a flow rate calculation sub-model for calculating the molar flow rate of the fluid inside the fuel cell stack node, and a molar fraction calculation sub-model for calculating the molar fraction of the fluid inside the node;

[0015] The combustion node model includes a fluid temperature calculation sub-model for calculating the fluid temperature of the combustion node, a flow rate calculation sub-model for calculating the molar flow rate of the fluid in the combustion node, and a molar fraction calculation sub-model for calculating the molar fraction of the fluid inside the node.

[0016] In one embodiment, the formula for the solid temperature calculation sub-model of the heat exchange node to calculate the solid temperature is:

[0017]

[0018] where ρ s , V s , C s , T s are respectively the density, volume, specific heat capacity and temperature of the solid s to be calculated inside the node, is the thermal energy input to the solid to be calculated by the adjacent object, where,

[0019] When the adjacent object i is a solid:

[0020]

[0021] When the adjacent object i is a fluid:

[0022]

[0023] where k si is the heat transfer coefficient between the solid s to be calculated and the object i, S area is the heat conduction surface area between the solid s to be calculated and the object i, T i is the temperature of the object i, and d is the length of the current node.

[0024] In one embodiment, the formula for the solid temperature calculation sub-model in the fuel cell stack node to calculate the solid temperature is:

[0025]

[0026] where ρ PEN , V PEN , C PEN , T PEN are respectively the density, volume, specific heat capacity and temperature of the solid oxide PEN to be calculated inside the node, is the thermal energy input to the solid to be calculated by the adjacent object,

[0027] is the total energy released during the electrochemical reaction process within the node, and the calculation formula is:

[0028]

[0029] wherein, are respectively the generation rate and molar specific enthalpy of water vapor, the calculation formula of is:

[0030]

[0031] wherein, I is the current density flowing through the node, S node is the node area of the node current output, and F is the Faraday constant;

[0032] is the electric energy generated by the stack at the node, and the calculation formula is:

[0033]

[0034] wherein, V cell is the voltage across the node.

[0035] In one embodiment, the formula for the fluid temperature calculation submodel in the heat exchange node and the combustion node to calculate the fluid temperature is:

[0036]

[0037] wherein, N, C V , T V are respectively the total amount of substance, constant volume specific heat capacity and temperature of the fluid to be calculated within the node, are respectively the molar flow rates of the fluid flowing into and out of the node, h in , h out are respectively the molar specific enthalpies when the fluid flows into and out of the node, is the heat energy transferred from the adjacent solid s to the fluid to be calculated;

[0038] wherein, the constant volume specific heat capacity C V within each node has the calculation formula:

[0039] C V =∑X i C P，i (T V ) - R

[0040] wherein, X i is the mole fraction of the fluid i within the node, C P，i (T V ) is the constant volume specific heat capacity of the fluid i at the node temperature T VThe constant-pressure molar specific heat capacity under [conditions], where R is the universal gas constant;

[0041] The molar flow rate and molar specific enthalpy of the fluid flowing into the current node are equivalent to those of the fluid in the previous adjacent node. The formula for calculating the molar specific enthalpy h of the fluid in each node is:

[0042] h = ∑X i h i

[0043] where h i is the molar specific enthalpy of substance i.

[0044] In one embodiment, the formula for the flow rate calculation sub-model in the stack node and the combustion node to calculate the fluid molar flow rate is:

[0045]

[0046] where are the molar flow rates of the fluid flowing into and out of the node respectively, and R i is the reaction rate of fluid i.

[0047] In one embodiment, the formula for the mole fraction calculation sub-model in the stack node and the combustion node to calculate the mole fraction is:

[0048]

[0049] where N is the amount of substance of the total fluid in the node, and X i is the mole fraction of fluid i to be calculated in the node. are the molar flow rates of the fluid flowing into and out of the node respectively, and X i，in , X i，out are the mole fractions of fluid i flowing into and out of the node respectively, and X i，out = X i , and R i is the reaction rate of fluid i.

[0050] According to another aspect of the present invention, a method for testing a solid oxide fuel cell is provided, which tests the influence of parameter adjustment on the output structure based on the above solid oxide fuel cell system model.

