Generalized predictive control method for once-through steam generators in nuclear power plants

Abstract

This invention discloses a generalized predictive control method for a DC steam generator in a nuclear power plant. The method includes: inputting a planned operating condition change into a numerical simulation model of the DC steam generator to predict its dynamic behavior over a future period, obtaining simulation results, and then optimizing the control vector of the DC steam generator using a generalized predictive control algorithm; applying the optimized control vector to the DC steam generator to achieve iterative optimization of the control vector, ultimately safely, economically, and stably adjusting the DC steam generator's operating conditions according to the planned operating condition change. This invention can improve response speed, reduce adjustment time, and decrease pressure fluctuations in the DC steam generator, indirectly improving plant safety, extending the lifespan of heat transfer tubes, and enabling automatic control of the DC steam generator under low-power conditions. It quantitatively incorporates various demands during the operation of the DC steam generator into the control constraints.

Description

Technical Field

[0001] This invention relates to the field of DC steam generator control technology, and in particular to a generalized predictive control method for a DC steam generator in a nuclear power plant. Background Technology

[0002] Steam generators are crucial equipment for energy transfer between the primary and secondary loops of a reactor. Based on the flow pattern of the working fluid on the secondary side, they can be mainly divided into natural circulation steam generators and once-through (CTO) steam generators. The main characteristic of a CTO steam generator is that the working fluid in the secondary loop is driven by the feedwater pump head through the steam generator, where it is converted into slightly superheated steam after passing through the heat transfer surface, with a circulation ratio of 1. Compared to the vertical U-tube natural circulation steam generator widely used in pressurized water reactor nuclear power plants, CTO steam generators have significant advantages such as simple structure, compact size, good static performance, rapid power increase and decrease, and improved system thermal efficiency. However, the low circulation ratio of CTO steam generators results in poor heat storage and buffering capabilities, making the secondary side pressure highly susceptible to fluctuations. Excessive pressure can compromise system safety, while insufficient pressure cannot meet the steam demands of downstream units. Therefore, maintaining stable secondary side pressure is the primary objective of automatic control for CTO steam generators. This involves controlling the feedwater flow to stabilize the steam pressure at the secondary side outlet of the steam generator, ensuring the safe and stable operation of the CTO steam generator and providing high-quality steam that meets the operating requirements of steam-consuming equipment.

[0003] Automatic control of once-through (DC) steam generators generally suffers from the following problems: 1. Strong nonlinearity exists between the control and controlled variables. The dynamic characteristics of DC steam generators change complexly with different power levels, further increasing the difficulty of secondary-side pressure control and making it difficult to achieve excellent results using simple control models. 2. Simple control methods cannot meet the diverse needs and constraints of the unit during operation, such as fluctuations in outlet pressure, dry-point, and feedwater flow rate. 3. Traditional methods struggle to identify and avoid unstable two-phase flow conditions. These problems collectively make it difficult to determine the optimal control strategy for DC steam generators. Furthermore, due to the reduced two-phase section length under low-power conditions, steam pressure is highly sensitive to changes in feedwater flow rate. Currently, the control of DC steam generators combines automatic control under high-power conditions with manual control under low-power conditions. While this method meets the current operational requirements of DC steam generators, it is difficult to adapt to the future development trend of miniaturization and unmanned operation in nuclear power plants.

[0004] For the automatic control of DC steam generators, the classic PID method was initially adopted. This method has been widely verified in various fields, with a simple principle and strong applicability, and can achieve relatively reliable results for various systems. The literature "Zhang Yusheng, Guo Lifeng, Cai Meng. Research on PID control system of DC steam generator based on fuzzy adaptive parameter tuning [J]. Nuclear Power Engineering, 2008(04):93-96" uses the PID method as the basis to design a three-impulse fuzzy adaptive tuning PID control system for DC steam generators. The primary loop feedwater temperature, steam flow rate, and feedwater flow rate are fed into the control system through a proportional element, and the three parameters of the PID system are tuned in real time using the fuzzy method. Although this improves the control effect of the PID method to a certain extent, the problems of large pressure fluctuation and long settling time of the PID method still exist. In order to further improve the performance of DC steam generator control system, in recent years, neural network method and fuzzy method have gradually become the main development direction of DC steam generator automatic control. These two methods have been tentatively applied to improve the automatic control system of DC steam generators in many literatures. However, the lack of interpretability of neural network method and the poor stability of fuzzy control have always made it difficult for these two methods to be applied on a large scale. The concept of digital nuclear power provides a new solution to the control problem of DC steam generators. The controller relies on the digital nuclear power system to obtain a large amount of data support, and uses this as a basis to improve the effect of automatic control of DC steam generators. Summary of the Invention

[0005] The purpose of this invention is to provide a generalized predictive control method for a DC steam generator in a nuclear power plant. By employing techniques such as generalized predictive control, synchronous disturbance random approximation, and numerical calculation, this method achieves the effects of improving response speed, reducing settling time, minimizing pressure fluctuations in the DC steam generator, quantitatively considering the operating requirements of the DC steam generator, and automatically controlling the DC steam generator under low-power conditions.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A generalized predictive control method for a direct current steam generator in a nuclear power plant, the method comprising the following steps:

[0008] S1. Input the operating condition change plan into the simulation calculation model of the DC steam generator based on numerical calculation to predict the dynamic behavior of the DC steam generator in the future and obtain the simulation results.

