A transfer function construction method for a supercritical carbon dioxide direct-cooling reactor system

Abstract

The application provides a transfer function construction method for a supercritical carbon dioxide direct-cooling reactor system. The method firstly extracts nonlinear models of components of the system, and prepares input and output parameter data required for correction; then linearizes the nonlinear models of the reactor core, turbine machinery and heat exchanger components by using a Taylor expansion method, and converts the linearized models into state space equation forms; corrects state matrices, output matrices and input matrices; and finally assembles the corrected three matrices into a new state space matrix, and converts the new state space matrix into a transfer function form. The application can accurately and effectively construct transfer function models of the supercritical carbon dioxide direct-cooling reactor system under different configurations, and can be used for stability analysis, controller design and operation optimization research of the system, and has the advantages of high calculation efficiency, good model precision, strong physical interpretability and the like.

Description

Technical Field

[0001] This invention relates to the field of nuclear reactor control and thermal-hydraulic system modeling technology, and in particular to a method for constructing transfer functions for supercritical carbon dioxide direct-cooled reactor systems. Background Technology

[0002] Supercritical carbon dioxide (S-CO2) direct-cooled reactors are one of the important development directions of fourth-generation nuclear energy systems. Unlike traditional pressurized water reactors that use water as a coolant, S-CO2 direct-cooled reactors utilize supercritical carbon dioxide as the cooling medium, flowing directly through the reactor core to remove fission heat. This technology has significant advantages such as high cycle efficiency, compact system structure, low thermal inertia, and excellent passive safety characteristics, showing broad application prospects in space nuclear power, land-based small modular reactors, and ship nuclear power. However, the physics of S-CO2 direct-cooled reactors... The thermal-engineering coupling characteristics are extremely complex. On the one hand, the physical properties of supercritical fluids change drastically with temperature and pressure near the quasi-critical point, leading to a strongly nonlinear thermal-engineering response in the reactor core coolant. On the other hand, rapid changes in coolant density introduce significant reactive feedback, which is coupled with fuel Doppler feedback and moderator temperature feedback. This strongly nonlinear, multivariable, and strongly coupled dynamic characteristic poses a severe challenge to the design of reactor control systems. Therefore, research on methods for constructing transfer functions for supercritical carbon dioxide direct-cooled reactor systems is of great significance for their safe and stable operation.

[0003] The transfer function method is a core tool in classical control theory for analyzing and designing linear feedback control systems. For nonlinear systems, linearization is typically performed near the steady-state operating point to obtain the transfer function matrix, which is then used to evaluate system stability and design regulators or controllers. However, existing methods for constructing transfer functions for S-CO2 direct-cooled reactors have the following main shortcomings: First, most studies employ perturbation experiments or numerical step response identification. These methods rely on high-precision transient simulations, which are computationally intensive and difficult to obtain analytical transfer functions, making it inconvenient for systematic tuning of control parameters. Second, existing linearization methods often simplify or neglect the nonlinear derivatives of coolant properties, reactive feedback, and hydraulic factors. The coupling relationship of thermodynamic processes results in low accuracy of the constructed transfer function model over a wide operating range, making it unable to accurately describe the dynamic behavior near the quasi-critical region.

[0004] Therefore, there is an urgent need for a method that can systematically and accurately construct the transfer function of S-CO2 direct-cooled reactors, so as to provide a reliable linearized model basis for subsequent controller design, stability analysis and operation optimization. Summary of the Invention

[0005] The purpose of this invention is to address the problems in existing technologies by proposing a method for constructing transfer functions for supercritical carbon dioxide direct-cooled reactor systems. This method, through modular linearization and coupling matrix assembly, can efficiently and accurately obtain the transfer function model from control input to controlled output, directly serving control system design and stability analysis.

