Quantification and optimization method for reversible efficiency of solid oxide battery system

Abstract

The invention provides a solid oxide battery system reversible efficiency quantification and optimization method, and belongs to the technical field of energy conversion and storage in renewable energy sources. The method specifically comprises the steps of determining a general form of generalized reversible efficiency definition; determining a generalized reversible efficiency deconstruction model based on the operation parameters; a mathematical quantification and solution strategy of generalized reversible efficiency is proposed, multiple constraints of the solid oxide battery system are coupled, and a comprehensive optimization mathematical model with reversible efficiency maximization and electrolysis process efficiency maximization or discharge process efficiency maximization as targets is constructed; solving the optimization model, and generating an optimal solution as a regulation and control scheme of the solid oxide battery system; and energy efficiency optimization of the solid oxide battery system in a complete switching period is realized through the regulation and control strategy. According to the method, the mode switching energy efficiency of the solid oxide battery system in a continuous complete period is optimized, the efficiency of the battery system is improved, and the improvement of a thermal management process of the system is promoted.

Description

Technical Field

[0001] The present invention relates to the technical field of energy conversion and storage in renewable energy, and in particular to a method for quantifying and optimizing the reversible efficiency of a solid oxide battery system. Background Art

[0002] The solid oxide battery system is a highly efficient energy conversion device that combines the dual functions of power generation (fuel cell mode) and energy storage (electrolysis cell mode). Its core advantage lies in the bidirectional conversion of energy and chemical energy through reversible reactions. Energy conversion efficiency is a key indicator for measuring the performance of solid oxide battery systems, and the reversible efficiency under one charge and discharge cycle is usually used as the evaluation standard. However, the actual operating efficiency of the solid oxide battery system is affected by factors such as multi-physics field coupling, reaction kinetics, and thermodynamic irreversibility. Its dynamic characteristics vary significantly in time scale and operating direction (power generation / electrolysis). It is necessary to deconstruct the efficiency composition from a mechanistic perspective and quantify the influence of each factor.

[0003] Existing methods for optimizing the reversible efficiency of solid oxide battery systems primarily focus on improving the steady-state performance of a single operating mode, including material electrode modification, electrolyte conductivity enhancement, or static optimization of operating parameters (temperature, gas flow rate, etc.). Alternatively, they analyze the overall efficiency of the charge-discharge cycle through experiments or modeling. However, these methods typically treat the cycling process as a time-symmetric, fixed path, ignoring the dynamic losses during mode switching, as well as the differential effects of operating direction and mode duration on reversible efficiency.

[0004] Therefore, the limitations of existing technologies are mainly reflected in three aspects: first, efficiency evaluation is limited to the overall cycle and ignores transient processes, resulting in insufficient identification of key loss links; second, the constraints of operating direction (such as the irreversibility difference between power generation and electrolysis) on efficiency are not considered, making it difficult to achieve coordinated optimization of bidirectional working conditions; third, there is a lack of dynamic scheduling solutions to adapt to the changing working conditions in actual scenarios, which limits the efficient application of the system in complex energy networks.

[0005] Therefore, a solid oxide battery system mode scheduling method is urgently needed to achieve the global optimal reversible efficiency under a complete switching cycle of the solid oxide battery system. Summary of the Invention

[0006] In view of this, the present invention provides a method for quantifying and optimizing the reversible efficiency of a solid oxide battery system. Based on the generalized mathematical model of reversible efficiency, a deconstruction strategy is proposed and a quantification and optimization model of generalized reversible efficiency is established. The system operation constraints are coupled to reveal the essential laws of periodic energy conversion. The solution is solved with the goal of maximizing the generalized reversible efficiency and inter-mode efficiency. The discharge or electrolysis process of the solid oxide battery system is regulated by using the optimal solution as a control strategy.

[0007] To this end, the present invention provides the following technical solutions:

[0008] A method for quantifying and optimizing the reversible efficiency of a solid oxide battery system, comprising:

[0009] A continuous and non-repeating complete cycle of any energy conversion direction of the solid oxide battery system is divided into two stages in time; the inverse of the ratio of the effective conversion energy corresponding to the two stages is defined as a generalized representation of reversible efficiency;

[0010] Introducing an intermediate medium factor associated with hydrogen production during the electrolysis process, transforming the generalized representation of reversible efficiency, and determining a generalized reversible efficiency model based on operating parameters;

[0011] Deconstructing the reversible efficiency model, establishing phased generalized reversible efficiency models for the electricity-gas-electricity stage and the gas-electricity-gas stage, and determining a solution representation for the generalized reversible efficiency;

[0012] Based on the generalized reversible efficiency solution representation, coupled with the solid oxide battery system operation constraints, a multi-objective optimization model is constructed with the goal of maximizing the generalized reversible efficiency and maximizing the efficiency of the solid oxide battery system during each mode;

[0013] Solving the multi-objective optimization model to generate an optimal solution as a control strategy for the solid oxide battery system;

[0014] The control strategy is used to optimize the energy efficiency of the solid oxide battery system during a complete charge and discharge cycle.