[0009] S2. Based on simulation results, the control vector of the DC steam generator is optimized using a generalized predictive control algorithm;

[0010] S3 applies the optimized control vector to the DC steam generator and uses sensors to measure the DC steam generator in real time to obtain thermal-hydraulic data.

[0011] S4. Based on the thermal-hydraulic data, the simulation results in S1 are corrected. Steps S2-S4 are repeated to achieve iterative optimization of the control vector. Finally, the operating condition change plan is implemented in the DC steam generator.

[0012] Furthermore, in S1, the simulation calculation model of the DC steam generator includes an operational simulation model and a fast solution model for the DC steam generator;

[0013] The method for constructing the simulation model is as follows:

[0014] Based on the structural parameters and static and dynamic operating characteristics of the DC steam generator, a full-size one-dimensional thermodynamic analysis model of the DC steam generator is constructed as the operating simulation model of the DC steam generator.

[0015] The method for constructing the fast solution model is as follows:

[0016] Based on the actual situation of the DC steam generator, a one-dimensional thermodynamic analysis model of the DC steam generator is established by taking a single heat transfer tube according to the heat transfer tube arrangement as a fast solution model. The fast solution model is used to solve the secondary side pressure drop.

[0017] The fast solution model interacts with the running simulation model, and the primary side inlet and outlet flow rates and the secondary side inlet and outlet flow rates are amplified by the corresponding factors.

[0018] Furthermore, prior to step S1, the simulation model is trained offline to build a runtime database. The specific method is as follows:

[0019] Based on the operational requirements of the DC steam generator, a large number of calculation examples with different load change rates and different start-up and end conditions are set up and input into the operation simulation model and the fast solution model. The synchronous disturbance stochastic approximation method is used for offline training. Through the offline training process, simulation calculation and control vector solution are performed to obtain the operation data and corresponding control vectors under different load change rates and different start-up and end conditions.

[0020] Based on the load change rate, the operating data and its corresponding control vectors are divided into several groups. Within each group, the operating data and its corresponding control vectors are arranged and stored based on the initial operating condition and the target operating condition, thus constructing an operating database.

[0021] Further, in step S1, the operating condition change plan is input into the numerical calculation-based DC steam generator simulation model to predict the dynamic behavior of the DC steam generator over a future period, and the simulation results are obtained, specifically including:

[0022] Based on the load change plan, a simulation model is run to perform simulation calculations and obtain the expected load change rate and start and end conditions.

[0023] Based on the constructed operating database, the selection range of the control vector is first determined according to the expected load change rate, and then the required control vector is determined according to the expected start and end conditions. The feedwater flow rate in the control vector is fitted according to the steam flow rate change trend, while ensuring that the fitted curve is equal to the integral of the feedwater flow rate with respect to time. Finally, the fitted curve is used as the initial value of the control vector during online operation.

[0024] After obtaining the initial value of the control vector, the control vectors of both positive and negative disturbances are simultaneously input into the fast solution model to predict the dynamic behavior of the DC evaporator over a period of time and obtain simulation results.

[0025] Furthermore, in step S2, based on simulation results, a generalized predictive control algorithm is used to optimize the control vector of the DC steam generator, specifically including:

[0026] The simulation results are processed to obtain the gradient of the loss function under the current control vector, and the control vector is optimized based on this gradient. This process is repeated until the termination criterion is met. Then, the first term of the control vector is passed to the running simulation model and it advances to the next control step based on this inlet flow.

[0027] Furthermore, the process of processing the simulation results to obtain the gradient of the loss function under the current control vector, and optimizing the control vector based on this gradient, repeating this process until the termination criterion is met, specifically includes:

[0028] Under the operating scheme where the secondary steam pressure remains constant, the square of the difference between the steam pressure and the rated value per unit time is selected as the loss function, and its expression is:

[0029]

[0030] In the formula, t′ is the current time, t″ is the simulation time required for the fast solution model, p is the steam pressure, p0 is the rated steam pressure or target steam pressure, and θ is the current control vector;

[0031] The current control vector is judged based on the calculated loss function value. If the loss function value is within an acceptable range, the DC steam generator is determined to be in a stable state, and the current control vector is output. Otherwise, the current control vector is optimized, and this process is repeated until the termination criterion is met.

[0032] Furthermore, the optimization of the current control vector, repeated until the termination criterion is met, includes:

[0033] Based on the current control vector, the simulation model is run to update the parameters. The synchronous perturbation stochastic approximation method is used to generate perturbation vectors, including forward perturbation vectors and reverse perturbation vectors. Through gradient approximation, the control vector is optimized and iterated.

[0034] The iteration ends when the maximum number of iterations is reached and the loss function value corresponding to the current control vector is less than the minimum loss function value that appears during the iteration process.

[0035] If the maximum number of iterations is reached, but the loss function value corresponding to the current control vector is not less than the minimum loss function value that appears during the iteration process, then the iteration ends with the control vector corresponding to the minimum loss function value during the iteration process as the result.

[0036] Furthermore, in step S4, steps S2-S4 are repeated, and the online iteration termination criterion for iterative optimization of the control vector is as follows:

[0037] The control vector is continuously optimized and iterated. After each iteration, the control vector with the minimum loss function generated during the iteration is updated. When the real time has passed one control step, the optimization stops and the first term of this control vector is directly output. At the same time, the time domain is shifted backward to start solving the next control step.

[0038] Furthermore, the method also includes performing database updates, as detailed below:

[0039] After implementing the operating condition change plan on the DC steam generator, the simulation results of the DC steam generator are compared and organized with the measurement data, erroneous data are corrected, and control cases are formed and stored in the operation database.