[0006] This invention is achieved through the following technical solution: This invention proposes a method for constructing the transfer function of a supercritical carbon dioxide direct-cooled reactor system, the method comprising: S1. Extract the nonlinear models of each component of the initial system and prepare the input and output parameter data required for correction; S2. Expand the nonlinear models of each component of the initial system using the Taylor method and discard higher-order derivatives to obtain the corresponding linearized models; S3. Convert all the linearized models obtained in S2 into the form of space state equations, including the space state matrix. A Input matrix B Output matrix C ; S4. The state matrix obtained from S3 A The order is reduced using diagonal prescaling transform, minimum realization method and singular perturbation theory; S5. Use the input and output parameter data from S1 to correct the output matrix using the multi-output weighted least squares method. C ; S6. Use the input and output parameter data of S1 to correct the input matrix using a nonlinear least squares method. B ; S7. The corrected matrix obtained from S4 to S6 A , B , C A new spatial state matrix is ​​formed; S8. Convert the spatial state matrix of S7 into transfer function form.

[0007] Furthermore, the initial system components include a core component, a turbine component, a compressor component, and a heat exchanger component; step S2 specifically includes: S21. Expand the nonlinear model of the core components in S1 using the Taylor method and discard higher-order derivatives to obtain the linearized model of the core theory. S22. Expand the nonlinear model of the turbine and compressor components in S1 using the Taylor method and discard the higher-order derivatives to obtain the linearized model of the turbomachinery theory. S23. Expand the nonlinear model of the heat exchanger components in S1 using the Taylor method and discard the higher-order derivatives to obtain the linearized model of the heat exchanger theory.

[0008] Furthermore, the spatial state equation is specifically in the following form:

[0009]

[0010] Where x(t) is the state variable, u(t) is the control variable, y(t) is the controlled variable, and D is the direct transfer matrix.

[0011] Furthermore, the linearized model of the reactor core theory is as follows:

[0012] in n The relative neutron density, Introducing reactivity to the outside, β For the total delayed neutron share, T f,fixed To reference the steady-state average fuel temperature, λ i For the first i The decay constant of the slow-emitting neutron precursor nucleus, C i For the first i Concentration of slow-emitting neutron precursor nuclei.

[0013] Furthermore, the theoretical linearized model of the compressor is as follows:

[0014] The theoretical linearized model of a gas turbine is as follows:

[0015] in, For nodes i Its own specific enthalpy, Let k be the specific enthalpy of node k itself. For inflow node k mass flow rate Q Power.

[0016] Furthermore, the theoretical linearized model for the hot side of the heat exchanger is as follows:

[0017]

[0018] The theoretical linearized model for the cold side of the heat exchanger is as follows:

[0019]

[0020] in, Let k be the specific enthalpy of node k itself. For nodes i Its own specific enthalpy, Let A be the heat flow transferred from the heat-side to the wall, k be the thermal conductivity of the wall material, and A be the heat transfer area. The convective heat transfer coefficient of the hot-side fluid is... For wall thickness, The heat flow transferred from the wall to the cold-side fluid. The convective heat transfer coefficient of the cold-side fluid is... This refers to the temperature of the fluid on the cold side.

[0021] Furthermore, the method for modifying the state matrix A is as follows: numerical stabilization is performed on the linear state-space model, and a robust order reduction strategy is used to extract a low-dimensional model that can characterize the essential dynamics of the system; the specific process includes three steps: diagonal prescaling transformation, minimum realization, and balanced truncation while maintaining DC gain.

[0022] Further, revision C and B The method is as follows: while maintaining the matrix A Under the premise of keeping the parameters unchanged, a hierarchical parameter reconstruction method was constructed to sequentially complete the output matrix. C Reconstruction and input matrix B Optimization; in the first layer of reconstruction, the output matrix C Identification is achieved by fitting a mapping from internal states to external outputs; the system matrix of the reduced-order model. A The modal and inertial characteristics of the original system are preserved, and the state trajectory can be obtained under standard input perturbation. In the second-level reconstruction, a nonlinear least squares framework is used to... B The matrix is ​​optimized through channel-by-channel iteration to simultaneously correct the input excitation direction, dynamic gain magnitude, and steady-state propagation deviation.

[0023] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method for constructing a transfer function for a supercritical carbon dioxide direct-cooled reactor system.

[0024] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the method for constructing a transfer function for a supercritical carbon dioxide direct-cooled reactor system.

[0025] The beneficial effects of this invention are: This invention provides a method for constructing the transfer function of a supercritical carbon dioxide direct-cooled reactor system. Based on modular Taylor expansion linearization and combined with state-space modeling and order reduction theory, it can systematically and efficiently obtain the analytical transfer function model from the control input to the controlled output.