[0051] In one embodiment, one or more parameters among the fuel utilization rate FU, air excess ratio AR, bypass valve opening BP, and stack current Is are adjusted, and the influence on the thermal output performance and electrical output performance is analyzed. Among them, the thermal output performance includes the maximum operating temperature of the stack, the maximum operating temperature gradient of the stack, the temperature difference of the inlet gas of the stack, and the combustion chamber temperature, and the electrical output performance includes the net output power and the output efficiency; where

[0052] The fuel utilization rate FU is the ratio of the hydrogen reaction rate to the hydrogen gas flow rate;

[0053] The air excess ratio AR is the ratio of the molar flow rate of oxygen to the electrochemical reaction rate of oxygen;

[0054] The bypass valve opening BP is the ratio of the air flow rate in the bypass subsystem to the molar flow rate of the total air.

[0055] Generally speaking, compared with the prior art, the above technical solution conceived by the present invention can achieve the following beneficial effects:

[0056] The heat exchanger, the fuel cell stack, and the combustion chamber are the three main components of the solid oxide fuel cell system. When modeling the present invention, a gradual method is adopted to divide the heat exchanger, the fuel cell stack, and the combustion chamber into multiple nodes with unequal lengths respectively, and a node model is established for the internal structure of each node. The small node models are connected in series to form a large component model, and the heat exchanger model, the fuel cell stack model, and the combustion chamber model are connected to form a solid oxide fuel cell system model. Moreover, the present invention makes different divisions for different components according to the reaction characteristics of the components. Among them, for the heat exchanger, considering that the heat exchanger is a countercurrent flow of cold and hot airflows, the fuel (cold air) and the high-temperature exhaust gas (hot air) flow in opposite directions to generate heat exchange. From the input end to the output end of the heat exchanger, the temperature of the fuel gradually increases, and from the output end to the input end of the heat exchanger, the temperature of the exhaust gas gradually decreases. For the region with a higher temperature, more accurate detection is usually required. Therefore, for the division of the heat exchanger, it is gradually divided into multiple heat exchange nodes with gradually decreasing lengths from the input end to the output end. The higher the temperature region, the finer the division and the more refined the monitoring. For the fuel cell stack, considering that the gas in the fuel cell stack flows unidirectionally, and the reaction of the fuel is slower when it first enters and then reaches the maximum reaction rate, it is necessary to accurately measure and control the performance parameters at its outlet. Therefore, for the division of the fuel cell stack, it is gradually divided into multiple heat exchange nodes with gradually decreasing lengths from the input end to the output end. The higher the temperature region, the finer the division and the more refined the monitoring. For the combustion chamber, since mainly flame combustion reactions occur in the combustion chamber and the reaction at the center point of the combustion reaction is the most intense. Therefore, for the division of the combustion chamber, a combination of an asymptotic method and a gradually distant method is adopted for division. The more intense the reaction in the middle region, the finer the division and the more refined the monitoring. In short, the present invention divides the components into multiple nodes with different lengths according to the parameter change trends inside different components, and improves the accuracy of performance parameters while reducing the model complexity and calculation amount. Description of the Drawings

[0057] Figure 1 It is a schematic structural diagram of the SOFC system of an embodiment;

[0058] Figure 2Schematic diagram of the gradual node division of the system components in an embodiment;

[0059] Figure 3 Schematic diagram of the heat exchanger modeling scheme in an embodiment;

[0060] Figure 4 Schematic diagram of the core stack modeling scheme in an embodiment;

[0061] Figure 5 Schematic diagram of the combustion chamber modeling scheme in an embodiment. Detailed implementation manners

[0062] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0063] As Figure 1 shown is a schematic diagram of the structure of a solid oxide fuel cell system in an embodiment, which mainly includes a fuel heat exchanger, an air heat exchanger, a stack and a combustion chamber, and also includes other peripheral auxiliary subsystems (Balance of plant, BOP) such as bypass pipelines, tail gas treatment systems, etc. The heat exchanger has a reaction gas channel, a tail gas channel and a heat conduction solid medium. For example, the reaction gas entering the air heat exchanger is an oxidant (such as air), and the reaction gas entering the fuel heat exchanger is a fuel (such as hydrogen). During the process that the reaction gas is input into the stack through the reaction gas channel in the heat exchanger, the tail gas of the combustion chamber is input into the tail gas channel and heats the reaction gas in the reaction gas channel through the heat conduction medium. The oxidant and fuel are sent to the cathode and anode of the stack after being heated and undergo an electrochemical reaction in the solid oxide layer in the stack. The unreacted oxidant and fuel in the stack enter the combustion chamber for combustion, and the tail gas generated by the combustion is sent into the tail gas channel in the heat exchanger to heat the reaction gas in the heat exchanger.