[0015] Furthermore, the inverse of the ratio of the effective conversion energies corresponding to the two stages is defined as a generalized representation of the reversible efficiency:

[0016]

[0017] in, Represents a continuous and non-repeating complete cycle in any energy conversion direction of the solid oxide battery system; When the electrolysis process is represented, Indicates the discharge process; Indicates the discharge process, Represents the electrolysis process; for any operating point in the system operating space The corresponding effective conversion can be expressed as The corresponding effective conversion can be expressed as The effective conversion energy represents the energy conversion cycle The total energy of the initial state of matter before and after and the total energy of the final state.

[0018] Furthermore, the intermediate medium factor associated with the hydrogen production during the electrolysis process is:

[0019] γ=I j *t k

[0020] Where γ represents the intermediate medium factor associated with the hydrogen production during the electrolysis process, I j represents the stack current at any point j in the system operating space, t k represents the system running time at any point k in the system operation space.

[0021] Furthermore, the generalized reversible efficiency model based on operating parameters is:

[0022] in, Indicates the total power consumption of electrolysis, represents the net discharge power; x(i) represents the system operating point; is a function of the operating point x(i) of the solid oxide battery system, and the operating parameters determine The operating parameters include: stack current I s 、Excess air ratio ε air , fuel utilization rate U f And the auxiliary gas concentration X in the fuel circuit fuel .

[0023] Furthermore, the generalized reversible efficiency is characterized by:

[0024]

[0025] in, Represents the effective conversion energy of the discharge process, represents the effective conversion energy of the electrolysis process, t s represents x(i) SOFC represents any operating point in the operating space of the discharge process system, x(i) SOE represents any operating point in the operating space of the electrolysis process system, t s Indicates the duration of the discharge process or electrolysis process; γ i,SOFC Indicates the intermediate dielectric factor during the discharge process, γ i,SOE Represents the intermediate medium factor in the electrolysis process.

[0026] Furthermore, the solid oxide battery system operation constraints include:

[0027] Determine the source-load power balance constraint based on the equivalent voltage;

[0028] Preset the maximum operating temperature limit of the fuel cell stack;

[0029] Preset the maximum temperature gradient upper limit of the fuel cell stack;

[0030] Limit the duration of the discharge and electrolysis processes based on the actual energy conversion scenario;

[0031] Preset heater limit temperature during electrolysis process;

[0032] Preset the value range of the current operating parameter and the gas supply volume operating parameter.

[0033] Furthermore, the multi-objective optimization model includes:

[0034]

[0035] stγ i,SOFC =γ i,SOE

[0036] U stack (x(i))=∑U BOP (x(i))

[0037]

[0038] Max.T≤T max

[0039] t s ≤12h

[0040] T pre =T set

[0041] [I s,min ,I s,max ]≤I cell,max

[0042]

[0043] Among them, Max.T represents the maximum operating temperature of the stack; represents the upper limit of the maximum operating temperature of the stack; Max.T grad Indicates the maximum temperature gradient of the stack in the gas flow direction; Indicates the upper limit of the maximum temperature gradient of the stack in the gas flow direction; T pre Indicates the heater temperature during the electrolysis process; T set Indicates the set value of the heater temperature during the electrolysis process; t s Indicates the duration of the discharge process or electrolysis process; I cell,max It represents the maximum current density that can be achieved by the solid oxide battery system in the system environment; represents the set of operation variables, Γ is The specific boundary conditions corresponding to each operation quantity.

[0044] Furthermore, the optimization model is solved by using an improved multi-objective differential evolution algorithm and an approximate ideal solution sorting method, including:

[0045] The Pareto frontier solution is obtained based on the improved multi-objective differential evolution algorithm;

[0046] The optimal solution of the optimization model is obtained based on the Pareto front by an approximate ideal solution ranking method.

[0047] Furthermore, the improvement of the multi-objective differential evolution algorithm includes:

[0048] Introduce an adaptive strategy to adjust the differential weight F and crossover probability CR;

[0049]

[0050] Among them, F x Indicates the lower limit of differential weight application, F s represents the upper limit of the differential weight; g and G represent the current evolutionary generation and the total evolutionary generation respectively;

[0051] Introduce a Gaussian mutation link to improve population diversity:

[0052]

[0053] Among them, w g+1 Indicates Gaussian variation individual; normrnd indicates taking u g+1 is the mean, ε is the standard deviation, and the random numbers generated conform to the normal distribution; lb and ub represent the lower limit and upper limit of the decision variable respectively; L represents the mutation rate control factor.

[0054] Furthermore, the control strategy includes:

[0055] The stack current and discharge process running time during the discharge process;

[0056] The stack current and running time of the electrolysis process.

[0057] Advantages and positive effects of the present invention:

[0058] The present invention quantifies the reversible efficiency by the ratio of the effective net energy generated by the discharge process to the original total energy consumed by the electrolysis process, significantly improving the universality of the reversible efficiency assessment and making it widely applicable to various practical application scenarios. At the same time, by constructing a system operation constraint system, the safe and stable operation of the battery system during the optimization process is ensured; the differential evolution algorithm is combined with the multi-objective decomposition strategy, and the approximate ideal solution sorting method is introduced for multi-objective optimization and solution, achieving the dual maximization goal of the electrolysis process efficiency and the discharge process efficiency. This not only ensures the battery system's ability to respond quickly to load changes, but also significantly improves the system's energy efficiency performance and effectively extends the battery's service life, which has important engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0060] Figure 1 This is a flow chart of a solid oxide battery system control method based on reversible efficiency in an embodiment of the present invention;