[0026] Furthermore, the nonlinear models of the components (core, turbomachinery, heat exchanger) are linearized using Taylor expansion and then uniformly transformed into state-space equations. This fully preserves the coupling characteristics of modules such as neutron dynamics, fuel heat conduction, coolant flow heat transfer, and rotating machinery, avoiding the accuracy loss caused by simplifying or ignoring key nonlinear derivatives. It is especially suitable for strongly nonlinear operating conditions in the quasi-critical region.

[0027] Furthermore, the initial state matrix is ​​subjected to diagonal prescaling transformation, minimum realization analysis, and singular perturbation order reduction in sequence. This effectively reduces the model order while maintaining the dominant mode and DC gain of the system. This not only reduces the computational burden of subsequent parameter identification but also ensures the numerical stability and physical consistency of the reduced-order model.

[0028] Furthermore, a hierarchical parameter reconstruction strategy was constructed: first, the output matrix C was corrected using the multi-output weighted least squares method to map the reduced state trajectory to the true observations to the greatest extent; then, the input matrix B was corrected using the nonlinear least squares method, and a steady-state gain (DC gain) consistency constraint was introduced into the objective function to ensure that the model has both high-precision dynamic response and accurate steady-state transfer relationship.

[0029] Furthermore, the final transfer function model has a clear input-output correspondence. For example, the transfer function matrices of bypass valve opening, regulating valve opening, external reactivity, and cooling water flow rate on compressor inlet temperature, core outlet temperature, shaft speed, and surge margin can be directly used for frequency domain stability analysis, controller parameter tuning, and operation optimization research, significantly improving engineering practicality.

[0030] In summary, this invention solves the problem in the prior art of simultaneously achieving analytical transfer function acquisition, wide operating condition accuracy, and computational efficiency, providing a reliable linearized model basis for the control design and dynamic analysis of supercritical carbon dioxide direct-cooled reactor systems. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0032] Figure 1 This is a flowchart of a method for constructing the transfer function of a supercritical carbon dioxide direct-cooled reactor system.

[0033] Figure 2 This is a schematic diagram of the structure of the present invention, taking the SCFR system as an example.

[0034] Figure 3 This is a schematic diagram of the node division of the reactor core.

[0035] Figure 4 This is a schematic diagram of the system's input and output parameters.

[0036] Figure 5 This is a schematic diagram of the overall system transfer function. Detailed Implementation

[0037] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] This invention provides a method for constructing the transfer function of a supercritical carbon dioxide direct-cooled reactor system. First, a theoretical linearized model of the entire system is obtained using Taylor expansion, and this model is transformed into a spatial state equation form. Then, real data of the main input and output parameters are obtained. Next, the state matrix A is reduced in order using diagonal prescaling, the minimum realization method, and singular perturbation theory. Then, the output matrix C is corrected using real data and a multi-output weighted least squares method. Then, the input matrix B is corrected using real data and a nonlinear least squares method. Finally, the three corrected matrices are combined to form a new spatial state matrix, which is then converted into a transfer function. Based on this solution method, a linearized model of each component can be obtained, thus forming a method for constructing the transfer function of a supercritical carbon dioxide direct-cooled reactor system. This invention can accurately and effectively construct transfer function models of supercritical carbon dioxide direct-cooled reactor systems under different configurations, and can be used for stability analysis, controller design, and operational optimization research of the system.

[0039] Specifically, in combination Figures 1-5 This invention proposes a method for constructing the transfer function of a supercritical carbon dioxide direct-cooled reactor system, comprising the following steps: S1. Extract the nonlinear models of each component of the initial system and prepare the input and output parameter data required for correction; The point-pile nonlinearization model used for the core components is as follows:

[0040]

[0041]

[0042]

[0043] in, n The relative neutron density, For reactivity, β To delay the issuance of neutron quotas, λ i For the first i The decay constant of the precursor nucleus. t For time, C i For the first i Concentration of slow-emission neutron precursor nuclei. α c Coolant density coefficient, α f Fuel temperature coefficient, The density of carbon dioxide, T fuel Core fuel temperature.

[0044] The formula used for heat-conducting components is:

[0045]

[0046]

[0047] in, C p,i For specific heat capacity, T i For the first i Temperature of each node κ Thermal conductivity, α is the convective heat transfer coefficient.