[0064] The solid oxide fuel cell system model established by the present invention mainly includes a heat exchanger model, a stack model and a combustion chamber model. As Figure 2As shown in the figure, according to the direction of the reaction gas flow, each system component is divided into a finite number of nodes in a gradual division manner. The parameters within the same node are the same and are equal to the parameters at the node outlet. That is, the characteristic value of the node outlet parameters represents the characteristic value of the parameters of this entire spatial computational sub-model. The outlet parameters of the previous node are equal to the inlet parameters of the next node. The main purpose of doing this is to make the modeling process more concise and accurate, and at the same time, be able to precisely grasp the parameter change process inside the system component. Each node constructs a node model according to its internal structure. Inside the node model, the parameters that need to be concerned are calculated as required, and the corresponding computational sub-model is selected according to the parameters that need to be concerned.

[0065] Specifically, the system component is gradually divided into N nodes. The model can specifically satisfy the following formula:

[0066] d n = K * n -τ + γ, (n = 1, 2, 3…N)

[0067] L = ∑d n , (n = 1, 2, 3…N)

[0068] Among them, d n is the length of node n, K is the proportionality coefficient, and its value is determined according to the macroscopic size of the component. τ is the interval distance coefficient, which is determined according to the required accuracy of the modeling. When τ is a positive value, it is an asymptotic modeling. When τ is a negative value, it is a receding modeling. γ is the correction coefficient, and its value is determined according to the distance correction requirements. L is the total length of the system component, and its value is equal to the sum of the lengths of each node.

[0069] Among them, since the heat exchanger has a countercurrent flow of cold and hot air, the fuel (cold air) and the high-temperature exhaust gas (hot air) flow in opposite directions to generate heat exchange. For the fuel, when the fuel just enters, the temperature change range is small, and the monitoring of the temperature does not need to be very precise. However, more accurate performance parameters need to be collected at the tail of the heat exchanger. Therefore, an asymptotic modeling scheme is adopted. For the high-temperature exhaust gas, it is equivalent to adopting a receding modeling scheme. More precise temperature parameters are required when the exhaust gas just enters, and when the heat of the exhaust gas is exchanged and cooled, the requirement for temperature parameters is relatively small. As Figure 3 shown, the heat exchanger is gradually divided into multiple heat exchange nodes with gradually decreasing lengths from the input end to the output end. Each heat exchange node builds a corresponding heat exchange node model based on the divided internal structure. The multiple heat exchange node models connected in series from the input end to the output end of the heat exchanger form a heat exchanger model.

[0070] Since the gas in the fuel cell stack flows unidirectionally, and the fuel reacts slowly when it first enters, and then the reaction speed reaches the maximum, it is necessary to accurately measure and control the performance parameters at its outlet. Therefore, an asymptotic unitary modeling scheme is adopted. AsFigure 4 As shown, the stack is gradually divided into a plurality of stack nodes with gradually decreasing lengths from the input end to the output end. Each stack node establishes a corresponding stack node model based on the divided internal structure. A plurality of stack node models connected in series from the input end to the output end of the stack form a stack model.

[0071] Since mainly flame combustion reactions occur in the combustion chamber, the reaction at the combustion reaction center point is the most intense and has the highest requirements for performance parameters, while the requirements for the inlet and outlet are relatively lower. Therefore, the combustion chamber is modeled using a combined scheme of progressive + remote. As Figure 5 shown, the front part of the combustion chamber from the input end to the output end is gradually divided into a plurality of combustion nodes with gradually decreasing lengths, and the rear part is remotely divided into a plurality of combustion nodes with gradually increasing lengths. Each combustion node establishes a corresponding combustion node model based on the divided internal structure. A plurality of combustion node models connected in series from the input end to the output end of the combustion chamber form a combustion chamber model.

[0072] After building the stack model, heat exchanger model, and combustion chamber model, they can be connected and encapsulated in MATLAB / Simulink to form a dynamic model of the SOFC independent power generation system.

[0073] In a solid oxide fuel cell system, parameters such as temperature, flow rate, and mole fraction are usually of concern. Therefore, it generally includes a temperature calculation sub-model, a flow rate calculation sub-model, and a mole fraction calculation sub-model. Among them, according to the internal material form of the node, the temperature calculation sub-model is further divided into a solid temperature calculation sub-model and a fluid temperature calculation sub-model. The flow rate calculation sub-model and the mole fraction calculation sub-model are for fluids. Since the parameter changes, reactions, and key concerns are different in different system components, for different system components, the calculation sub-models established in their node models will be somewhat different, but the forms of different node models in the same system component are the same.