[0061] Figure 2 This is a schematic diagram of the process flow of a solid oxide battery system according to an embodiment of the present invention;

[0062] Figure 3 Schematic diagram of the reversible efficiency of the solid oxide battery system in an embodiment of the present invention;

[0063] Figure 4 This is a diagram showing the reversible efficiency of a solid oxide battery system according to an embodiment of the present invention;

[0064] Figure 5 This is a flow chart of solving an optimization model using a multi-objective decomposition and approximate ideal solution ranking method based on differential evolution in an embodiment of the present invention;

[0065] Figure 6 A distribution diagram of the optimal compromise solution of the Pareto front and the approximate ideal solution sorting method in an embodiment of the present invention;

[0066] Figure 7 The optimal decision variable distribution diagram corresponding to the Pareto front in an embodiment of the present invention;

[0067] Figure 8 is the optimal compromise solution after interpolation in the embodiment of the present invention Surface and η SOFC Surface plot;

[0068] Figure 9 The factor γ in the global operation domain corresponds to distribution map;

[0069] Figure 10 The optimal solution corresponding to different γ in the electrolysis process in the embodiment of the present invention;

[0070] Figure 11 In the embodiment of the present invention, variable I s and the optimal η of t RT trajectory. DETAILED DESCRIPTION

[0071] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0072] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0073] The present invention provides a method for quantifying and optimizing the reversible efficiency of a solid oxide battery system. By quantifying the generalized reversible efficiency through operable variables, a universally applicable form of the reversible efficiency in a complete continuous cycle is obtained. In combination with the constraints of the solid oxide battery system, a reversible efficiency optimization model for the solid oxide battery system is constructed and solved. A reversible efficiency optimization strategy applicable to solid oxide battery systems in practice is obtained, which is applicable to a wide range of real-world operating scenarios.

[0074] Combine Figure 1 The method of the present invention is further described:

[0075] S1. Determine the generalized reversible efficiency deconstruction and quantification model based on operating parameters;

[0076] Solid oxide battery system workflow Figure 2shown.

[0077] With reversible efficiency η RT As an indicator to quantify the global energy conversion performance of solid oxide battery system, the formula of reversible efficiency is expressed as:

[0078]

[0079] Among them, for any operating point of the solid oxide battery system The amount of hydrogen produced in an electrolysis process is n(mol). When the electrolysis current I SOE and discharge current I SOFC When the electrolysis process and the discharge process have the same running time, Indicates the net amount of electricity generated by the hydrogen consumption n (mol) during the discharge process, indicating The ratio of the amount of hydrogen produced n (mol) to the total electrical energy consumed during the electrolysis process.

[0080] S11. In order to accurately characterize the reversible efficiency, in this embodiment, the definition of reversible efficiency is broadened; that is, the ratio of effective conversion energy is defined as the generalized reversible efficiency, and the conversion energy On a macro level, the operating current and operating time are no longer considered. A continuous and non-repeating complete cycle in any energy conversion direction of the solid oxide battery system is divided into two stages according to the time sequence; the inverse of the ratio of the effective conversion energy corresponding to the two stages is defined as a generalized representation of reversible efficiency:

[0081]

[0082] in, Represents a continuous and non-repeating complete cycle in any energy conversion direction of the solid oxide battery system; When the electrolysis process is represented, Indicates the discharge process; Indicates the discharge process, Represents the electrolysis process; for any operating point in the system operating space Corresponding effective conversion energy The corresponding effective conversion energy Effective conversion energy represents the energy conversion cycle The total energy of the initial state of matter before and after and the total energy of the final state.

[0083] S12. Introduce an intermediate medium factor associated with the hydrogen production in the electrolysis process, transform the generalized representation of the reversible efficiency, and determine a generalized reversible efficiency model based on the operating parameters; deconstruct the reversible efficiency model, establish staged generalized reversible efficiency models for the electricity-gas-electricity stage and the gas-electricity-gas stage respectively, and determine the solution representation of the generalized reversible efficiency.

[0084] Represents the Power-Gas-Power or Gas-Power-Gas process in the solid oxide battery system, denoted as P2G2P and G2P2G respectively. It includes an electrolysis process and a discharge process, and each process is independent in time and state.

[0085] Combine Figure 3 , in the P2G2P stage, the P2G process is expressed as That is, the electrolysis process; represents the G2P process, i.e., the discharge process; and Proceed in P2G2P order.

[0086] For the initial state total energy and final state total energy in the P2G2P process, it is expressed as the original total energy consumed by the electrolysis process The effective net energy generated by the discharge process

[0087] The same applies to G2P2G; cycle The energy forms of the initial and final states are consistent. P2G2P exists in the form of electrical energy, while G2P2G exists in the form of hydrogen.

[0088] 1) When When hydrogen is used as an energy storage medium, the amount of hydrogen determines the effective conversion energy of the electrolysis process and the discharge process. The value range is only The hydrogen production was 100% consumption, can be based on the cycle The effective conversion of the initial and final states can effectively solve η RT .

[0089] The amount of hydrogen produced is only related to the electrolysis current I SOE It is related to the system operation time t; therefore, the two variables of electrolysis current and system operation time are infinitely discretized in their operation domain, and the decision factor corresponding to the electrolysis hydrogen production n (mol) can be solved to obtain the optimal η RT There is more than one.