[0048] The formula for using hydraulic components is:

[0049]

[0050]

[0051] in, m For quality, h For enthalpy, For quality flow, A For area, P For pressure.Q Power.

[0052] The formulas for using gas turbine components are as follows:

[0053] The formulas for compressor components are as follows:

[0054] The formulas for the heat exchanger components are as follows:

[0055]

[0056]

[0057] S2. Expand the nonlinear model of the core components in S1 using the Taylor method and discard higher-order derivatives to obtain the linearized model of the core theory. Taylor's method is specifically defined as follows: δx is defined as:

[0058] The nonlinear mathematical model of the controlled object can be expressed as:

[0059] At time t, F [ x ( t ), u ( t )]exist( x 0, u The Taylor series expansion at (0) can be expressed as:

[0060] At the selected steady-state point, i.e. ( x 0, u At position 0):

[0061] exist t At that moment, combining the above two equations and ignoring higher-order terms, we get:

[0062] Therefore, in t At any given time, the nonlinear mathematical model can be represented as a state-space mode:

[0063] in , .

[0064] In this method, the state variable x(t), control variable u(t), and controlled variable y(t) are selected as follows:

[0065] The complete space state equation is in the form of:

[0066]

[0067] Therefore, the theoretical linearized model of the reactor core obtained through Taylor's method is as follows:

[0068] in n The relative neutron density, Introducing reactivity to the outside, β For the total delayed neutron share, T f,fixed To reference the steady-state average fuel temperature, λ i For the first i The decay constant of the slow-emitting neutron precursor nucleus, C i For the first i Concentration of slow-emitting neutron precursor nuclei.

[0069]

[0070]

[0071]

[0072]

[0073] in The fuel center node temperature, For the gap node temperature, This refers to the node temperature on the outer surface of the casing. The values ​​represent volumetric heat capacity. Subscripts 1, 6, and 9 correspond to nodes, including fuel center nodes, gap nodes, and outer cladding surface nodes. For normalized line power density, The sum of the squares of the radii of the first five fuel nodes. k is the thermal conductivity.

[0074]

[0075] The above formula represents the specific enthalpy corresponding to a reactor core without heat exchange, where H It is the enthalpy value. For nodes i The density of the fluid at that location, For nodes i The volume of the control volume.

[0076]

[0077] The above formula represents the specific enthalpy corresponding to heat transfer in the reactor core, where For nodes i Its own specific enthalpy, The external fluid temperature The temperature of the fluid at the current node.

[0078]

[0079] The pressures in both the heat-exchange and non-heat-exchange sections of the reactor core satisfy the above equation, where... For inflow node k mass flow rate outflow node i mass flow rate For nodes i The volume of the control volume.

[0080] S3. Expand the nonlinear model of the turbine and compressor components in S1 using the Taylor method and discard the higher-order derivatives to obtain the linearized model of the turbomachinery theory. The theoretical linearized model of the compressor is as follows:

[0081] The theoretical linearized model of a gas turbine is as follows:

[0082] in, For nodes i Its own specific enthalpy, Let k be the specific enthalpy of node k itself. For inflow node k mass flow rate Q Power.

[0083]

[0084] The pressure parameters of both the gas turbine and the compressor are expressed by the above formula, where outflow node i mass flow rate For density.

[0085] S4. Expand the nonlinear model of the heat exchanger components in S1 using the Taylor method and discard the higher-order derivatives to obtain the theoretical linearized model of the heat exchanger. The theoretical linearized model for the hot side of the heat exchanger is as follows:

[0086]

[0087] The theoretical linearized model for the cold side of the heat exchanger is as follows:

[0088]

[0089] in, The specific enthalpy of the upstream node. The specific enthalpy of the current control volume. Let A be the heat flow transferred from the heat-side to the wall, k be the thermal conductivity of the wall material, and A be the heat transfer area. The convective heat transfer coefficient of the hot-side fluid is denoted as . For wall thickness, The heat flow transferred from the wall to the cold-side fluid. The convective heat transfer coefficient of the cold-side fluid is... This refers to the temperature of the fluid on the cold side.

