A method for optimizing operating parameters of a multi-stack SOFC power generation system

Abstract

The present invention discloses a method for optimizing operation parameters of a multi-stack SOFC power generation system, belonging to the field of fuel cell systems. The present invention establishes a multi-stack SOFC power generation system model including the inconsistency of gas flow distribution among stacks, and this model can reflect the influence of the inconsistency of gas flow distribution among stacks on system efficiency and safety; based on this model, the present invention proposes a method for optimizing its operation parameters. Using this method, the optimal efficiency operation point that satisfies the system safety constraints under a specific fuel flow rate can be obtained; the optimal operation points under various fuel flow rates within the actual operating conditions of the system can also be obtained, so that the system can operate at the optimal efficiency operation point under different external load powers. Therefore, this method can improve system efficiency and reduce the system operation cost to the greatest extent.

Description

Technical Field

[0001] The present invention belongs to the field of fuel cell systems, and more specifically, relates to a method for optimizing operation parameters of a multi-stack SOFC power generation system. Background Art

[0002] The extensive exploitation and use of fossil energy have caused serious adverse effects on the ecological environment. Hydrogen energy, as a new energy source harmless to the environment, has attracted wide attention. Technologies for the preparation, storage, and transportation of hydrogen energy are also developing rapidly. Moreover, hydrogen energy can be used to store other clean energy sources such as solar energy and wind energy. Therefore, hydrogen energy is a clean and renewable energy source with great potential. Fuel cells (FCs) that can utilize hydrogen energy, especially solid oxide fuel cells (SOFCs), are considered to be the most promising new energy technologies at present. An SOFC is an energy conversion device that can directly convert the chemical energy in fuels such as hydrogen into electrical energy through an electrochemical reaction. Due to the absence of an intermediate energy conversion process, its efficiency is higher. Compared with other types of fuel cells, SOFCs also have the advantages of high efficiency, low cost, and a wide range of fuel types.

[0003] Currently, the main factors restricting the large-scale application of fuel cells are efficiency, reliability, and service life, etc. The multi-stack fuel cell (MFC) system has relatively obvious advantages in the above aspects compared with the single-stack system. Therefore, the MFC system is the basis for the large-scale application of fuel cells. The MFC system has multiple fuel cell stacks. Therefore, the MFC system can provide a larger output power compared with the single-stack system. The MFC system can also flexibly distribute the total required power to each stack according to factors such as the different working conditions, current performance indicators, and aging degree of each stack, so as to achieve the purposes of improving the overall efficiency of the system and slowing down the aging of the stacks. Under a certain system structure, the MFC system has better reliability compared with the single-stack system, and the failure of a single stack has less impact on the entire system.

[0004] In a multi-stack SOFC system using a parallel reactant supply system, the gases to be introduced into each stack have a relatively high temperature after heat exchange. Therefore, it is impossible to install solenoid valves on each branch to accurately control the gas flow rate into each stack, which may cause inconsistent gas flow distribution between the stacks. This inconsistency will not only reduce the operating efficiency of the entire system but also make the system operate in an unsafe state. Therefore, it is of great practical significance to study the inconsistency of gas flow distribution between stacks in a multi-stack SOFC system and explore its impact on aspects such as system efficiency and safety.

[0005] There is little research on this problem at present. Existing research has only verified through simulation at a specific fuel flow rate that for a multi-stack system with inconsistent gas flow distribution among fuel cells, controlling the current of each fuel cell separately can improve the power generation efficiency of the system. First, existing research has only simulated and analyzed the system at a specific fuel flow rate. However, in actual situations, it is necessary to change the system fuel flow rate according to the change of the external load. Therefore, analyzing only the specific fuel flow rate situation is not sufficient to meet the needs of actual applications. Second, existing research has not studied how to make the system reach the optimal efficiency at a specific fuel flow rate. However, in actual applications, when the system operates at the optimal efficiency, fuel can be saved to the greatest extent and the system operation cost can be reduced. Summary of the Invention

[0006] In view of the above defects or improvement requirements of the existing technology, the present invention provides an optimization method for operating parameters of a multi-stack SOFC power generation system, aiming to solve the optimal operating parameters of the system, make the system operate at the optimal efficiency, save fuel to the greatest extent, and reduce the system operation cost.