[0090] Assume that there is a mapping in a bounded two-dimensional space is the electrolysis current I in the associated operating space SOE and system operation time t, for a fixed electrolysis hydrogen production, the set of decision variables that meet the conditions (I SOE ,t) is expressed as:

[0091]

[0092] Among them, S n represents all the SOE ,t)=n's I SOE and t; when there is a unique factor γ associated with the amount of hydrogen produced by electrolysis, record Then the unique factor γ formula is expressed as:

[0093] Among them, j∈m, k∈n, as long as there is an infinite set in the sets m and n, the fixed electrolysis hydrogen production corresponding to There are infinite combinations; k Indicates the system running time corresponding to any point in the system operation space; Represents the stack current at any point within the operating space of the electrolysis process system.

[0094] Similarly, for γ corresponding to the fixed discharge hydrogen consumption in the stage i There are also infinite options.

[0095] and Different γ corresponds to different operating values ​​of solid oxide battery system, which directly leads to the corresponding and The complexity of the value space increases, making it difficult to find the optimal η RT .

[0096] Therefore, η RT Translates to:

[0097] in, Indicates the total power consumption of electrolysis, Indicates the net discharge power; It is a function of the solid oxide battery system operating point x(i), operating parameters: stack current I s 、Excess air ratio ε air , fuel utilization rate U f And the auxiliary gas concentration X in the fuel circuit fuel Decide value.

[0098] therefore, is x(i) and t s function, in the P2G2P cycle η RT The decision variables are With t S Therefore, η RT The optimization can be expressed as:

[0099]

[0100] Among them, x(i) s1 express System operating point in the process, x(i) s2 express System operating point in the process, x(i) s1 and x(i) s2 Belong to different processes and do not interfere with each other; γ is the series connection of Opt[η RT ] The interface between the numerator and denominator, corresponding to when the upper and lower γ values ​​are equal and The ratio of the values ​​of is the effective maxη RT , t s2 express Process duration, t s1 express Duration of the process.

[0101] Optimization η of P2G2P process RT The solution: As long as I j and t k If the factors γ are equal, the optimal η in two-dimensional space can be solved. RT .

[0102] 2) When When the net electrical energy W generated during the discharge process SOFC,net The total electrical energy consumed by electrolysis W SOE Equal, η RT It is equal to the ratio of the amount of hydrogen in the final state to the amount of hydrogen in the initial state.

[0103] However, by operating point It is difficult to describe W SOFC,net or W SOE function;

[0104] If according to η SOFC and η SOE Determine the effective η RT To solve, we need to Obviously, η is also the output in the multi-dimensional operation space, and it is still difficult to establish an effective and Link. Solving η for the G2P2G process RT The complexity increases significantly.

[0105] S13. Determine a solvable quantitative model of reversible efficiency around γ, i.e., a solvable representation of generalized reversible efficiency;

[0106] For the P2G2P process, the strategy of "fixing the middle and using both ends" is adopted; for the G2P2G process, the strategy of "fixing both ends and using the middle" is adopted. Figure 4Further explanation:

[0107] Figure 4 The dotted line in (a) represents the cycle Any two consecutive processes and and The energy values ​​of have no relationship with each other, that is, Figure 4 The original state of the solid lines in (a) and (b) is as follows: for P2G2P, “fix the middle and use both ends” is as shown in 4(a); for G2P2G, “fix both ends and use the middle” is as shown in Figure 4 (b).

[0108] In this embodiment, the strategy adopted by G2P2G is: first, by ensuring the cycle The amount of hydrogen consumed in the initial and final state discharge process is consistent with the amount of hydrogen produced in the electrolysis process, and the intermediate medium factor γ=I is required for the discharge process and the electrolysis process. j t k Equal, I j represents the stack current at any point j in the system operating space, t k Represents the system running time at any point k in the system operation space. Then according to η RT Can be further converted into W SOFC,net With W SOE The premise is that the corresponding γ between the modes is consistent. According to Opt[η RT ], the numerator corresponds to the discharge process and the denominator is the electrolysis process, although they are carried out in different orders in the P2G2P and G2P2G processes. Is it P2G2P or G2P2G, η RT The formula is expressed as:

[0109]

[0110] in, Represents the effective conversion energy of the discharge process, represents the effective conversion energy of the electrolysis process, t s represents the duration of the electrolysis process or the discharge process, x(i) SOFC represents any operating point in the operating space of the discharge process system, x(i) SOE represents any operating point in the operating space of the electrolysis process system, t s Indicates the duration of the discharge process or electrolysis process; γ i,SOFC Indicates the intermediate dielectric factor during the discharge process, γ i,SPE Represents the intermediate medium factor in the electrolysis process.