[0040] After the case storage is completed, the database update will begin. Based on the recording time of a case and the data density in a certain area around the case, when establishing the database update mechanism, experts will set different data densities in different areas based on their experience. Frequently occurring or complex working conditions require a larger data density, while less frequent or less complex working conditions require a smaller data density.

[0041] When updating the running database, the historical data near the new case is first traversed in chronological order from oldest to newest. If the data density around a case exceeds the local standard, the data in that group is deleted.

[0042] The present invention also provides a control device, including a memory, a processor, and a program stored in the memory, wherein the processor executes the program to implement the generalized predictive control method for a nuclear power plant DC steam generator as described above.

[0043] According to specific embodiments provided by the present invention, the generalized predictive control method for a DC steam generator in a nuclear power plant disclosed by the present invention has the following technical effects:

[0044] (1) This invention realizes a generalized predictive control algorithm through numerical calculation and gradient optimization of control vector. On the one hand, it realizes the advance response of water flow rate. On the other hand, it can also complete the automatic control task of DC steam generator under low power conditions. At the same time, the control method combined with numerical calculation not only ensures the strong interpretability of this control scheme, but also improves the control accuracy and robustness to a certain extent. It can effectively cope with the simultaneous disturbance of multiple parameters and provide a reliable control scheme, achieve stable and efficient control effect, and effectively improve the safety of the device, reduce parameter fluctuations and extend the life of heat transfer tube.

[0045] (2) This invention integrates the use of a runtime database, which significantly improves computational efficiency while endowing the control method with autonomous learning and optimization capabilities. By collecting and storing operating condition data in real time during operation, the runtime database, which implicitly contains the dynamic characteristics of the system, not only provides rich data support for the formulation of control strategies, but also becomes the cornerstone for the self-evolution and optimization of the control method.

[0046] (3) This invention, through a fast solution model combined with a gradient optimization algorithm, indirectly considers the intrinsic relationship between the thermal-hydraulic parameters of the DC steam generator in the control system. Simultaneously, by linking the controller coefficients and power levels, it better considers the dynamic characteristics of the DC steam generator, enabling the fast solution model to intuitively and accurately reflect changes occurring in the DC steam generator. It effectively utilizes the DC steam generator data provided by the digital nuclear power system, and the accuracy of the results is enhanced by modifying the fast solution model.

[0047] (4) This invention achieves a simplified algorithm structure and high robustness to coefficient settings by applying a synchronous disturbance stochastic approximation algorithm, making coefficient tuning simpler while enhancing the fault tolerance of the control method during operation. Furthermore, the synchronous disturbance stochastic approximation algorithm, through its unique mechanism, cleverly simplifies the feedback correction link of predictive control, making the entire control method more concise and clear, and avoiding the increased system complexity and failure risk caused by combining multiple control algorithms in complex control. Simultaneously, by setting the penalty function, it can quantitatively consider various constraints in the operation of the DC steam generator and provide a control scheme with optimal overall performance. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a schematic diagram of the generalized predictive control method for a DC steam generator in a nuclear power plant, according to an embodiment of the present invention.

[0050] Figure 2 This is a flowchart of a generalized predictive control method for a DC steam generator in a nuclear power plant, according to an embodiment of the present invention.

[0051] Figure 3 This is a flowchart of the synchronous perturbation random approximation algorithm according to an embodiment of the present invention;

[0052] Figure 4 The diagram below is a schematic of the Relap5 model of the DC steam generator according to an embodiment of the present invention. In this diagram, 101-105 represent the inlet control body, inlet pipe, tube bundle, outlet pipe and outlet control body of the primary side, respectively, and 201-205 represent the inlet control body, inlet pipe, tube bundle, outlet pipe and outlet control body of the secondary side, respectively. The heat transfer solution domain between the primary side and the secondary side is the heat transfer domain of the heat exchange tube wall.

[0053] Figure 5 This is a schematic diagram of the database operation in an embodiment of the present invention;

[0054] Figure 6 This is a schematic diagram illustrating the database update process in an embodiment of the present invention;

[0055] Figure 7 This is a schematic diagram comparing the effects of the generalized predictive control method and the PID control method under the secondary frequency regulation and power reduction conditions of a nuclear power plant according to an embodiment of the present invention.

[0056] Figure 8This is a schematic diagram comparing the effects of the generalized predictive control method and the PID control method under emergency power reduction conditions according to an embodiment of the present invention;

[0057] Figure 9 This is a schematic diagram of a coefficient perturbation example according to an embodiment of the present invention. Detailed Implementation

[0058] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments 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 are within the scope of protection of the present invention.

[0059] The purpose of this invention is to provide a generalized predictive control method for a direct-current (DC) steam generator in a nuclear power plant. This method combines numerical calculation and gradient optimization with thermal-hydraulic data to improve the control performance of the DC steam generator. Through generalized predictive control, synchronous disturbance stochastic approximation, and numerical calculation, this invention establishes an effective control scheme that achieves the goals of improving response speed, reducing settling time, minimizing DC steam generator pressure fluctuations, quantitatively considering the constraints of DC steam generator operating requirements, and automatically controlling the DC steam generator under low-power conditions.

[0060] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] like Figures 1 to 5 As shown, the generalized predictive control method for a direct-current steam generator in a nuclear power plant provided by the present invention is executed by the generalized predictive control system of the direct-current steam generator in the nuclear power plant. The method includes the following steps:

[0062] S1. Input the operating condition change plan into the simulation calculation model of the DC steam generator based on numerical calculation to predict the dynamic behavior of the DC steam generator in the future and obtain the simulation results.