[0007] To achieve the above object, the present invention provides an optimization method for operating parameters of a multi-stack SOFC power generation system, including:

[0008] S1. Modeling each SOFC stack in the multi-stack SOFC system;

[0009] S2. Modeling each auxiliary component in the multi-stack SOFC system;

[0010] S3. Changing the air excess ratio, the current of each SOFC stack, and the opening degree of the bypass valve at different fuel flow rates, and calculating the system efficiency by using each SOFC stack model and the auxiliary component model of the multi-stack SOFC system to obtain the operating parameters corresponding to the highest system efficiency at different fuel flow rates.

[0011] Further, the calculation method of the system efficiency is as follows,

[0012]

[0013] where n is the number of fuel cell stacks in the multi-stack system, I i 、V i are the current and voltage of the i-th fuel cell stack respectively, n H2 is the amount of substance of hydrogen consumed by the system, and LHV H2 is the lower heating value of hydrogen.

[0014] Further, the following constraint conditions are satisfied when calculating the highest system efficiency: current constraint, maximum fuel cell stack temperature constraint, fuel cell stack temperature gradient constraint, fuel cell stack inlet gas temperature difference constraint, and maximum combustion chamber temperature constraint; among them, the current constraint is,

[0015]

[0016] FU min 、FU max are the minimum and maximum fuel utilization rates for the normal operation of the stack, respectively; N cell is the number of cell pieces in a single stack; r j represents the proportion of the gas flow into stack j in the total system flow rate, I j is the current of stack j, F is the Faraday constant, and n is the number of stacks in the multi-stack system.

[0017] Furthermore, the single SOFC stack model includes an electrochemical sub-model, an energy conservation sub-model, and a mass conservation sub-model.

[0018] Furthermore, the auxiliary components in the multi-stack SOFC system include a heat exchanger, a combustion chamber, and a blower.

[0019] Furthermore, the calculation method for the temperature of gas i in the heat exchanger is as follows,

[0020]

[0021] where represents the heat conduction between gas i and gas j in the heat exchanger; ρ i 、V i 、C i 、T i are the density, volume, specific heat capacity, and temperature of gas i, respectively.

[0022] Furthermore, the calculation method for the temperature of the gas at the outlet of the combustion chamber is as follows,

[0023]

[0024] where is the heat generated by the complete combustion of hydrogen, ρ gas 、V gas 、C gas 、T gas are the density, volume, specific heat capacity, and temperature of the mixed gas, respectively.

[0025] Furthermore, the specific calculation formula for the power of the blower is as follows,

[0026]

[0027] where is the amount of substance of air, C P,air is the specific heat capacity of air at normal pressure, T air,in is the temperature of the air flowing into the blower, η bl is the efficiency of the blower, P bl,in 、P bl,outare the pressures of the air flowing into and out of the fan, respectively, and γ is the specific heat capacity ratio of the air.

[0028] Generally speaking, compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects.

[0029] The present invention establishes a multi-stack SOFC power generation system model that includes the inconsistency of gas flow distribution among stacks. This model can reflect the impact of the inconsistency of gas flow distribution among stacks on system efficiency and safety. Based on this model, the present invention proposes a method for optimizing its operating parameters. First, using this method, the optimal efficiency operating point that satisfies the system safety constraints under a specific fuel flow rate can be obtained. Second, using this method, the optimal operating points under various fuel flow rates within the actual operating conditions of the system can be obtained, enabling the system to operate at the optimal efficiency operating point under different external load powers. Therefore, this method can improve system efficiency and minimize the system operation cost. Description of the Drawings

[0030] Figure 1 is the flowchart for optimizing the operating parameters of the SOFC multi-stack power generation system provided by the present invention;

[0031] Figure 2 is the structure diagram of the SOFC multi-stack power generation system;

[0032] Figure 3 is the schematic diagram of the SOFC stack, single cell, and node. Detailed Embodiments

[0033] In order to make the objectives, technical solutions, and advantages of the present invention clearer, 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.