[0111] Therefore, η RTThe optimization mathematical model is expressed as:

[0112]

[0113] S2. Based on the generalized reversible efficiency mathematical quantification model and coupled with the operating constraints of the solid oxide battery system, an optimization model is constructed with the goal of maximizing the reversible efficiency and maximizing the efficiency of the electrolysis process or the discharge process;

[0114] S21: During homogeneous energy conversion, η cannot be maximized at the expense of efficiency during the mode. RT , so the optimal η RT At the same time, we must ensure continuous cycle The stages within and The efficiency is maximized, and the formula is expressed as:

[0115] Reversible efficiency η RT The optimization problem is transformed into a multi-objective function, and the formula is expressed as: Based on the continuity on the time scale and the non-interference of variables in the decision space, f is transformed into:

[0116]

[0117] Among them, f * Optimize η for P2G2P cycle and G2P2G cycle RT All are established, η SOFC Discharge process efficiency, η SOE Indicates the efficiency of the electrolysis process.

[0118] S22. Determine the operating constraints of the solid oxide battery system:

[0119] In this embodiment, the operating constraints of the high-temperature solid oxide battery system include:

[0120] 1) Maximum temperature gradient Max.T of the solid oxide battery system stack in the gas flow direction grad within a certain range;

[0121] 2) Preset the maximum operating temperature Max.T of the battery stack to prevent excessive temperature from damaging the battery cells;

[0122] 3) The operating point of the solid oxide battery system x(i) = {I s ,ε air ,U f ,X fuel The operation variables in} take values ​​in a finite range:

[0123] ① According to the electrochemical performance of the single cell, preset the stack current Is The upper limit of its range [I s,min ,I s,max ] is less than the current upper limit I cell,max ;

[0124] ② Excess air ratio ε air Indicates the air flow into the stack, ε air The value range of air,min ,ε air,max ] to maintain the stack temperature within the safety limit;

[0125] 4) Auxiliary gas concentration X in the fuel circuit fuel By setting upper and lower limits, the auxiliary gas can protect the electrode material and maintain the partial pressure balance in the chamber;

[0126] 5) To prevent fuel shortage, limit the fuel utilization rate U f The value range of

[0127] 6) According to the actual energy conversion scenario, limit and Duration t s ;

[0128] 7) Heater temperature T during electrolysis pre impose restrictions;

[0129] 8) Determine the equation constraint of the source-load power balance of the solid oxide battery system in the form of equivalent voltage. This constraint will vary depending on the system state and process. The formula is expressed as:

[0130] U stack (x(i))=∑U BOP (x(i))

[0131] Among them, U stack and U BOP Represent the equivalent voltage of the battery stack and the system auxiliary component BOP respectively.

[0132] S23. In this embodiment, the reversible efficiency optimization model of the photovoltaic high-temperature solid oxide battery system is expressed as:

[0133]

[0134] stγ i,SOFC =γ i,SOE

[0135] U stack (x(i))=∑U BOP (x(i))

[0136]

[0137] Max.T≤T max

[0138] t s ≤12h

[0139] T pre =T set

[0140] [I s,min ,I s,max ]≤I cell,max

[0141]

[0142] Among them, Max.T represents the maximum operating temperature of the stack; represents the upper limit of the maximum operating temperature of the stack; Max.T grad Indicates the maximum temperature gradient of the stack in the gas flow direction; Indicates the upper limit of the maximum temperature gradient of the stack in the gas flow direction; T pre Indicates the heater temperature during the electrolysis process; T set Indicates the set value of the heater temperature during the electrolysis process; t s Indicates the duration of the discharge process or electrolysis process; I cell,max It represents the maximum current density that can be achieved by the solid oxide battery system in the system environment; represents the set of operation variables, Γ is The specific boundary conditions corresponding to each operation quantity.

[0143] S3, solving the optimization model in S2 and generating the optimal solution as the control strategy of the solid oxide battery system;

[0144] In this embodiment, the optimal control strategy of the solid oxide battery system is obtained by combining the improved multi-objective differential evolution algorithm with the multi-attribute decision-making TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). The solution process is as follows: Figure 5 shown.

[0145] Improvements to the multi-objective differential evolution algorithm include:

[0146] Introduce an adaptive strategy to adjust the differential weight F and crossover probability CR;

[0147]

[0148] Among them, F x Indicates the lower limit of differential weight application, F srepresents the upper limit of the differential weight; g and G represent the current evolutionary generation and the total evolutionary generation respectively;

[0149] Introducing a Gaussian mutation link and adding Gaussian distributed random noise to improve population diversity:

[0150]

[0151] Among them, w g+1 Indicates Gaussian variation individual; normrnd indicates taking u g+1 is the mean, ε is the standard deviation, and the random numbers generated conform to the normal distribution; lb and ub represent the lower limit and upper limit of the decision variable respectively; L represents the mutation rate control factor.

[0152] For both the period P2G2P and the period G2P2G, f * The optimal η is solved in the form of RT .

[0153] For f P2G We need to maximize η SOE , while minimizing the total energy consumption when producing hydrogen m Based on η SOE Basic definition: η SOE Equal to the total energy contained in the amount of hydrogen produced by the solid oxide battery system n and the total energy consumption Assuming maxη SOE and There is no contradiction between There is a unique optimal solution. Otherwise, f G2P The objective functions in are necessarily conflicting in the decision space.

[0154] 1) According to the principle of multi-objective differential evolution algorithm, f G2P The transformation minimization solution is expressed as:

[0155]

[0156] 2) Considering the low gas flow rate of the fuel pipeline and U f and X fuel In the operating range, the effect on system efficiency η is minimal, so U is ignored. f and X fuel f G2P The impact of optimization is to speed up the iterative calculation efficiency; x(i) SOFC Simplified to x(i)' SOFC ={I s ,ε air ,t s} to optimize the solution.