[0074] In one embodiment, the solid temperature calculation sub-model is:

[0075]

[0076] Where ρ s 、V s 、C s 、T s are respectively the density, volume, specific heat capacity, and temperature of the solid s to be calculated in the node, is the thermal energy input from the adjacent object to the solid to be calculated.

[0077] When the adjacent object i is a solid:

[0078]

[0079] When the adjacent object i is a fluid:

[0080]

[0081] where k si is the heat transfer coefficient between the solid s to be calculated and the object i, S area is the heat conduction surface area between the solid s to be calculated and the object i, T i is the temperature of the object i, and d is the length of the current node.

[0082] In one embodiment, the fluid temperature calculation sub-model is

[0083]

[0084] where N, C V , T V are respectively the total amount of substance, constant volume specific heat capacity, and temperature of the fluid to be calculated in the node, are respectively the molar flow rates of the fluid flowing into and out of the node, h in , h out are respectively the molar specific enthalpies of the fluid when flowing into and out of the node, is the heat energy transferred from the adjacent solid s to the fluid to be calculated.

[0085] Among them, there are generally more than two kinds of mixed gases in the node, and the calculation formula of the constant volume specific heat capacity C V in each node is:

[0086] C V = ∑X i C P,i (T V ) - R (5)

[0087] where X i is the mole fraction of the fluid i in the node, C P,i (T V ) is the constant pressure molar specific heat capacity of the fluid i at the node temperature T V , and R is the universal gas constant.

[0088] The molar flow rate and molar specific enthalpy of the fluid flowing into the current node are equivalent to those of the fluid in the previous adjacent node. Among them, the calculation formula of the molar specific enthalpy h of the fluid in each node is:

[0089] h = ∑X i h i (6)

[0090] where h iis the molar specific enthalpy of substance i, and its calculation formula is:

[0091]

[0092] where h i,298.15 is the molar specific enthalpy of component substance i at the standard temperature of 298.15 K, and C P,i (T V ) is the constant-pressure molar specific heat capacity of fluid component substance i and can be calculated according to experience. Among them, the calculation formulas for the constant-pressure molar specific heats of H 2 , O 2 , H 2 O, N 2 are as follows:

[0093]

[0094]

[0095]

[0096]

[0097] In one embodiment, the flow rate calculation sub-model is:

[0098]

[0099] where are the molar flow rates of the fluid at the inlet node and the outlet node respectively, and R i is the reaction rate of fluid i.

[0100] In one embodiment, the mole fraction calculation sub-model is:

[0101]

[0102] where N is the amount of substance of the total fluid in the node, and X i is the mole fraction of fluid i to be calculated in the node, are the molar flow rates of the fluid at the inlet node and the outlet node respectively, X i,in , X i,out are the mole fractions of fluid i at the inlet node and the outlet node respectively, X i,out = X i , and R i is the reaction rate of fluid i.

[0103]

[0104] where P, V, and T are the pressure, volume, and temperature of the fluid in the node respectively, and R is the universal gas constant.

[0105] Since the parameter changes in different system components are different, the reactions that occur are different, and the key points of concern are different. Therefore, for different system components, there will be deviations in the calculation sub-models established in their node models.

[0106] In the heat exchanger, the fuel and oxidant enter the stack through two separate pipes, and there is only heat exchange between the cold and hot airflows inside. This heat exchange is a physical process and does not involve chemical reactions like those in the stack and combustion chamber. Therefore, the temperature change of the gas in the heat exchanger will also affect the pressure change. Therefore, when modeling, a solid temperature calculation sub-model and a fluid temperature calculation sub-model are established in the heat exchange node. The solid temperature calculation sub-model can calculate the temperature of the heat-conducting solid medium through formula (1). At this time, in formula (1), is the heat energy input from adjacent objects to the heat-conducting solid medium. The adjacent objects are the fluids in the two channels and the heat-conducting solid medium in the previous node. Therefore, when calculating the heat energy it is necessary to consider both the case where the adjacent object is a solid and the case where the adjacent object is a fluid, that is, calculate the heat energy through formula (2) and formula (3) The fluid temperature calculation model of the heat exchange node calculates the temperatures of the reaction gas and the exhaust gas in the node through formula (4). At this time, in formula (4), is the heat energy transferred from the adjacent heat-conducting solid medium to the fluid to be calculated. In the heat exchanger, since there is no consumption of substances, it can be considered that the flow rates of each node are the same.

