A dynamic optimization method and system for multi-module nuclear power unit plant-level load distribution

Abstract

The application discloses a dynamic optimization method and system for plant-level load distribution of a multi-module nuclear power unit, and the method comprises the following steps: a continuous-time mechanism model of the multi-module nuclear power unit is established, and time-domain discretization is performed to construct a discrete estimation model and a discrete control model; a dynamic parameter estimation optimization proposition is established, and a first constraint is applied; a multi-objective economic type stage cost function is established according to power generation efficiency, operation reliability and load matching degree indexes, and a second constraint is applied; a nonlinear programming problem is solved in a power grid dispatching cycle to obtain a steady-state optimal working point of each module as a reference set point; in each control cycle, each module thermal hydraulic parameter is identified on-line through dynamic parameter estimation, an economic type nonlinear model predictive control optimization proposition with a stability inequality constraint is constructed after the parameter estimation value is fixed, and the proposition is solved, the first-step control quantity is applied to the unit, and iterative updating is performed according to a change signal, and the non-equilibrium load distribution dynamic optimization of the multi-module nuclear power unit under the condition of performance difference between the modules is realized.

Description

Technical Field

[0001] This invention belongs to the field of nuclear power plant operation optimization technology, and in particular relates to a dynamic optimization method and system for plant-level load allocation of multi-module nuclear power units. Background Technology

[0002] Large pressurized water reactor power plants have achieved commercial operation, and multi-module high-temperature gas-cooled reactor demonstration projects have been connected to the grid for power generation. Unlike single-reactor large-capacity nuclear power units represented by pressurized water reactors and boiling water reactors, new nuclear power units such as multi-module high-temperature gas-cooled reactors are composed of several nuclear steam supply system modules with the same design connected in parallel in terms of engineering structure. The superheated steam generated by each module is collected in the pipeline in front of the turbine on the conventional island side to form the main steam and drive the turbine to generate electricity, forming a "multi-reactor one-unit" system configuration.

[0003] With the large-scale grid connection of high-proportion renewable energy sources such as wind power and photovoltaics, the randomness and volatility of grid load have significantly increased. The operational role of advanced nuclear power units is shifting from simply supplying baseload power to having flexible adjustment capabilities. Against this backdrop, multi-module nuclear power units face a new plant-level operation optimization task: plant-level load allocation, which means achieving overall optimal operation at the unit level by coordinating the thermal power output of each nuclear steam supply system module, given the total grid load demand.

[0004] Currently, common load allocation schemes in engineering practice often rely on relatively simple heuristic principles, such as equal load allocation, equal variable load allocation, extreme value priority allocation, and preset value allocation. While these methods are easy to implement, they do not fully consider the objective differences between different nuclear steam supply system modules in terms of heat exchange efficiency, equipment aging, and coolant condition. Therefore, it is difficult to take into account the differences in heat exchange performance between different modules to fully improve the unit's economic efficiency.

[0005] More importantly, the optimization decision-making for load allocation in multi-module nuclear power units must be carried out under the premise of ensuring system stability and safety, and its dynamic process must always meet the complex operational constraints involved in unit coordinated control, specifically including the safety boundaries of key state variables, the operationally feasible region of control variables, and the time-varying dynamic characteristics of the system. Under the traditional predictive control framework, the standard economic nonlinear model predictive control method can significantly improve the economic performance of the system in the dynamic process by directly using economic indicators as optimization objectives; however, since its cost function in the economic stage no longer has strict positive definiteness and boundedness, it generally cannot be directly used as a candidate Lyapunov function, making it difficult to provide universal stability guarantees for closed-loop systems.

[0006] On the other hand, chemical process systems often adopt an operation scheme that combines steady-state economic optimization and load tracking control. This "two-stage" design of first allocating and then tracking makes it difficult to take into account the economic performance of dynamic processes, and has certain limitations in engineering practice.