[0063] S2. Based on simulation results, the control vector of the DC steam generator is optimized using a generalized predictive control algorithm;

[0064] S3 applies the optimized control vector to the DC steam generator and uses sensors to measure the DC steam generator in real time to obtain thermal-hydraulic data.

[0065] S4. Repeat steps S2-S4 to achieve iterative optimization of the control vector, and finally implement the operating condition change plan on the DC steam generator.

[0066] The present invention adopts the following technical solution, specifically including as follows: Figure 2 The process is shown below. This scheme consists of two main stages: offline training and online execution. It should be noted that offline training does not include the process of obtaining initial values ​​for the control scheme from a historical database. The method for determining the initial values ​​of the control scheme is as follows: the control quantity for the new control step is the average of the control quantities for the previous four control steps.

[0067] Specifically, in S1, the simulation calculation model of the DC steam generator includes an operation simulation model and a fast solution model of the DC steam generator;

[0068] The method for constructing the simulation model is as follows:

[0069] Based on the structural parameters of the DC-DC steam generator (such as heat transfer tube dimensions, arrangement, and shell dimensions) and its static and dynamic operating characteristics, a full-scale one-dimensional thermodynamic analysis model of the DC-DC steam generator is constructed as its operational simulation model. The static characteristics consider the generator's performance under stable operating conditions, including temperature and pressure distribution. The dynamic characteristics consider the generator's dynamic response under load changes and temperature fluctuations. This full-scale one-dimensional thermodynamic analysis model of the DC-DC steam generator includes one-dimensional thermodynamic analysis of all key components, providing detailed information on changes in parameters such as temperature, pressure, and flow rate.

[0070] The method for constructing the fast solution model is as follows:

[0071] Based on the actual conditions of the DC steam generator, a one-dimensional thermodynamic analysis model of the DC steam generator is established using a single heat transfer tube according to the heat transfer tube arrangement as a rapid solution model. During the simulation calculation, after completion, the steam pressure, steam temperature, steam flow rate, feedwater flow rate, feedwater temperature, feedwater pressure, and relevant parameters of the primary side inlet and outlet working fluid are stored. In the rapid solution model, the main objective to be solved is the secondary side pressure drop; therefore, this method can save computational resources and accelerate the calculation speed. It is particularly important to note that when the rapid solution model and the running simulation model interact, the primary side inlet and outlet flow rates, as well as the secondary side inlet and outlet flow rates, need to be amplified by the corresponding factors.

[0072] This is because the fast solution model is based on a single heat transfer tube, while an actual DC steam generator consists of multiple heat transfer tubes. The magnification factor is usually determined based on the number of heat transfer tubes.

[0073] Before step S1, the simulation model is trained offline to build a runtime database. The specific method is as follows:

[0074] Based on the operational requirements of the DC steam generator, a large number of calculation examples with different load change rates and different start-up and end conditions are set up and input into the operation simulation model and the fast solution model. The synchronous disturbance stochastic approximation method is used for offline training. Through the offline training process, simulation calculation and control vector solution are performed to obtain the operation data and corresponding control vectors under different load change rates and different start-up and end conditions.

[0075] Based on the load change rate, the operating data and its corresponding control vectors are divided into several groups. Within each group, the operating data and its corresponding control vectors are arranged and stored based on the initial operating condition and the target operating condition, thus constructing an operating database.

[0076] Offline training is performed in this invention to accelerate convergence during operation by using optimized initial values ​​for the control vector. Therefore, an operational database is established to extend the experience gained from offline training to online operation. Specifically, this involves querying historical data under the same operating conditions from the operational database and fitting the control vector obtained during offline training using the synchronous perturbation random approximation method to the online operation as the initial value for the control vector.

[0077] After establishing the simulation model, the control principles need to be determined based on the selected operating scheme, and reflected through a loss function. In this invention, an operating scheme with constant secondary steam pressure is selected during testing; therefore, steam pressure is directly chosen as the controlled variable, and the loss function is constructed based on this.

[0078] A control step refers to the time interval during which the controller updates its output or executes a control action. It determines how often the controller adjusts its control direction. At the beginning of each control step, the controller needs to be initialized, and initial values ​​for the control vector to be optimized need to be selected. The selection of initial values ​​for the control scheme differs from offline training. In offline training, the control quantities newly incorporated into the moving time domain as time progresses are obtained by a weighted average of the first few elements of the control vector. However, in online operation, these initial values ​​are directly provided by the operating database based on the initial operating conditions and the load change rate. Specifically, the range of the target control scheme is first determined based on the load change rate, then the required control scheme is determined based on the start and end operating conditions. The feedwater flow rate in the control scheme is fitted according to the steam flow rate change trend, while ensuring that the fitted curve is equal to the integral of the feedwater flow rate with respect to time. Finally, this fitted curve is used as the initial value of the control quantity for online operation.

[0079] Specifically, S1 involves inputting the operating condition change plan into a numerical calculation-based simulation model of a DC steam generator to predict the dynamic behavior of the DC steam generator over a future period, obtaining simulation results, including:

[0080] Based on the operating condition variation plan, a simulation model is run to perform simulation calculations and obtain the expected load variation rate and start and end operating conditions. The operating condition variation plan refers to the design of the start and end points and paths of operating condition changes for the once-through steam generator, set by operators according to demand and environmental conditions. Figure 2 The figure shows that the water flow rate q is q0 before time t0 and q1 after time t1, and changes linearly between time t0 and time t1.