[0107] In the stack, since there are hydrogen and oxygen in the stack that will undergo an electrochemical reaction, which will consume substances, affect the flow rate, molar fraction, and generate heat. Therefore, a temperature calculation sub-model, a flow rate calculation sub-model, and a molar fraction calculation sub-model are established in the stack node at the same time. Considering that the main temperature in the stack comes from the solid oxide layer (electrolyte), the solid temperature calculation sub-model is selected for the temperature calculation sub-model. Among them, the flow rate calculation sub-model calculates the molar flow rates of each fluid flowing into and out of the node through formula (12), and the molar fraction calculation sub-model calculates the molar fraction of each fluid component i in the node through formula (13). Since there are hydrogen and oxygen in the stack that will undergo an electrochemical reaction, this reaction is an exothermic reaction, and it is not possible to simply use formula (1) to calculate the stack node temperature, and the following corrections need to be made:

[0108]

[0109] Among them, ρ PEN 、V PEN 、C PEN 、T PEN are the density, volume, specific heat capacity, and temperature of the solid oxide PEN to be calculated in the node respectively. The thermal energy input to the solid to be calculated by adjacent objects. At this time, the adjacent object is the temperature of the solid oxide PEN calculated for the previous node.

[0110] Is the total energy released during the electrochemical reaction process within the node, and the calculation formula is:

[0111]

[0112] Where, Are respectively the generation rate and molar specific enthalpy of water vapor, The calculation formula of is:

[0113]

[0114] Where, I is the current density flowing through the node, S node Is the node area of the node current output, and F is the Faraday constant.

[0115] Is the electric energy generated by the stack at the node, and the calculation formula is:

[0116]

[0117] Where, V cell Is the voltage across the node, that is, the single cell voltage.

[0118] In the combustion chamber, the remaining hydrogen after participating in the stack reaction will be completely burned in the combustion chamber, and the high-temperature flue gas generated by the combustion chamber serves as the high-temperature gas source of the heat exchanger. The reaction rates of various substances in the combustion chamber can be calculated by the following formula:

[0119]

[0120] Where, Are respectively the reaction rates of H 2 , O 2 , H 2 O, taking positive means consumption and negative means generation, Represents H in the fluid flowing into the node 2

[0121] In the combustion chamber, hydrogen and oxygen undergo an electrochemical reaction, consuming substances, affecting the flow rate, molar fraction, and generating heat. Therefore, a temperature calculation sub-model, a flow rate calculation sub-model, and a molar fraction calculation sub-model are established simultaneously in the combustion node. Considering that the main temperature in the combustion chamber comes from the internal fluid, the fluid temperature calculation sub-model is selected for the temperature calculation sub-model. The fluid temperature calculation sub-model calculates the combustion node temperature through formula (4), the flow rate calculation sub-model calculates the molar flow rates of each fluid flowing into and out of the node through formula (12), and the molar fraction calculation sub-model calculates the molar fraction of each fluid component i in the node through formula (13).

[0122] In one embodiment, the gas supply systems involved in the SOFC independent power generation system mainly include a hydrogen supply system, an air supply system, and a bypass air supply system. When adjusting the gas flow rate through a flow meter, the change in the gas flow rate is not instantaneous but has a certain time delay. To reduce the computational complexity, the dynamic response process of the gas supply system is simplified into a first-order inertia link plus a delay link, and its transfer function is as follows:

[0123]

[0124] where τ is the delay time and T is the inertia time constant.

[0125] By adopting a gradual change method, the heat exchanger, the fuel cell stack, and the combustion chamber are respectively divided into multiple nodes with unequal lengths, and a node model is established for the internal structure of each node. Small node models are connected in series to form a large component model, and the heat exchanger model, the fuel cell stack model, and the combustion chamber model are connected to form a solid oxide fuel cell system model. Since this model is refined to node parameters, different calculation sub-models are established according to the actual situation in different node models. Therefore, the system parameters in different intervals within the system components can be clearly grasped, and its dynamic response process can be understood.

[0126] Correspondingly, the present invention also relates to a test method for a solid oxide fuel cell, which tests the influence of output structure based on the test parameter adjustment of the solid oxide fuel cell system model introduced above.