[0157] In this embodiment, the decision variable x(i)' SOFC The operating range of is shown in Table 1; Table 2 is the parameter setting of the improved multi-objective differential evolution algorithm; Table 3 is the TOPSIS weight distribution scheme of the discharge process. In Table 3, f1 and f2 each represent f G2P Objective function and -η SOFC , its weight is mainly set according to actual needs, and four distribution schemes from W1 to W4 are set to significantly distinguish the distribution of TOPSIS solutions under different weight schemes. Figure 5 The strategy flow shown solves the problem f G2P The Pareto frontier.

[0158] Table 1

[0159] Decision variables and fixed values Discharge process electrolysis process <![CDATA[I s [A]]]> 20～70 (-20)～(-60) <![CDATA[ε air ]]> 7～10 5～12 t[h] 2～12 2～12 <![CDATA[U f ]]> 0.8 0.8 <![CDATA[X fuel ]]> 0.9 0.9

[0160] Table 2

[0161] Algorithm parameters scope Population size N 200 The number of weight vectors in the neighborhood q 20 The number of objective functions m 2 Mutation operator F <![CDATA[F x =0.1,F s =0.9]]> Crossover operator CR <![CDATA[C0=0.32,C1=0.5]]> Maximum evolutionary generation G 500

[0162] Table 3

[0163] plan <![CDATA[f1 weight value]]> <![CDATA[f2 weight value]]> W1 0.05 0.95 W2 0.08 0.92 W3 0.1 0.9 W4 0.2 0.8

[0164] The improved multi-objective differential evolution algorithm is used to P2G The solution is obtained to further confirm that there is only one solution in the electrolysis process.

[0165] Objective function f * The solution set is as follows Figure 6 As shown, Figure 6 The results of TOPSIS solution in (a) are expressed as @W i The form of is shown, i corresponds to the number of the scheme in Table 3. SOFC and There is a Pareto front between f1 and f2, and f1 and f2 conflict with each other. Figure 6 (b) It is known that the solution is unique.

[0166] And due to the difference in the attribute values ​​of f1 and f2, the optimal compromise solution will move towards maxη only when the weight of f2 is large enough. SOFC The directions are closer, that is, in the attribute decision process, f1 has a higher degree of discrimination for the alternatives in the Pareto front.

[0167] Figure 7 Shows Figure 6 The optimal decision variable value corresponding to the Pareto front in (a) is determined by @W i The index of has marked the position of the optimal compromise solution corresponding to each TOPSIS solution. It can be found that the optimal solution x(i)' opt ε inair Without limiting the solution accuracy, ε air The value basically falls around the lower limit of 7, which means that under the premise of meeting the temperature constraint, ε air The lower the auxiliary power consumption, the lower the parasitic energy loss and the lower the ε air Able to maximize efficiency.

[0168] When t s When they are not equal and vary within the given interval [2h,12h] Will follow s The two are positively correlated. s Does not affect η SOFC But it cannot be increased indefinitely, which depends on the limited hydrogen reserve n. According to γ=I j t k , t s The value of is negatively correlated with the current. Under the premise that n is finite, I s The larger the value is within its operating domain, the longer the running time t of the mode s The shorter it is. s By I SOFC Indirect and η SOFC Therefore, t s And the operating current I in each mode s These are the key decision variables in the solution process.

[0169] 3) Consider the system feed and power operating point P x(i) The relationship between the two is replaced by the fuel supply amount FUEL (unit SLPM) x(i) .

[0170] I s There is a constant linear correlation between γ and FUEL, so γ can be equivalent to FUEL*t k To solve the f corresponding to the hydrogen storage in all working conditions + time domain G2P The optimal compromise solution.

[0171] According to I s The range determines the threshold of FUEL to be [20,70].

[0172] 4) Because it is necessary to solve the optimization problem corresponding to different hydrogen consumption amounts f G2P The optimal solution of ; and n is only related to FUEL and time t, so by fixing t, FUEL and t in the optimization domain are discretized according to a certain accuracy to obtain several sub-optimization problems; solve each sub-optimization problem to meet the constraints of the solid oxide battery system and make f G2P Optimal εair and I s . And according to the correlation between n and γ n∝γ(I s t) It can be obtained that as long as γ is the same, the amount of hydrogen consumed in the discharge process is consistent with the amount of hydrogen produced in the electrolysis process.

[0173] Specifically, by discretizing FUEL and t with the precision of 5 and 0.5 respectively, a total of 231 groups of sub-optimization problems are obtained. The Pareto front solutions generated by multi-objective optimization are calculated according to the TOPSIS scheme W i Take the optimal compromise solution, the corresponding decision variable is ε air and I s , while I s The value depends on FUEL, but by setting the fuel utilization rate U to 0.6~0.9 f To limit I s The range of this is also related to the solution Figure 6 difference.

[0174] In this embodiment, preferably, weight W4 is used because for maximizing η RT For example, by sacrificing 0.xx% efficiency to maximize the net power output W during the discharge process SOFC,net .