[0034] The present invention first establishes a multi-stack SOFC power generation system model that includes the inconsistency of gas flow distribution among stacks, and then optimizes the operating parameters of the multi-stack SOFC power generation system with the inconsistency of gas flow distribution among stacks based on this model to enable the system to operate efficiently and safely.

[0035] Referring to Figure 1 , the method of the present invention includes the following steps:

[0036] S1. Model each SOFC stack in the multi-stack SOFC system;

[0037] The structure of the SOFC multi-stack power generation system is as shown in Figure 2As shown, it includes multiple hydrogen - fueled SOFC stacks connected in parallel. Hydrogen undergoes an electrochemical reaction with oxygen in the air inside the stack to generate electrical energy. The system also includes a heat exchanger and a combustion chamber, whose functions are to pre - heat the gases entering the stack and provide a heat source for the heat exchanger respectively. In addition, the fan, which is the main parasitic loss of the power generation system, also needs to be reflected in the model. Before the heat exchanger, adjustable - flow valves are installed on both the fuel and air pipelines to control the gas flow rate entering the system. A bypass is also installed on the air pipeline, and its function is to allow a part of the air to bypass the heat exchanger and mix with the pre - heated air. By adjusting the opening degree of the valve on this bypass, the temperature of the system can be controlled.

[0038] The structure of a single SOFC stack is as Figure 3 shown. The stack is composed of multiple single - cell batteries. Each single - cell battery includes a bipolar plate, a PEN (anode, electrolyte, cathode), a fuel flow channel, and an air flow channel. To reflect the temperature change inside the stack, the stack is evenly divided into multiple nodes along the gas flow direction. Each node mainly includes three parts: an electrochemical sub - model, an energy conservation sub - model, and a mass conservation sub - model.

[0039] 1) Electrochemical sub - model

[0040] The voltage of a single SOFC cell (i.e., the voltage of a single node) can be calculated from the Nernst voltage and three loss voltages, namely:

[0041] V cell = V Nernst - η ohm - η act - η conv

[0042] Among them, the calculation formula for the Nernst voltage V Nernst is:

[0043]

[0044] Among them, E 0 is the Gibbs free energy of the reaction, R is the ideal gas constant, T PEN is the temperature of the PEN, F is the Faraday constant, are the partial pressures of hydrogen, oxygen, and water vapor respectively.

[0045] η ohm is the ohmic loss. The ohmic loss is generated when ions flow in the electrolyte and encounter resistance, and it is proportional to the current density i.

[0046]

[0047] Among them, a0 and a1 are constants, a0 = 7509.6, a1 = - 25.885.

[0048] η act is the activation loss, and the activation loss can be obtained by the Butler-Volmer equation.

[0049]

[0050] where i 0,fuel , i 0,air represent the exchange current densities of the anode and cathode respectively, and i 0,fuel = 5300 A / m -2 , i 0,air = 2000 A / m -2 . n e represents the number of electrons participating in the electrochemical reaction, and n e = 2, and sinh -1 represents the inverse hyperbolic sine function.

[0051] where η conv is the concentration loss, and its calculation method is as follows.

[0052]

[0053] where i L is the limiting current density, and i L = 1×10 4 A / m -2 .

[0054] 2) Energy conservation sub-model

[0055] For the fluid control unit, that is, the fuel flow channel and the air flow channel in the stack, the differential equation describing its temperature change law is as follows:

[0056]

[0057] where C V is the volume specific heat capacity of the gas in the control unit; are the enthalpies of the gas entering and leaving the fluid control unit respectively; represents the heat exchange between the fluid control unit in this node and the adjacent solid control unit, that is, the heat exchange with the PEN and the connector control units;

[0058] can all be expressed in the following form:

[0059]

[0060] N is the flow rate of this fluid control unit, with the unit of mol / s -1 ; X i is the mole fraction of gas i; h iis the enthalpy of gas i, which is a function of the gas temperature;

[0061] can be expressed in the following form,

[0062]

[0063] S area represents the heat exchange area, k gs represents the heat exchange coefficient between the gas in the fluid control unit and the adjacent solid control unit, T i represents the temperature of the fluid control unit i, T j represents the temperature of the solid control unit j, and IC represents the bipolar plate.