[0127] In one embodiment, the following operating parameters are first selected:

[0128] (a) Fuel utilization rate FU: FU is the ratio of the hydrogen reaction rate to the hydrogen flow rate. The general value range of the fuel utilization rate FU is 0.6 - 0.9. Generally speaking, when FU is lower than 0.6, at this time, the molar flow rate of hydrogen is large, too much hydrogen is introduced, resulting in an increase in power generation cost, waste of fuel, and low system efficiency. When FU is higher than 0.9, less hydrogen is introduced at this time, which is likely to cause unstable electrical output or power generation failure.

[0129] (b) Air Excess Ratio AR: AR is the ratio of the molar flow rate of oxygen to the electrochemical reaction rate of oxygen. The value range of the air excess ratio AR is generally 6 - 12. When the value of AR is lower than 6, the molar flow rate of air is relatively small at this time, the cold air introduced into the stack is relatively low, and the heat dissipation of the stack is slow, which easily leads to the stack temperature exceeding the rated value. When the value of AR exceeds 12, the molar flow rate of air is very large at this time, and too much cold air is introduced, taking away more stack temperature, which easily causes the stack to lose temperature and fail to reach the temperature for normal electrochemical reactions.

[0130] (c) Bypass Valve Opening BP: BP is the ratio of the air flow rate in the bypass subsystem to the total molar flow rate of air. The value of BP is generally 0.0 - 0.3. If the value of BP is higher than 0.3, it will cause the air temperature at the stack inlet to be relatively low, resulting in a decline in the performance of the SOFC system.

[0131] (d) Stack Current Is: The stack current is determined by the load demand power outside the SOFC system.

[0132] After selecting the operating parameters, adjust one or more of these parameters to verify the impact on the thermal output performance and electrical output performance.

[0133] The function of the SOFC is to carry out electrochemical reactions at high temperatures. To ensure the absolute safety of the stack, the maximum temperature of the SOFC stack must be limited within a certain working range. At the same time, the temperature gradient in the internal space of the stack cannot be too large. When the temperature gradient is too large, it will cause excessive internal thermal stress in the stack and lead to stack damage. For the peripheral BOP system, the temperature difference between the hydrogen temperature and the air temperature at the stack inlet cannot be too large, and the maximum temperature of the combustion chamber must also be within the maximum tolerance range of the material. Temperature safety and controllability are the prerequisite for the stable operation of the entire SOFC stack. Therefore, the thermal output performance parameters can include:

[0134] (a) PEN Maximum Operating Temperature Max.T PEN :

[0135] Max.T PEN =max{T PEN (i)},{i=1,2,...,N - 1} (21)

[0136] During the construction of the SOFC single - cell model, it is divided into N nodes, and the PEN maximum operating temperature of the stack is the maximum value of the temperatures of all nodes.

[0137] (b) PEN Maximum Operating Temperature Gradient Max.|ΔT PEN |:

[0138] Max.|ΔT PEN |=max|TPEN (i + 1)-T PEN (i)|, {i = 1, 2, ..., N - 1}(22)

[0139] The maximum working temperature gradient of the PEN is the maximum value of the temperature gradient within the cell

[0140] (c) The temperature difference ΔT of the inlet gas of the stack inlet :

[0141] ΔT inlet = max|T HE,fuel -T HE,air | (23)

[0142] The difference between the inlet gases of the anode and cathode of the stack is defined as the inlet temperature difference of the stack, and this difference is also equal to the temperature T of the outlet gas of the hydrogen heat exchanger HE,fuel and the temperature T of the outlet gas of the air heat exchanger HE,air difference.

[0143] (d) Combustor temperature T B :

[0144] The combustor temperature can be calculated by the fluid temperature calculation sub - model.

[0145] By adjusting the operating parameters, calculate the change trend of the above - mentioned thermal output performance parameters, so as to analyze the relationship between the operating parameters and the thermal output performance, and select the operating parameters with better thermal output performance during actual operation.

[0146] The electrical characteristic parameters of the SOFC independent power generation system mainly include the net output power and the output efficiency. When the SOFC is operating normally, its operating efficiency is generally between 30% - 60%. Different input parameters have a comprehensive impact on the operating temperature and output efficiency of the SOFC. Therefore, on the premise of ensuring the thermal safety of the SOFC, it is necessary to comprehensively analyze the efficiency of the SOFC at different powers.

[0147] The electrical characteristic parameters of the SOFC independent power generation system mainly include the net output power and the output efficiency. When the SOFC is operating normally, its operating efficiency is generally between 30% - 60%. Different input parameters have a comprehensive impact on the operating temperature and output efficiency of the SOFC. Therefore, on the premise of ensuring the thermal safety of the SOFC, it is necessary to comprehensively analyze the efficiency of the SOFC at different powers.