[0175] The obtained discrete optimal compromise solution is plotted in the form of interpolation to obtain the corresponding and η SOFC ,like Figure 8 As shown. Figure 8 (a): As FUEL and time increase, η SOFC It has nothing to do with time, but its maximum value appears at the minimum point of FUEL ( Figure 8 (b)). In fact, when FUEL is a constant, I s It will maximize its own value within the corresponding interval to ensure The highest. For γ, t increases by I s It will inevitably decrease. On the surface there exists a constant value γ i There are multiple sets of optimal compromise solutions.

[0176] According to Figure 8 Analysis: There is no unique correspondence between γ and γ, which is determined by the factor γ (γ=I s t) to find all the optimal compromise solutions in the interval corresponding to γ like Figure 9 As shown. Obviously, γ and There is a strong linear relationship between them. According to the γ corresponding to each discrete value in the figure iYou can search for all potential I s -t solution. As long as γ is the same, the corresponding intermediate variable n (the amount of hydrogen produced or consumed) is equal, and then search for the value of γ corresponding to the discharge process. During the electrolysis process The ratio of the two is the optimal η RT The value of each mode The maximum value of corresponds to the optimal decision variable solution, and according to γ, we can get η RT Optimal operating current in each mode I s and running time t.

[0177] During the electrolysis process Figure 9 In the effective range of γ, by taking different γ values ​​in the nonlinear equation I s t=γ i Under the constraints of P2G . And γ i Corresponding I s and t will have multiple solutions; the solver still uses the multi-objective differential evolution strategy, because The solution set is not the Pareto frontier, so there is no TOPSIS multi-attribute decision-making problem; and by replacing n links with γ and The starting state energy allows γ i,SOE and γ i,SOFC There is an error of 1‰ between them. To reduce the computational complexity, only Figure 9 The value of γ is an integer multiple of 100. Since the effective stack current range during the electrolysis process is between [20,60], for a given I s If the value of γ is not within the range of t, then the value of γ cannot reach 800. Therefore, γ is set to [100,700]. Taking γ = 100 as an example, FUEL can be taken within the entire interval ([20,60]), but as γ increases, the FUEL interval shortens. At the same time, it can be taken to satisfy the constraint I s t=γ i The number of optimal solutions also decreases.

[0178] Figure 10 It describes the optimal solution for different γ in the electrolysis process and the corresponding I s According to the given γ value, the s Solve for the corresponding t. Each I s Corresponding They are all unique minimum solutions obtained by the multi-objective differential evolution algorithm. The number of solutions obtained by optimization is the same as that of the nonlinear equality constraint I s t=γ i When the algorithm is I s The search results are related to the solution interval. Due to the additional constraints (Is t=γ i ) exists, and I cannot be restricted here any more. s and the solution accuracy of t.

[0179] First, according to Figure 8 The results can be obtained for each γ i During the electrolysis process Established by γ and Figure 7 middle The corresponding contact, and The ratio is the optimal reversible efficiency η RT .

[0180] Next, we will continue to improve the accuracy of γ, and then use the same solution strategy to solve multiple groups of γ corresponding value.

[0181] Finally, by interpolation, we plot the range of η within the range of the intermediate variable n (corresponding to γ). RT Optimal continuous I s Trajectory (longitudinal γ corresponds to the only process of discharge and electrolysis η RT The optimal current solution) is given by Calculate η RT Get the final continuous η RT Curves, such as Figure 11 shown.

[0182] according to Figure 11 It can be seen that when the amount of hydrogen converted increases (the larger γ is), the overall optimal η RT It shows a downward trend, which can be attributed to the fact that in the energy conversion cycle u, I s The increase will lead to increased energy loss, mainly including thermal energy diffusion and internal energy loss, γ i Within the interval η RT Trend and I s The corresponding relationship between η and η can better illustrate this point. Therefore, by reducing the energy loss caused by heat diffusion and conversion into internal energy, the global energy conversion performance of the solid oxide battery system can be effectively improved, that is, η RT This also indirectly proves that the thermal management method for secondary utilization of fuel cell tail gas has an important effect on η RT In addition, the reference γ value can be used to establish the reversible efficiency η RT The optimal discharge process and electrolysis process are the operating current trajectories, at U f and X fuel Take the lowest ε when it is a fixed value air When, according to I sThe operation domain constructed with t can guide the solid oxide battery system to complete a complete cycle It can represent either a P2G2P process or a G2P2G process) and is the mode switching schedule with the highest global energy conversion efficiency.

[0183] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for quantifying and optimizing the reversible efficiency of a solid oxide battery system, characterized in that: include: A continuous and non-repeating complete cycle of any energy conversion direction of the solid oxide battery system is divided into two stages in chronological order; The inverse of the ratio of the effective conversion energies corresponding to the two stages is defined as a generalized representation of reversible efficiency; Introducing an intermediate medium factor associated with hydrogen production during the electrolysis process, transforming the generalized representation of reversible efficiency, and determining a generalized reversible efficiency model based on operating parameters; Deconstructing the reversible efficiency model, establishing phased generalized reversible efficiency models for the electricity-gas-electricity stage and the gas-electricity-gas stage, and determining a solution representation for the generalized reversible efficiency; Based on the generalized reversible efficiency solution representation, coupled with the solid oxide battery system operation constraints, a multi-objective optimization model is constructed with the goal of maximizing the generalized reversible efficiency and maximizing the efficiency of the solid oxide battery system during each mode; Solving the multi-objective optimization model to generate an optimal solution as a control strategy for the solid oxide battery system; The control strategy is used to optimize the energy efficiency of the solid oxide battery system during a complete charge and discharge cycle.