[0064] For the solid control unit PEN, its energy conservation equation is as follows,

[0065]

[0066] represents the heat energy released during the electrochemical reaction process; represents the heat conduction between the PEN solid control unit and the adjacent fuel and air fluid control units; then represents the heat conduction between PEN and the IC of this node and the PEN of the adjacent node; ρ PEN 、V PEN 、C PEN respectively represent the density, volume, and specific heat capacity of PEN, I, V cell respectively represent the current and voltage of the battery. represents the heat generated by the electrochemical reaction, and its specific form is as follows:

[0067]

[0068]

[0069] where r is the electrochemical reaction rate, which can be calculated according to Faraday's law, A active is the reaction zone area, respectively represent the molar specific enthalpies of oxygen, hydrogen, and water vapor.

[0070] can be expressed in the following form, where k ss represents the heat exchange coefficient between the solid control units, and L represents the distance between the two control units.

[0071]

[0072] For the solid control unit IC, its energy conservation equation is as follows, and the meanings of its terms are similar to those of the PEN energy conservation equation.

[0073]

[0074] ρ IC 、V IC 、C IC respectively represent the density, volume, and specific heat capacity of the bipolar plate.

[0075] 3) Mass conservation sub-model

[0076] Mass conservation mainly describes the change in the molar fraction of each gas before and after the chemical reaction in the stack and the combustion chamber. Among them, N is the amount of substance of the gas in the fluid control unit, and R i represents the reaction rate of gas i, with the unit of mol / s -1 .

[0077]

[0078] respectively represent the amount of substance of the gas flowing into and out of the gas control unit, and X i,in 、X i,out respectively represent the molar fraction of gas i in the gas flowing into and out of the gas control unit.

[0079] S2. Model the auxiliary components in the multi-stack SOFC system;

[0080] 1) Heat exchanger

[0081] The main function of the heat exchanger is to preheat the fuel and air to enter the stack with the exhaust gas of the combustion chamber to improve the system efficiency. To improve the accuracy of the heat exchanger model, the present invention establishes a 1-D heat exchanger model including 5 nodes. The calculation method of the temperature of gas i in the heat exchanger is as follows.

[0082]

[0083] Among them represents the heat conduction between gas i and gas j in the heat exchanger; ρ i 、V i 、C i 、T i are respectively the density, volume, specific heat capacity, and temperature of gas i.

[0084] 2) Combustion chamber

[0085] The main function of the combustion chamber is to burn the remaining hydrogen in the stack exhaust gas and use the high-temperature gas generated after combustion as the heat source of the heat exchanger. The combustion chamber model is a 0-D model, that is, it only contains one node. Since the combustion process is relatively complete and its reaction rate is very fast, it can be considered that the hydrogen and oxygen entering the combustion chamber are completely burned to produce water. The calculation method of the combustion chamber outlet gas temperature is as follows,

[0086]

[0087] where is the heat generated by the complete combustion of all hydrogen, ρ gas , V gas , C gas , T gas are the density, volume, specific heat capacity, and temperature of the mixed gas, respectively.

[0088] 3) Blower

[0089] The blower is the main parasitic loss in the system. Therefore, the main function of the blower model is to calculate the power consumed by the blower under a certain air flow rate, and then calculate the power generation efficiency of the system. The specific calculation formula of the blower power is as follows,

[0090]

[0091] where is the amount of substance of air, C P,air is the specific heat capacity of air at atmospheric pressure, T air,in is the temperature of the air flowing into the blower, η bl is the efficiency of the blower, P bl,in , P bl,out are the pressures of the air flowing into and out of the blower, respectively, and γ is the specific heat capacity ratio of air.

[0092] S3. Optimize the operating parameters of the multi-stack SOFC power generation system based on the system model;

[0093] Specifically, after experimentally verifying the model, at different fuel flow rates, change the air excess ratio, the current of each SOFC stack, and the bypass valve opening, and use the multi-stack SOFC system auxiliary component model and each SOFC stack model to calculate the system efficiency, and obtain the operating parameters corresponding to the highest system efficiency at different fuel flow rates.