[0081] Based on the constructed operating database, the selection range of the control vector is first determined according to the expected load change rate, and then the required control vector is determined according to the expected start and end conditions. The feedwater flow rate in the control vector is fitted according to the steam flow rate change trend, while ensuring that the fitted curve is equal to the integral of the feedwater flow rate with respect to time. Finally, the fitted curve is used as the initial value of the control vector during online operation.

[0082] After obtaining the initial value of the control vector, the control vectors of both positive and negative disturbances are simultaneously input into the fast solution model to predict the dynamic behavior of the DC evaporator over a period of time and obtain simulation results.

[0083] Specifically, S2, based on simulation results, optimizes the control vector of the DC steam generator using a generalized predictive control algorithm, specifically including:

[0084] The simulation results are processed to obtain the gradient of the loss function under the current control vector, and the control vector is optimized based on this gradient. This process is repeated until the termination criterion is met. Then, the first term of the control vector is passed to the running simulation model, and the model is moved forward according to the inlet flow, moving forward in the time domain.

[0085] This invention employs a synchronous perturbation stochastic approximation method to optimize the control vector. This method typically controls the optimization outcome by the number of iterations. For simple problems, a large number of iterations can be set to ensure convergence to the optimal solution. In this invention, the following convergence criterion is selected:

[0086] (1) The number of iterations must be greater than 20;

[0087] (2) The loss function value corresponding to the current control vector is less than the minimum loss function value that appears during the iteration process;

[0088] The iteration ends when both (1) and (2) are satisfied. When (1) is satisfied but (2) is not satisfied, the control vector corresponding to the minimum value of the loss function during the iteration process is taken as the result and the iteration ends.

[0089] Since online operation requires guaranteed computational speed, continuing to use the iteration termination criterion used in offline training may lead to excessively slow solutions. The iteration termination criterion for online operation is as follows: continuously optimize and iterate the control vector, update the control vector with the minimum loss function generated during each iteration after each iteration, stop optimization when one control step has elapsed in real time and directly output the first term of this control vector, while simultaneously shifting the time domain backward to begin solving for the next control step.

[0090] The method also includes performing database updates, as detailed below:

[0091] After the change in operating conditions is completed, the simulation data and measured data of the DC steam generator are compared and organized, errors are corrected, and cases are stored in the operational database. As the DC steam generator operates, the number of cases stored in the operational database increases. Therefore, to ensure the timeliness of the operational database, it is necessary to delete overly redundant and outdated data to update the database. The database update process begins below, considering two quantities: the duration of a case from its recording to the current moment, and the data density in a certain area surrounding the case. When establishing the operational database update mechanism, experts set different data densities for different areas based on experience. Frequently occurring or complex operating conditions require higher data densities, and vice versa. When updating the operational database, historical data near the new operating condition is first traversed chronologically from oldest to newest. If the data density around a certain set of historical data exceeds the local standard, that set of data is deleted. This method ensures that the database covers as many operating conditions as possible and also keeps pace with potential changes in the DC steam generator, such as scaling.

[0092] Example:

[0093] I. Simulation Calculation of DC Steam Generator

[0094] This invention establishes a rapid solution model and an operational simulation model for a direct-flow steam generator using the Relap5 program, taking a B&W straight-tube direct-flow steam generator experimental device as an example. First, a rapid solution model and an operational simulation model are established with reference to the parameters shown in Table 1. For example... Figure 4 As shown, Figure 4 The DC steam generator is divided into sixty nodes on the primary and secondary sides, and each node is connected to a control unit representing the upstream and downstream equipment of the primary and secondary circuits via a time interface.

[0095] The next step is to use the Relap5 program to build a simulation model to obtain the initial operating conditions for the offline training examples, preparing for offline training. During the development phase, the calculations are completed by reading the output text of the Relap5 program and automatically generating the next execution file. In practical applications, when dealing with specific DC steam generator control objects, a one-dimensional movable boundary simulation model embedded in the control program is established as a fast solution model to improve computational efficiency.

[0096] Table 1 Main parameters of DC steam generator

[0097]

[0098]

[0099] II. Handling of Control Variables and Input to the Fast Solution Model

[0100] First, the control quantity is initialized. In this invention, the control quantity, i.e., the water supply flow rate, in the moving time domain is discretized into the following form using the "black box" method, which is called the control vector:

[0101] [θ0,θ1,θ2,θ3,θ4]

[0102] In the control vector, the index of each component represents its position in the shift time domain. The shift time domain refers to the time range within which the predictive control model is considered in the optimization of each control step [t]. p ,t p+N Its length is determined by the dimension of the control vector and the duration covered by a single control step.

[0103]

[0104] Among them, t p Indicates the current time, t p+N Δt represents the end time of the current move time domain, p represents the sequence number of the first control step in the current move time domain within the entire example, N represents the number of control steps covered by the move time domain, and Δt represents the number of control steps covered by the current move time domain. i Indicates the duration of a single control step coverage;

[0105] During offline training, the fifth component of the control vector is obtained by weighted averaging of the first four components. During online operation, the feedwater flow rate in the control scheme is fitted based on the steam flow rate variation trend, while ensuring that the fitted curve is equal to the integral of the feedwater flow rate over time. Finally, this fitted curve is used as the initial value of the control variable during online operation.

[0106] The inputs required for the fast solution model include: the initial state of the system, the boundary conditions of the DC steam generator in the moving time domain, and the initial values ​​of the control vector.