2. The method for quantifying and optimizing the reversible efficiency of a solid oxide battery system according to claim 1, characterized in that: The definition of the inverse ratio of the effective conversion energy corresponding to the two stages is used as a generalized representation of the reversible efficiency: in, Represents a continuous and non-repeating complete cycle in any energy conversion direction of the solid oxide battery system; When the electrolysis process is represented, Indicates the discharge process; Indicates the discharge process, Represents the electrolysis process; for any operating point in the system operating space The corresponding effective conversion can be expressed as The corresponding effective conversion can be expressed as The effective conversion energy represents the energy conversion cycle The total energy of the initial state of matter before and after and the total energy of the final state.

3. The method for quantifying and optimizing the reversible efficiency of a solid oxide battery system according to claim 1, wherein: The intermediate medium factor associated with the hydrogen production during the electrolysis process: γ=I j *t k Where γ represents the intermediate medium factor associated with the hydrogen production during the electrolysis process, I j represents the stack current at any point j in the system operating space, t k represents the system running time at any point k in the system operation space.

4. The method for quantifying and optimizing the reversible efficiency of a solid oxide battery system according to claim 3, wherein: The generalized reversible efficiency model based on operating parameters: in, Indicates the total power consumption of electrolysis, represents the net discharge power; x(I) represents the system operating point; is a function of the operating point x(i) of the solid oxide battery system, and the operating parameters determine The operating parameters include: stack current I s 、Excess air ratio ε air , fuel utilization rate U f And the auxiliary gas concentration X in the fuel circuit fuel .

5. A method for quantifying and optimizing the reversible efficiency of a solid oxide battery system according to claim 4, characterized in that: The generalized reversible efficiency solution is characterized by: in, Represents the effective conversion energy of the discharge process, represents the effective conversion energy of the electrolysis process, t s represents x(i) SOFC represents any operating point in the operating space of the discharge process system, x(i) SOE represents any operating point in the operating space of the electrolysis process system, t s Indicates the duration of the discharge process or electrolysis process; γ i,SOFC Indicates the intermediate dielectric factor during the discharge process, γ i,SOE Represents the intermediate medium factor in the electrolysis process.

6. A method for quantifying and optimizing the reversible efficiency of a solid oxide battery system according to claim 5, characterized in that: The solid oxide battery system operating constraints include: Determine the source-load power balance constraint based on the equivalent voltage; Preset the maximum operating temperature limit of the fuel cell stack; Preset the maximum temperature gradient upper limit of the fuel cell stack; Limit the duration of the discharge and electrolysis processes based on the actual energy conversion scenario; Preset heater limit temperature during electrolysis process; Preset the value range of the current operating parameter and the gas supply volume operating parameter.

7. A method for quantifying and optimizing the reversible efficiency of a solid oxide battery system according to claim 6, characterized in that: The multi-objective optimization model includes: stγ i,SOFC =c i,SOE U stack (x(i))=∑U BOP (x(i)) Max.T≤T max t s ≤12h T pre =T set [I s,min ,I s,max ]≤I cell,max Among them, Max.T represents the maximum operating temperature of the stack; represents the upper limit of the maximum operating temperature of the stack; Max.T grad Indicates the maximum temperature gradient of the stack in the gas flow direction; Indicates the upper limit of the maximum temperature gradient of the stack in the gas flow direction; T pre Indicates the heater temperature during the electrolysis process; T set Indicates the set value of the heater temperature during the electrolysis process; t s Indicates the duration of the discharge process or electrolysis process; I cell,max It represents the maximum current density that can be achieved by the solid oxide battery system in the system environment; represents the set of operation variables, Γ is The specific boundary conditions corresponding to each operation quantity.

8. A method for quantifying and optimizing the reversible efficiency of a solid oxide battery system according to claim 7, characterized in that: The optimization model is solved by using an improved multi-objective differential evolution algorithm and an approximate ideal solution sorting method, including: The Pareto frontier solution is obtained based on the improved multi-objective differential evolution algorithm; The optimal solution of the optimization model is obtained based on the Pareto front by an approximate ideal solution ranking method.

9. The method for quantifying and optimizing the reversible efficiency of a solid oxide battery system according to claim 7, wherein: The improvement of the multi-objective differential evolution algorithm includes: Introduce an adaptive strategy to adjust the differential weight F and crossover probability CR; Among them, F x Indicates the lower limit of differential weight application, F s represents the upper limit of the differential weight; g and G represent the current evolutionary generation and the total evolutionary generation respectively; Introduce a Gaussian mutation link to improve population diversity: Among them, w g+1 Indicates Gaussian variation individual; normrnd indicates taking u g+1 is the mean, ε is the standard deviation, and the random numbers generated conform to the normal distribution; lb and ub represent the lower limit and upper limit of the decision variable respectively; L represents the mutation rate control factor.

10. The method for quantifying and optimizing the reversible efficiency of a solid oxide battery system according to claim 1, characterized in that: The control strategy includes: The stack current and discharge process running time during the discharge process; The stack current and running time of the electrolysis process.

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