[0148] The net output power P of the SOFC system net The calculation formula is as follows:

[0149] P net = U s I s -P bl(24)

[0150] Where U s is the stack voltage, I s is the stack current, P bl is the power consumption of the blower, and the calculation formula is as follows:

[0151]

[0152] Proportional coefficient The calculation formula is as follows:

[0153]

[0154] In the above formula, C p,air is the constant-pressure specific heat capacity of air, T air,in is the temperature when air enters, generally room temperature, η bl is the efficiency of the blower, P bl,out and P bl,in are the inlet and outlet pressures of the blower respectively, and γ is the specific heat ratio of air, and its value is generally 1.4.

[0155] Finally, the calculation formula for the output efficiency of the SOFC independent power generation system is as follows:

[0156]

[0157] In the formula, is the lower calorific value of hydrogen, and its value is generally 241.83 KJ / mol -1 .

[0158] By adjusting the operating parameters, calculate the change trend of the above-mentioned electrical output performance parameters, so as to analyze the relationship between the operating parameters and the electrical output performance, and select the operating parameters with better electrical output performance during actual operation.

[0159] It is easy for those skilled in the art to understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A solid oxide fuel cell system model, characterized in that, it includes: a heat exchanger model, a stack model, and a combustion chamber model, where the heat exchanger model includes a plurality of heat exchange node models connected in series from the input end to the output end of the heat exchanger. Among them, the heat exchanger is progressively divided into a plurality of heat exchange nodes with gradually decreasing lengths from the input end to the output end, and each heat exchange node establishes a corresponding heat exchange node model based on the divided internal structure; the stack model includes a plurality of stack node models connected in series from the input end to the output end of the stack. Among them, the stack is progressively divided into a plurality of stack nodes with gradually decreasing lengths from the input end to the output end, and each stack node establishes a corresponding stack node model based on the divided internal structure; the combustion chamber model includes a plurality of combustion node models connected in series from the input end to the output end of the combustion chamber. Among them, the front part of the combustion chamber from the input end to the output end is progressively divided into a plurality of combustion nodes with gradually decreasing lengths, and the rear part is divided into a plurality of combustion nodes with gradually increasing lengths in a gradually distant manner. Each combustion node establishes a corresponding combustion node model based on the divided internal structure; wherein, the output parameter of each node represents the entire node parameter, and the output parameter of the previous node is the input parameter of the next node.

2. The solid oxide fuel cell system model according to claim 1, characterized in that, It also includes a gas supply system lag model, which is used to simplify the dynamic response process of gas flow regulation in a solid oxide fuel cell system into a first-order inertia link with delay. The transfer function of the gas supply system lag model is where τ is the delay time, T is the inertia time constant.

3. The solid oxide fuel cell system model according to claim 1, characterized in that, the heat exchanger has a reaction gas channel, an exhaust gas channel, and a heat-conducting solid medium. During the input of the reaction gas through the reaction gas channel in the heat exchanger to the stack, the exhaust gas of the combustion chamber is input into the exhaust gas channel and heats the reaction gas in the reaction gas channel through the heat-conducting solid medium. The reaction gas includes an oxidant and a fuel. The oxidant and the fuel are heated and then sent to the cathode and anode of the stack and undergo an electrochemical reaction in the solid oxide layer in the stack. The unreacted oxidant and fuel in the stack enter the combustion chamber for combustion, and the exhaust gas generated by the combustion is sent to the exhaust gas channel in the heat exchanger to heat the reaction gas in the heat exchanger; wherein, each of the heat exchange node models includes a solid temperature calculation sub-model for calculating the temperature of the heat-conducting solid medium inside the heat exchange node and a fluid temperature calculation sub-model for calculating the temperature of the fluid inside the heat exchange node respectively; the stack node model includes a solid temperature calculation sub-model for calculating the temperature of the solid oxide layer inside the stack node, a flow rate calculation sub-model for calculating the molar flow rate of the fluid inside the stack node, and a molar fraction calculation sub-model for calculating the molar fraction of the fluid inside the node; the combustion node model includes a fluid temperature calculation sub-model for calculating the fluid temperature of the combustion node, a flow rate calculation sub-model for calculating the molar flow rate of the fluid of the combustion node, and a molar fraction calculation sub-model for calculating the molar fraction of the fluid inside the node.