[0107] The method for determining the initial state of the system is as follows: During the first system initialization, the DC steam generator (running the simulation model) is brought to a stable state. Subsequently, under this operating condition, a stable flow field solution is obtained using a fast-solver model. This flow field solution can then be used as the initial state of the system. Subsequent initial states are obtained by correcting the solution from the fast-solver model in the previous control step using sensor data from the DC steam generator (the flow field solution from the simulation model).

[0108] In this invention, the boundary conditions of the fast solution model in the moving time domain are the inlet and outlet parameters of the primary and secondary working fluids, excluding the feedwater flow rate, provided by the sensor data of the DC steam generator (the flow field solution of the running simulation model).

[0109] III. Determine the loss function:

[0110] The loss function is designed based on the operational scheme of the control objective: The control scheme established in this invention uses a fast solution model to determine the values ​​of the objective function and the loss function given the initial conditions and the input control vector θ within the moving time domain of N control steps. In this embodiment, an operational scheme with constant secondary steam pressure is selected. Therefore, the square of the difference between the steam pressure and the rated value per unit time is selected as the loss function, and its expression is:

[0111]

[0112] In the formula, t′ represents the current time, t″ represents the simulation duration required for rapid model solving, p represents the steam pressure, p0 represents the rated steam pressure or target steam pressure, and θ represents the control vector. In practical applications, a regularization term that quantitatively describes the operating requirements of the DC steam generator can be added to this function.

[0113] The control vector is judged based on the obtained loss function value. When the loss function value is within an acceptable range, the DC steam generator is considered to be basically stable and the control vector can be directly output. Otherwise, the control vector is optimized and iterated.

[0114] IV. Optimization and Iteration of Control Vectors

[0115] The control vector is then iterated and optimized:

[0116] The first step is to initialize the SPSA (Synchronous Perturbation Stochastic Approximation) system. Set the counter k to 0 and determine the SPSA gain sequence a. k and c k The coefficients in the equation are a, c, α, β, and γ. Among them, a affects θ during the iteration process. kThe correction speed is crucial; too small an 'a' will lead to slow convergence, while too large an 'a' will cause iterative divergence. It is worth noting that in the control process of a DC steam generator, a fixed 'a' cannot meet the control requirements under conditions of large power variations. Therefore, in this paper, 'a' is represented by a function with the current feedwater flow rate as the independent variable:

[0117] a = 0.1(θ) kp +1)

[0118] Where, θ kp This represents the water flow rate of the first control step in the k-th iteration of the current time domain.

[0119] c determines the magnitude of the gradient value used to update the water flow rate; as the iteration progresses, a smaller c becomes... k This ensures the convergence of the results. Based on the experience presented in this paper, the additional perturbation should keep the steam pressure difference between the forward and reverse perturbations within 0.005 MPa, with approximately 0.001 MPa yielding better results. α and γ determine the rate of decrease in the correction amount during each feedwater flow rate iteration.

[0120]

[0121] Among them, a k c k , k, and A are internal coefficients of the SPSA algorithm and have no specific meaning.

[0122] β is a coefficient that correlates the correction amount with the rate of load change, and it needs to be obtained through experimental tuning.

[0123]

[0124] Where Q is the current load of the DC steam generator, and f represents a function with the load change rate as the independent variable.

[0125] The second step is to generate an N-dimensional random perturbation vector Δ using the Monte Carlo method. k A classic and effective method is to assign ±1 to each choice according to a Bernoulli distribution, with probabilities of 0.5. The disturbance vector is then appended to the feedwater flow vector in both the positive and negative directions as follows: θ k +c k Δ k and θ k -c k Δ k .

[0126] The third step is to input the disturbed water flow vector into the fast solution model to obtain two measured values ​​y(θ) of the loss function. k +c k Δ k ) and y(θk -c k Δ k And obtain the gradient vector g. k :

[0127]

[0128] The role of τ is to correlate the gradient optimization process with the power level, adjust the order of magnitude of the resulting gradient vector, and is a single-valued function of the power level, which needs to be obtained through experimental tuning. The meaning is: the elements of the random perturbation vector generated in the k-th iteration of the moving time domain from the p-th control step to the p+N-th control step.

[0129] Fourth, substitute the obtained gradient vector into the following formula to update the water flow rate θ. k Then return to step two until the convergence condition is met.

[0130] θ k+1 =θ k -a k g k (θ k )

[0131] V. Iteration Termination Criteria

[0132] For the SPSA method, a simple approach is to use the number of iterations as the iteration termination criterion; alternatively, the corrected value of the input vector or the measured value of the loss function can be used. In this invention, the iteration termination criterion is set as a certain number of iterations and a loss function value that are less than the historical minimum value during the current control step optimization process.

[0133] k>k max ,y <y min

[0134] In the formula, k represents the number of iterations, k max Let y be the maximum number of iterations, and y represent the loss function value corresponding to the control vector. min This represents the minimum value of the loss function that occurs during the iteration process.

[0135] The iteration termination criterion during online runtime is as follows: continuously optimize and iterate the control vector, update the control vector with the minimum loss function generated during each iteration, stop optimization when the real time has passed one control step, directly output the first term of this control vector, and simultaneously move the time domain backward to start solving the next control step.

[0136] VI. Running database updates

[0137] like Figure 5As shown, when the DC steam generator finishes regulation and stabilizes under the new operating conditions, the entire process of the operating condition change is recorded in the operation database with the disturbance start time set to 0. Taking the steam flow rate change condition as an example, the operation database stores control cases with the steam flow rate change rate as the z-axis, the initial operating condition as the x-axis, and the target operating condition as the y-axis.