[0090] All linearized models obtained from S5, S2 to S4 are converted into the form of space state equations, including the space state matrix. A Input matrix B Output matrix C ; S6. The state matrix obtained from S5 A The order is reduced using diagonal prescaling transform, minimum realization method and singular perturbation theory; The linear state-space model is numerically stabilized and coupled with a robust order reduction strategy to extract a low-dimensional model that characterizes the system's essential dynamics. The specific process includes three steps: pre-scaling, minimum realization, and balanced truncation while preserving DC gain. First, a diagonal pre-scaling transformation is performed. Let the state transition be:

[0091] in, For diagonal scaling matrices:

[0092] The transformed system can then be written as:

[0093]

[0094] in:

[0095]

[0096]

[0097] After pre-scaling, a minimum realization analysis is further performed on the linearized model. Generally, the linearization process of high-dimensional partial linearization introduces some redundant internal states, which do not affect the input-output response. These generally originate from uncontrollable / observable subspaces and non-minimum realization pole-zero cancellations. To eliminate redundant states, the controllability matrix and observability matrix of the system are constructed based on state-space geometry methods, and are expressed as follows:

[0098]

[0099] If the following conditions are met:

[0100]

[0101] If the system satisfies the requirements of controllability and observability, then a minimal realization can be constructed. After minimal realization processing, a more numerically stable full-order intermediate model is obtained. Based on this, the order reduction method is further applied using a balanced truncation approach. For an asymptotically stable system, its controllable Gram matrix... W c With observable Gram matrix W o They respectively satisfy the following continuous Lyapunov equations:

[0102]

[0103] By employing appropriate coordinate transformations, the system can satisfy the following conditions in the new state coordinates:

[0104] in:

[0105] And satisfy:

[0106] Among them, diagonal terms Known as Hankel singular values, they reflect the combined contribution of each state to both controllability and observability. For the reduced-order model obtained by equilibrium truncation... The classical theory can give the following: ∞ Upper bound of error:

[0107] This result indicates that the order reduction error is mainly determined by the sum of the Hankel singular values ​​corresponding to the truncated states, thus providing a quantifiable theoretical basis for selecting the order reduction order. A DC gain matching strategy is employed during the order reduction process. Specifically, the balanced system is divided into retained slow states. x 1 and fast states to be eliminated x 2 can be written as:

[0108]

[0109] For the fast variables to be eliminated x 2. Instead of directly setting it to zero, we assume it can instantaneously reach a local steady state, and let:

[0110] Then we have:

[0111] Substituting it back into the original equation, we obtain the reduced-order system:

[0112]

[0113] in:

[0114]

[0115]

[0116]

[0117] The above processing can essentially be reduced to a singular perturbation approximation of the equilibrium system. Based on the numerical stabilization and robust order reduction methods described above, a reduced-order state-space model that combines numerical stability, physical consistency, and computational efficiency is finally obtained, which serves as the basis for subsequent gray-box parameter identification.

[0118] S7. Use the input and output parameter data from S1 to correct the output matrix using the multi-output weighted least squares method. C ; In preserving the matrix A Under the premise of keeping the parameters unchanged, a hierarchical parameter reconstruction method was constructed to sequentially complete the output matrix. C Reconstruction and input matrix B Optimization. In the first layer of reconstruction, the output matrix... C Identification is achieved by fitting a mapping from internal states to external outputs. The system matrix of the reduced-order model. AThe main modal and inertial characteristics of the original system are preserved, and the state trajectory can be obtained under standard input perturbation. Let the state at discrete time be... The corresponding reference output is Then the output equation can be written as:

[0119] When the matrix is ​​directly passed D When the output of slow variables of the system has a weak impact, the output matrix C The determination of can be mainly transformed into a multi-output weighted least squares problem, that is:

[0120] Where N is the total number of sampling points; It is the weighting matrix at time k. The objective function minimizes the weighted residual between the model output and the black-box reference output, so that the reduced state trajectory can be mapped to the real physical observations to the greatest extent.

[0121] To improve the model's response consistency during critical transient phases, a time-domain weighting mechanism is introduced. During model order reduction, different weights are assigned to errors according to time intervals, allowing the algorithm to prioritize response accuracy within a specified time period, while allowing for a moderate sacrifice in accuracy during non-critical periods. By assigning higher weights to key dynamic processes, the model's ability to fit peaks, inflection points, and rapidly changing phases is enhanced. This approach improves the gray-box model's reconstruction of nonlinear prototype peak responses and rapid transition processes.