[0007] Therefore, there is an urgent need for a plant-level load allocation optimization method that can integrate multi-objective economic indicators, unit operation constraints, online identification of heat exchange performance differences between modules, and closed-loop robust stability assurance, so as to support multi-module nuclear power units to participate in grid dispatching and operation safely, stably, and efficiently in the new power system. Summary of the Invention

[0008] To address the technical challenges of existing plant-level load allocation methods for multi-module nuclear power units, which struggle to simultaneously maximize economic benefits, identify online differences in heat transfer performance between modules, and ensure robust closed-loop stability, this invention provides a dynamic optimization method and system for plant-level load allocation in multi-module nuclear power units. By integrating multi-objective economic indicators, unit operating constraints, online identification of differences in heat transfer performance between modules, and robust closed-loop stability assurance, this method fully leverages the differences in heat transfer performance between various nuclear steam supply system modules to achieve unbalanced load allocation while ensuring both unit operational safety and closed-loop stability.

[0009] A dynamic optimization method for plant-level load allocation in multi-module nuclear power units includes the following steps: Step 1: Establish a continuous-time mechanism model for a multi-module nuclear power unit and discretize it in the time domain to construct a discrete estimation model and a discrete control model respectively; Step 2: Using the discrete estimation model as the state recursion equation constraint, establish a dynamic parameter estimation optimization proposition and apply the first constraint; establish a multi-objective economic stage cost function based on the power generation efficiency index, operation reliability index and load matching index, and apply the second constraint using the discrete control model as the state prediction equation constraint. Step 3: Solve the nonlinear programming problem with the multi-objective economic stage cost function as the objective and the nuclear power unit steady-state equation and the second constraint as the constraint during the power grid dispatch cycle. Obtain the steady-state optimal operating point of each module as the reference set point and send it to the economic nonlinear model predictive controller. Step 4: In each control cycle, the estimated values ​​of the thermal-hydraulic parameters of each module are identified online through dynamic parameter estimation. After fixing the parameter estimates, an economic nonlinear model with stability inequality constraints is constructed to predict and solve the control optimization problem. The first step control quantity is then applied to the nuclear power unit. Step 5: Continuously monitor the load demand change signals issued by the power grid dispatching layer, update the reference setpoint as needed, otherwise continue to recursively execute the parameter estimation and predictive control steps.

[0010] Preferably, the first constraint includes: a feasible region constraint for the state variable and an allowable set constraint for the parameters to be estimated; The second constraint includes: safety boundary constraints for key state variables, operational constraints for control variables, and power operation constraints.

[0011] Furthermore, the safety boundary constraints of the key state variables include at least one of the following: safety limit of the reactor relative thermal power, limit of the rate of change of the reactor relative thermal power, safety limit of the reactor outlet coolant temperature, safety limit of the superheated steam temperature at the steam generator outlet, and safety limit of the main steam pressure in front of the turbine. The operational constraints of the control variables include at least one of the following: the adjustable range of reactor inlet coolant flow rate, the adjustable range of reactor external reactivity introduced by control rods, the adjustable range of steam generator inlet feedwater flow rate, and the opening range of the main steam regulating valve. The power operation constraints include at least one of the following: load change rate limit, single load adjustment mileage limit, minimum stable operating power limit for a single module, and relative thermal power imbalance limit between modules.

[0012] Preferably, step 1 specifically includes: For nuclear power units with multiple nuclear steam supply system modules, a continuous-time mechanism model in the form of a system of differential-algebraic equations is established under the plant-level load distribution operation scenario; The continuous-time mechanism model is discretized in the time domain using the finite element orthogonal collocation method, and a discrete estimation model for estimating thermal-hydraulic parameters and a discrete control model for economic predictive control are constructed respectively. The discrete estimation model uses uncertain thermal-hydraulic parameters as decision variables and constructs a historical sampling window using a first number of finite element methods. In each finite element method, a first number of Gauss-Radau configuration points located at the end of the finite element method are set. The discrete control model uses the future control variable sequence as the decision variable and constructs a future prediction window by using a second number of finite element methods, with a second number of Gauss-Radau configuration points set in each finite element. The second quantity is greater than the first quantity.