[0138] like Figure 6 As shown, after the control case storage is completed, the database update begins, based on the record time of a case and the data density within a certain area R around the case. When establishing the database update mechanism, experts set different data densities for different areas based on experience. Frequently occurring or complex operating conditions require higher data densities, and vice versa. When updating the database, the historical data within the vicinity R of the new case is first traversed chronologically from oldest to newest. If the data density around a case exceeds the local standard, that group of data is deleted.

[0139] like Figure 7 As shown, this invention can effectively stabilize the steam pressure within a small range under emergency power reduction conditions. Compared to traditional PID control methods, this invention is still capable of automatically controlling the DC steam generator under low power conditions. In the industry, automatic control of DC steam generators is generally only considered under 30%-100% load conditions, while this invention can still perform the automatic control task well under low load conditions of 15% of the DC steam generator's rated power.

[0140] The following examples cover common load regulation conditions of DC steam generators and Figure 7 , Figure 8 As can be seen from the present invention, it can not only effectively reduce pressure fluctuations in DC steam generators, but also significantly shorten the duration of pressure fluctuations. This not only improves the safety of the device, but also extends its lifespan to a certain extent. For DC steam generators with a long service life, it can greatly reduce the probability of failure.

[0141] Table 2 Comparison of Maximum Pressure Fluctuation Between the Two Controllers

[0142]

[0143]

[0144] like Figure 9As shown, in the example of high-load secondary frequency regulation and power reduction, the main coefficients a, c, α, and γ of the control system in this invention are perturbed by ±20%, and the robustness of the invention is verified by comparing the simulation results. It can be found that the optimization of the control vector in this invention mainly depends on the intrinsic relationship between the feedwater flow rate and pressure of the DC steam generator. The controller coefficients only determine the process of the control vector approaching the optimal solution; therefore, within a certain range, even without meticulous tuning of the controller coefficients, this invention can still achieve good control performance.

[0145] Finally, to address the various operational requirements of a DC steam generator, regularization terms can be quantitatively established as constraints. This functionality enables the DC steam generator to move from automatic control to intelligent control. The following example illustrates the fluctuations in the dry-out point and the superheat of the outlet steam, which are related to the lifespan of the heat transfer tubes:

[0146]

[0147] In the formula, h represents the dry point height, T(t,θ) represents the outlet steam temperature, and T0 represents the saturated steam temperature at the outlet pressure. For practical applications, researchers need to design the weights of each regularization term based on the operating criteria and requirements of the once-through steam generator to obtain satisfactory results. Taking the above formula as an example, the importance of stable steam pressure is far greater than the fluctuation of the dry point, while the importance of outlet steam superheat is the least. Therefore, a higher weight should be assigned to pressure fluctuations, and a lower weight should be assigned to outlet steam superheat.

[0148] In summary, the generalized predictive control method for DC steam generators in nuclear power plants provided by this invention combines simulation calculation, generalized predictive control (GPC), and real-time feedback correction. The following is a detailed explanation and step-by-step breakdown of the entire process: Obtain the operating condition change plan from the database or scheduling system of the digital nuclear power system; input the operating condition change plan into a numerical simulation program; use a suitable mathematical model (such as a transfer function, state-space model, or one-dimensional thermodynamic analysis model) to simulate the dynamic behavior of the DC steam generator; predict key parameters of the DC steam generator, such as temperature, pressure, and flow rate, over a future period through simulation calculations; use the simulation results as input to generalized predictive control (GPC) to judge and optimize the control variables; use sensors installed on the DC steam generator to measure key parameters in real time and obtain actual thermo-hydraulic data; compare the actual data measured by the sensors with the simulation results; adjust the parameters of the simulation model based on the differences between the actual data and the simulation results to ensure that the simulation model can more accurately reflect the dynamic characteristics of the DC steam generator; re-perform simulation calculations using the corrected model to further improve the accuracy of predictions; apply the optimized control variables to the DC steam generator and gradually implement the operating condition change plan. Throughout the process, continuously monitor the system's operating status and make real-time adjustments as needed to ensure the system's stability and safety. This closed-loop control method not only improves control accuracy but also enhances the robustness and adaptability of the system.

[0149] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A generalized predictive control method for a direct current steam generator in a nuclear power plant, characterized in that, Includes the following steps: S1. Input the operating condition change plan into the simulation calculation model of the DC steam generator based on numerical calculation to predict the dynamic behavior of the DC steam generator in the future and obtain the simulation results. S2. Based on simulation results, the control vector of the DC steam generator is optimized using a generalized predictive control algorithm; S3 applies the optimized control vector to the DC steam generator and uses sensors to measure the DC steam generator in real time to obtain thermal-hydraulic data. S4. Based on the thermal-hydraulic data, the simulation results in S1 are corrected. Steps S2-S4 are repeated to achieve iterative optimization of the control vector. Finally, the operating condition change plan is implemented in the DC steam generator.

2. The generalized predictive control method for a direct current steam generator in a nuclear power plant according to claim 1, characterized in that, In S1, the DC steam generator simulation calculation model includes an operation simulation model and a fast solution model for the DC steam generator; The method for constructing the simulation model is as follows: Based on the structural parameters and static and dynamic operating characteristics of the DC steam generator, a full-size one-dimensional thermodynamic analysis model of the DC steam generator is constructed as the operating simulation model of the DC steam generator. The method for constructing the fast solution model is as follows: Based on the actual situation of the DC steam generator, a one-dimensional thermodynamic analysis model of the DC steam generator is established by taking a single heat transfer tube according to the heat transfer tube arrangement as a fast solution model. The fast solution model is used to solve the secondary side pressure drop. The fast solution model interacts with the running simulation model, and the primary side inlet and outlet flow rates and the secondary side inlet and outlet flow rates are amplified by the corresponding factors.