[0122] S8. Use the input and output parameter data of S1 to correct the input matrix using a nonlinear least squares method. B ; In completing the matrix C After reconstruction, the mapping relationship between the system's internal state and external observations has been basically established. In the second-level reconstruction, a nonlinear least squares framework is used to... B The matrix is ​​iteratively optimized channel by channel to simultaneously correct the input excitation direction, dynamic gain magnitude, and steady-state propagation deviation. Let the optimized input matrix be... B The reference output trajectory is The current model output is based on the parameters. B The model under action at the first k The output at each sampling time is denoted as To simultaneously ensure the model's fitting accuracy to the dynamic response process and its ability to preserve the steady-state input-output relationship, the following comprehensive objective function is constructed, consisting of a time-domain response error term and a steady-state gain constraint term:

[0123] in, These are the steady-state constraint weighting coefficients; This represents the steady-state gain matrix of the current linear model at zero frequency. The target static gain matrix extracted from nonlinear prototype or steady-state experimental data; F This represents the Frobenius norm.

[0124] For a continuous-time state-space model, its transfer function matrix is:

[0125] Ignoring directly transitive terms, at zero frequency it can be approximated as:

[0126] Therefore, the matrix B Even small deviations can affect not only the system's transient response but also directly impact the steady-state gain matrix. By introducing a DC gain consistency term into the optimization objective and assigning it a significant weight, the parameter search process prioritizes the consistency of the steady-state input-output relationship, and then further compresses the dynamic residuals based on this.

[0127] S9. The corrected matrix obtained from S6 to S8 A , B , C A new spatial state matrix is ​​formed; S10. Convert the spatial state matrix of S9 into transfer function form. The transfer function conversion method used is as follows: In a fixed reduced-order system matrix A Then, first fit the output matrix. C Match the target observations and then correct the input matrix. B To reflect the relationship between actual excitation and steady-state transmission, a linear gray-box model that highly matches the nonlinear prototype was ultimately constructed. This model contains four inputs and four outputs. The four inputs are the bypass valve opening, the regulating valve opening, the precooler cooling water flow rate, and external reactivity; the four outputs are the compressor inlet temperature, the core outlet temperature, the shaft speed, and the compressor surge margin, with goodness-of-fit values ​​of 84.27%, 97.14%, 97.50%, and 93.70%, respectively.

[0128] The transfer function model for the four-input four-output system under consideration is shown in the table below. G The transfer function is represented by the following equation, which shows the transfer function at the steady-state point under full load.

[0129]

[0130]

[0131]

[0132] This invention proposes a method for constructing the transfer function of a supercritical carbon dioxide direct-cooled reactor system. The method first extracts the nonlinear models of each component of the system and prepares the input and output parameter data required for correction. Then, Taylor expansion is used to linearize the nonlinear models of the core, turbomachinery, and heat exchanger components, transforming them into state-space equations. Next, diagonal prescaling transformation, minimum realization analysis, and singular perturbation reduction are sequentially applied to the state matrix to obtain a reduced-order state-space model. Then, using real data, the output matrix is ​​corrected using multi-output weighted least squares, and the input matrix is ​​corrected using nonlinear least squares. Finally, the three corrected matrices are combined to form a new state-space matrix, which is then converted into a transfer function. This invention can accurately and effectively construct transfer function models of supercritical carbon dioxide direct-cooled reactor systems under different configurations. It can be used for system stability analysis, controller design, and operational optimization research, and has advantages such as high computational efficiency, good model accuracy, and strong physical interpretability.

[0133] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method for constructing a transfer function for a supercritical carbon dioxide direct-cooled reactor system.

[0134] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the method for constructing a transfer function for a supercritical carbon dioxide direct-cooled reactor system.

[0135] The memory in this application embodiment can be volatile memory or non-volatile memory, or it can include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0136] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state disks (SSDs)).