4. The solid oxide fuel cell system model according to claim 3, characterized in that, the formula for the solid temperature calculation sub-model of the heat exchange node to calculate the solid temperature is: Among them, ρ s , V s , C s , T s are respectively the density, volume, specific heat capacity and temperature of the solid s to be calculated within the node, is the thermal energy input to the solid to be calculated by the adjacent object, where, When the adjacent object i is a solid: When the adjacent object i is a fluid: where k si is the heat transfer coefficient to be calculated between the solid s and the object i, S area is the heat conduction surface area to be calculated between the solid s and the object i, T i is the temperature of the object i, and d is the length of the current node.

5. The solid oxide fuel cell system model according to claim 3, characterized in that, the formula for the solid temperature calculation sub-model in the stack node to calculate the solid temperature is: Among them, ρ PEN , V PEN , C PEN , T PEN are respectively the density, volume, specific heat capacity, and temperature of the solid oxide PEN to be calculated within the node, is the thermal energy input to the solid to be calculated by adjacent objects, It is the total energy released during the electrochemical reaction process within the node, and the calculation formula is as follows: wherein, are respectively the generation rate of water vapor and the molar specific enthalpy, The calculation formula of is: where I is the current density flowing through the node, S node is the node area of the node current output, and F is the Faraday constant; is the electric energy generated by the stack at the node, and the calculation formula is: Among them, V cell is the voltage on the node.

6. The solid oxide fuel cell system model according to claim 3, characterized in that, the formula for the fluid temperature calculation sub-model in the heat exchange node and the combustion node to calculate the fluid temperature is: Among them, N and C V , and T V are respectively the total amount of substance, constant volume specific heat capacity, and temperature of the fluid to be calculated in the node, are respectively the molar flow rates of the fluid flowing into and out of the node, h in , and h out are respectively the molar specific enthalpies when the fluid flows into and out of the node, is the heat energy transferred from the adjacent solid s to the fluid to be calculated; Among them, the constant-volume specific heat capacity C within each node V is calculated by the formula: C V = ∑X i C P,i (T V ) - R where X i is the mole fraction of fluid i in the node, C P,i (T V ) is the constant-pressure molar heat capacity of fluid i at the node temperature T V , and R is the universal gas constant; The molar flow rate and molar specific enthalpy of the fluid flowing into the current node are equivalent to the molar flow rate and molar specific enthalpy of the fluid in the previous adjacent node, wherein the formula for the molar specific enthalpy h of the fluid in each node is: h = ∑X i h i where h i is the molar specific enthalpy of substance i.

7. The solid oxide fuel cell system model according to claim 3, characterized in that, the formula for the flow rate calculation sub-model in the stack node and the combustion node to calculate the fluid molar flow rate is: wherein, are the molar flow rates of the fluid flowing into and out of the node, respectively, and R i is the reaction rate of fluid i.

8. The solid oxide fuel cell system model according to claim 3, characterized in that, the formula for the mole fraction calculation sub-model in the stack node and the combustion node to calculate the mole fraction is: where N is the amount of substance of the total fluid in the node, X i is the mole fraction of the fluid i to be calculated in the node, are the molar flow rates of the fluid flowing into and out of the node respectively, X i,in 、X i,out are the mole fractions of the fluid i flowing into and out of the node respectively, X i,out = X i , R i is the reaction rate of the fluid i.

9. A test method for a solid oxide fuel cell, characterized in that, the influence of the test parameter adjustment on the output structure is tested based on the solid oxide fuel cell system model according to any one of claims 1 to 8.

10. The test method for a solid oxide fuel cell according to claim 9, characterized in that, one or more parameters of the fuel utilization rate FU, the air excess ratio AR, the bypass valve opening BP, and the stack current Is are adjusted, and the influence on the heat output performance and the electrical output performance is analyzed, wherein the heat output performance includes the maximum operating temperature of the stack, the maximum operating temperature gradient of the stack, the temperature difference of the inlet gas of the stack, and the combustion chamber temperature, and the electrical output performance includes the net output power and the output efficiency; wherein, the fuel utilization rate FU is the ratio of the hydrogen reaction rate to the hydrogen flow rate; the air excess ratio AR is the ratio of the molar flow rate of oxygen to the electrochemical reaction rate of oxygen; the bypass valve opening BP is the ratio of the air flow rate in the bypass subsystem to the molar flow rate of the total air.

Images