3. The generalized predictive control method for a direct current steam generator in a nuclear power plant according to claim 2, characterized in that, Before step S1, the simulation model is trained offline to build a runtime database. The specific method is as follows: Based on the operational requirements of the DC steam generator, a large number of calculation examples with different load change rates and different start-up and end conditions are set up and input into the operation simulation model and the fast solution model. The synchronous disturbance stochastic approximation method is used for offline training. Through the offline training process, simulation calculation and control vector solution are performed to obtain the operation data and corresponding control vectors under different load change rates and different start-up and end conditions. Based on the load change rate, the operating data and its corresponding control vectors are divided into several groups. Within each group, the operating data and its corresponding control vectors are arranged and stored based on the initial operating condition and the target operating condition, thus constructing an operating database.

4. The generalized predictive control method for a direct current steam generator in a nuclear power plant according to claim 3, characterized in that, S1 involves inputting the operating condition change plan into a numerical calculation-based simulation model of a DC steam generator to predict the dynamic behavior of the DC steam generator over a future period, obtaining simulation results, specifically including: Based on the load change plan, a simulation model is run to perform simulation calculations and obtain the expected load change rate and start and end conditions. Based on the constructed operating database, the selection range of the control vector is first determined according to the expected load change rate, and then the required control vector is determined according to the expected start and end conditions. The feedwater flow rate in the control vector is fitted according to the steam flow rate change trend, while ensuring that the fitted curve is equal to the integral of the feedwater flow rate with respect to time. Finally, the fitted curve is used as the initial value of the control vector during online operation. After obtaining the initial value of the control vector, the control vectors of both positive and negative disturbances are simultaneously input into the fast solution model to predict the dynamic behavior of the DC evaporator over a period of time and obtain simulation results.

5. The generalized predictive control method for a direct current steam generator in a nuclear power plant according to claim 4, characterized in that, S2, based on simulation results, optimizes the control vector of the DC steam generator using a generalized predictive control algorithm, specifically including: The simulation results are processed to obtain the gradient of the loss function under the current control vector, and the control vector is optimized based on this gradient. This process is repeated until the termination criterion is met. Then, the first term of the control vector is passed to the running simulation model and it advances to the next control step based on this inlet flow.

6. The generalized predictive control method for a direct current steam generator in a nuclear power plant according to claim 5, characterized in that, The process of processing the simulation results to obtain the gradient of the loss function under the current control vector, and optimizing the control vector based on this gradient, repeating this process until the termination criterion is met, specifically includes: Under the operating scheme where the secondary steam pressure remains constant, the square of the difference between the steam pressure and the rated value per unit time is selected as the loss function, and its expression is: In the formula, t′ is the current time, t″ is the simulation time required for the fast solution model, p is the steam pressure, p0 is the rated steam pressure or target steam pressure, and θ is the current control vector; The current control vector is judged based on the calculated loss function value. If the loss function value is within an acceptable range, the DC steam generator is determined to be in a stable state, and the current control vector is output. Otherwise, the current control vector is optimized, and this process is repeated until the termination criterion is met.

7. The generalized predictive control method for a direct current steam generator in a nuclear power plant according to claim 6, characterized in that, The optimization of the current control vector, repeated until the termination criterion is met, includes: Based on the current control vector, the simulation model is run to update the parameters. The synchronous perturbation stochastic approximation method is used to generate perturbation vectors, including forward perturbation vectors and reverse perturbation vectors. Through gradient approximation, the control vector is optimized and iterated. The iteration ends when the maximum number of iterations is reached and the loss function value corresponding to the current control vector is less than the minimum loss function value that appears during the iteration process. If the maximum number of iterations is reached, but the loss function value corresponding to the current control vector is not less than the minimum loss function value that appears during the iteration process, then the iteration ends with the control vector corresponding to the minimum loss function value during the iteration process as the result.

8. The generalized predictive control method for a direct current steam generator in a nuclear power plant according to claim 7, characterized in that, In step S4, steps S2-S4 are repeated, and the online iteration termination criterion for iterative optimization of the control vector is as follows: The control vector is continuously optimized and iterated. After each iteration, the control vector with the minimum loss function generated during the iteration is updated. When the real time has passed one control step, the optimization stops and the first term of this control vector is directly output. At the same time, the time domain is shifted backward to start solving the next control step.

9. The generalized predictive control method for a direct current steam generator in a nuclear power plant according to claim 7, characterized in that, The method also includes performing database updates, as detailed below: After implementing the operating condition change plan on the DC steam generator, the simulation results of the DC steam generator are compared and organized with the measurement data, erroneous data are corrected, and control cases are formed and stored in the operation database. After the case storage is completed, the database update will begin. Based on the recording time of a case and the data density in a certain area around the case, when establishing the database update mechanism, experts will set different data densities in different areas based on their experience. Frequently occurring or complex working conditions require a larger data density, while less frequent or less complex working conditions require a smaller data density. When updating the running database, the historical data near the new case is first traversed in chronological order from oldest to newest. If the data density around a case exceeds the local standard, the data in that group is deleted.

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