[0094] First, arrange the stack model established in step 1 above and the auxiliary component model established in step 2 according to Figure 2The combined system structure diagrams shown are the system model. Next, taking the case where the system includes two 5kW-class SOFC stacks and the gas flow distribution ratio is 3:2 as an example, it is illustrated how to optimize the system parameters based on the above model. The system altogether includes 5 operating parameters, namely fuel flow rate, air excess ratio, current of stack 1, current of stack 2, and bypass valve opening. The optimization objective is to find the operating point with the highest system efficiency under a certain fuel flow rate. The calculation method of the system efficiency is as follows,

[0095]

[0096] where I1 and V1 are respectively the current and voltage of stack 1, and I2 and V2 are respectively the current and voltage of stack 2, is the amount of substance of hydrogen consumed by the system, is the lower heating value of hydrogen.

[0097] The reason why the present invention uses this absolute quantity of fuel flow rate to replace the common fuel utilization rate as one of the system control parameters is that if the fuel utilization rate of the system is used, then under a certain system fuel utilization rate, changing the working current of one of the stacks will affect the fuel and air flow rates of the other stack, and further change its working state, which is not convenient for analysis.

[0098] When the stack is working, its fuel utilization rate needs to meet certain constraints to avoid fuel deficit caused by too high fuel utilization rate or too high system temperature caused by too low fuel utilization rate. Although the fuel utilization rate is not used as a direct control parameter, this constraint condition still needs to be considered in the simulation. The fuel utilization rate of the stack depends on the amount of fuel flowing into the stack and the stack current, and its specific calculation method is as follows.

[0099]

[0100] where FU j is the fuel utilization rate of stack j, I j is the current of stack j, N cell is the number of cell pieces of a single stack, r j represents the gas flow distribution ratio of stack j, r1 = 0.6, r2 = 0.4, is the amount of substance of hydrogen flowing into the system, and F is the Faraday constant.

[0101] The fuel utilization rate constraint is as follows,

[0102] FU min ≤FU j ≤FU max , j = 1, 2

[0103] where FU min 、FU maxThey are the minimum and maximum fuel utilization rates for the normal operation of the stack, FU min and FU max which are generally 0.6 and 0.9 respectively.

[0104] Combining the relationship between the fuel utilization rate of the stack and the current, the above constraints on the fuel utilization rate can be transformed into constraints on the current:

[0105]

[0106] In addition to the above constraints, the system also needs to meet certain temperature constraints. The main temperature constraints and their general values are as follows:

[0107] The maximum temperature constraint of the stack, that is, the highest temperature inside the stack should be lower than 1173K. Corresponding to the stack model established in step 1, it means that the highest temperature of a single node is lower than 1173K.

[0108] The temperature gradient constraint of the stack, that is, the temperature gradient inside the stack should be less than 8K / cm. Corresponding to the stack model established in step 1, it means that the temperature difference between adjacent nodes (the length of a single node is 2cm) is less than 16K.

[0109] The temperature difference constraint of the inlet gas of the stack, that is, the temperature difference between the fuel and air at the inlet of the stack should be less than 200K. Corresponding to the stack model established in step 1, it means that the temperature difference between the fuel and air at the inlet of the first node is less than 200K.

[0110] The maximum temperature constraint of the combustion chamber, that is, the highest temperature of the combustion chamber should be lower than 1273K. Corresponding to the combustion chamber model established in step 3, it means that the highest temperature of the combustion chamber gas is lower than 1273K.

[0111] First, determine the ranges and discrete step sizes of the five operating parameters respectively, as shown in the following table. On this basis, the currents of the two stacks also need to meet the above constraints to achieve the constraints on the fuel utilization rate.

[0112] Control parameter Parameter range Discretization step size Fuel flow rate / SLPM 20～150 10 Excess air ratio 6～12 0.5 Stack 1 current / A 0～80 2 Stack 2 current / A 0～80 2 Bypass valve opening 0～0.3 0.05

[0113] Among the operating points that satisfy the above current constraints and temperature constraints under a certain fuel flow rate, the operating point with the highest system efficiency is the optimal operating point under this fuel flow rate. The specific steps to find the optimal operating point of the system under a certain fuel flow rate are as follows:

[0114] Set the air excess ratio, the current of stack 1, the current of stack 2, and the bypass valve opening of the operating point according to the above table.