[0137] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0138] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as execution by a hardware decoding processor, or as a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0139] The above provides a detailed description of a method for constructing the transfer function of a supercritical carbon dioxide direct-cooled reactor system proposed in this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for constructing the transfer function of a supercritical carbon dioxide direct-cooled reactor system, characterized in that, The method includes: S1. Extract the nonlinear models of each component of the initial system and prepare the input and output parameter data required for correction; S2. Expand the nonlinear models of each component of the initial system using the Taylor method and discard higher-order derivatives to obtain the corresponding linearized models; S3. Convert all the linearized models obtained in S2 into the form of space state equations, including the space state matrix. A Input matrix B Output matrix C ; S4. The state matrix obtained from S3 A The order is reduced using diagonal prescaling transform, minimum realization method and singular perturbation theory; S5. Use the input and output parameter data from S1 to correct the output matrix using the multi-output weighted least squares method. C ; S6. Use the input and output parameter data of S1 to correct the input matrix using a nonlinear least squares method. B ; S7. The corrected matrix obtained from S4 to S6 A , B , C A new spatial state matrix is ​​formed; S8. Convert the spatial state matrix of S7 into transfer function form.

2. The method according to claim 1, characterized in that, The initial system components include a reactor core, a gas turbine, a compressor, and a heat exchanger; step S2 specifically includes: S21. Expand the nonlinear model of the core components in S1 using the Taylor method and discard higher-order derivatives to obtain the linearized model of the core theory. S22. Expand the nonlinear model of the turbine and compressor components in S1 using the Taylor method and discard the higher-order derivatives to obtain the linearized model of the turbomachinery theory. S23. Expand the nonlinear model of the heat exchanger components in S1 using the Taylor method and discard the higher-order derivatives to obtain the linearized model of the heat exchanger theory.

3. The method according to claim 2, characterized in that, The spatial state equation is specifically in the following form: Where x(t) is the state variable, u(t) is the control variable, y(t) is the controlled variable, and D is the direct transfer matrix.

4. The method according to claim 3, characterized in that, The linearized model of the reactor core theory is as follows: in n The relative neutron density, Introducing reactivity to the outside, β For the total delayed neutron share, T f,fixed To reference the steady-state average fuel temperature, λ i For the first i The decay constant of the slow-emitting neutron precursor nucleus, C i For the first i Concentration of slow-emitting neutron precursor nuclei.

5. The method according to claim 4, characterized in that, The theoretical linearized model of the compressor is as follows: The theoretical linearized model of a gas turbine is as follows: in, For nodes i Its own specific enthalpy, Let k be the specific enthalpy of node k itself. For inflow node k mass flow rate Q Power.

6. The method according to claim 5, characterized in that, The theoretical linearized model for the hot side of the heat exchanger is as follows: The theoretical linearized model for the cold side of the heat exchanger is as follows: in, Let k be the specific enthalpy of node k itself. For nodes i Its own specific enthalpy, Let A be the heat flow transferred from the heat-side to the wall, k be the thermal conductivity of the wall material, and A be the heat transfer area. The convective heat transfer coefficient of the hot-side fluid is denoted as . For wall thickness, The heat flow transferred from the wall to the cold-side fluid. The convective heat transfer coefficient of the cold-side fluid is... This refers to the temperature of the fluid on the cold side.

7. The method according to claim 6, characterized in that, The method for correcting the state matrix A is as follows: numerical stabilization of the linear state-space model is performed, and a robust order reduction strategy is used to extract a low-dimensional model that can characterize the essential dynamics of the system. The specific process includes three steps: diagonal prescaling transformation, minimum implementation, and balanced truncation while maintaining DC gain.

8. The method according to claim 6, characterized in that, Correction C and B The method is as follows: while maintaining the matrix A Under the premise of keeping the parameters unchanged, a hierarchical parameter reconstruction method was constructed to sequentially complete the output matrix. C Reconstruction and input matrix B Optimization; in the first layer of reconstruction, the output matrix C Identification is achieved by fitting a mapping from internal states to external outputs; the system matrix of the reduced-order model. A The modal and inertial characteristics of the original system are preserved, and the state trajectory can be obtained under standard input perturbation. ; In the second-level reconstruction, a nonlinear least squares framework is used to... B The matrix is ​​optimized through channel-by-channel iteration to simultaneously correct the input excitation direction, dynamic gain magnitude, and steady-state propagation deviation.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-8.

10. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-8.

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