[0115] Check whether the currents of stack 1 and stack 2 meet the current constraint conditions. If they are met, proceed to the next step; if not, go back to step 1 and initialize to the next operating point.

[0116] Use the operating parameters as the input of the model, run the simulation and collect the simulation data.

[0117] Check whether the system temperature constraint is satisfied during the simulation. If it is satisfied, proceed to the next step; if not, return to step 1 and initialize to the next operating point.

[0118] Save the data such as the operating parameters and system efficiency of this simulation. Return to step 1 and initialize to the next operating point.

[0119] After completing the above steps, all the operating points that satisfy the current constraint and temperature constraint and their corresponding system efficiencies at this fuel flow rate are obtained. Among them, the operating point with the highest system efficiency is the optimal operating point at this fuel flow rate.

[0120] Repeat the above process for all fuel flow rates, and the optimal operating points of the system at various fuel flow rates can be obtained as shown in the following table.

[0121]

[0122] 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 within the protection scope of the present invention.

Claims

1. A method for optimizing the operating parameters of a multi-stack SOFC power generation system, characterized in that, Including: S1. Modeling each SOFC stack in a multi-stack SOFC system; the single SOFC stack model includes an electrochemical sub-model, an energy conservation sub-model, and a mass conservation sub-model; S2. Modeling each auxiliary component in the multi-stack SOFC system; the auxiliary components in the multi-stack SOFC system include a heat exchanger, a combustion chamber, and a blower; S3. Changing the air excess ratio, the current of each SOFC stack, and the bypass valve opening at different fuel flow rates, and calculating the system efficiency using each SOFC stack model and the auxiliary component model of the multi-stack SOFC system to obtain the operating parameters corresponding to the highest system efficiency at different fuel flow rates; The calculation method of the system efficiency is as follows: where n is the number of fuel cells in the multi-stack system, and I i , V i are the current and voltage of fuel cell i respectively, is the amount of substance of hydrogen consumed by the system, is the low calorific value of hydrogen.

2. The method for optimizing the operating parameters of a multi-stack SOFC power generation system according to claim 1, characterized in that, The following constraints are satisfied when calculating the highest system efficiency: current constraint, maximum stack temperature constraint, stack temperature gradient constraint, stack inlet gas temperature difference constraint, and maximum combustion chamber temperature constraint; among them, the current constraint is: FU min and FU max are the minimum and maximum fuel utilization rates for the normal operation of the fuel cell stack, respectively; N cell is the number of cells in a single fuel cell stack; r j represents the proportion of the gas flow into stack j in the total system flow rate, I j is the current of stack j, F is the Faraday constant, and n is the number of fuel cell stacks in the multi-stack system.

3. The method for optimizing the operating parameters of a multi-stack SOFC power generation system according to claim 1, characterized in that, The calculation method of the temperature of gas i in the heat exchanger is as follows: Among them represents the heat conduction between gas i and gas j in the heat exchanger; ρ i , V i , C i , T i are the density, volume, specific heat capacity, and temperature of gas i, respectively.

4. The method for optimizing the operating parameters of a multi-stack SOFC power generation system according to claim 1, characterized in that, The calculation method of the gas temperature at the outlet of the combustion chamber is as follows: wherein is the heat generated by complete combustion of hydrogen, ρ gas , V gas , C gas , T gas are the density, volume, specific heat capacity, and temperature of the mixed gas, respectively.

5. The method for optimizing the operating parameters of a multi-stack SOFC power generation system according to claim 1, characterized in that, The specific calculation formula of the blower power is as follows: where is the amount of substance of air, C P,air is the specific heat capacity of air at atmospheric pressure, T air,in is the temperature of the air flowing into the fan, η bl is the efficiency of the fan, P bl,in and P bl,out are the pressures of the air flowing into and out of the fan respectively, and γ is the specific heat capacity ratio of air.

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