[0013] Furthermore, the continuous-time mechanism model in the form of a system of differential-algebraic equations includes the following types of equations: The equations describing the fundamental conservation of mass, energy, and momentum of the system; Neutron kinetic equations describing nuclear fission chain reactions; Thermohydraulic equations describing the heat transfer and flow processes in the primary and secondary loops; Equations for calculating the physical properties of the working fluid in the primary and secondary loops; And the combined dynamic equations of the turbine-generator that describe the work done by the main steam expansion and the electrical energy output.

[0014] Preferably, in step 2, the construction of the dynamic parameter estimation optimization proposition includes: combining the prior mean and covariance information of the thermal-hydraulic parameters to be estimated and the measurement noise covariance information to construct a dynamic parameter estimation optimization proposition in the form of maximum a posteriori probability estimation. The dynamic parameter estimation optimization proposition is expressed as: , , , , , , , In the formula, The estimation time domain for dynamic parameter estimation. , and These represent the first and second samples within the historical sampling window. Estimated state variables, estimated output variables, and predicted residuals at each time step; Indicates the first Actual measurement data at each time step; This represents the vector of thermal-hydraulic parameters to be estimated. This represents the prior mean of the parameter; and These are the measurement noise covariance matrix and the prior parameter covariance matrix, respectively. and These are the state transition function and output function of the discrete estimation model, respectively. and These are the feasible region constraints for the state variables and the allowable set constraints for the parameters to be estimated, respectively.

[0015] Furthermore, the prior covariance matrix of the parameters in the dynamic parameter estimation optimization problem is refreshed online in each control cycle based on the inverse of the simplified Hessian matrix at the optimal solution of the problem in the previous cycle, thereby realizing the recursive update and adaptive estimation of the prior parameter information. The estimated thermal-hydraulic parameters include global parameters that do not change over time and local parameters that change with operating conditions; wherein the global parameter is the helium leakage rate of the reactor primary loop, and the local parameter is the heat transfer coefficient of the subcooling section on the secondary side of the steam generator.

[0016] Preferably, the objective function of the dynamic parameter estimation optimization problem in step 2 includes: The quadratic term obtained by weighting the predicted residuals with the measurement noise covariance matrix is ​​used to reflect the degree of fit of the model to historical observation data; The quadratic term, obtained by weighting the deviation between the estimated value of the parameter to be estimated and its prior mean using the parameter prior covariance matrix, is used to reflect the confidence level of the parameter prior information.

[0017] Preferably, the power generation efficiency index in step 2 is defined as the negative value of the ratio of the unit's electrical power output to the sum of the products of the relative thermal power and rated power of each module; The operational reliability index is defined as the sum of squared norms of the normalized deviations between key state variables and their process design values. The load matching index is defined as the absolute value of the deviation between the unit's electrical power output and the total load demand of the power grid, normalized to the unit's total rated thermal power.

[0018] More preferably, the established multi-objective economic stage cost function is expressed as follows: In the formula, , , These are the weighting coefficients for the three indicators. For power generation efficiency indicators, For operational reliability indicators, This is a load matching index.

[0019] Preferably, in the economic nonlinear model predictive control optimization problem in step 4, the stability potential function is taken as the cumulative value of the tracking stage cost corresponding to the optimal control sequence of the current control cycle along the prediction time domain. The cost of the tracking phase is defined as the sum of the quadratic form of the deviation between the predicted state and the reference setpoint, and the quadratic form of the deviation between the predicted control variable and the corresponding control quantity of the reference setpoint.

[0020] The stability potential function provided by this invention is a path-dependent function that depends simultaneously on the initial state of the system, the parameter perturbation sequence up to the current time step, and the time step, unlike the traditional Lyapunov function that only depends on the current state. Under nominal conditions, the stability inequality constraint holds strictly in each control cycle. When parameter perturbations exist, the feasibility of the optimization proposition is maintained by introducing non-negative relaxation variables, and the degree of weakening of the decrease is limited by the boundedness of the perturbation norm.

[0021] More preferably, the economic nonlinear model predictive control optimization proposition further includes a stability inequality constraint, wherein the stability inequality constraint is: the cumulative cost of the tracking stage corresponding to the optimal control sequence of the current period does not exceed the decreasing threshold determined in the previous period, and the decreasing threshold is jointly determined by the value of the stability potential function of the previous period, the actual tracking stage cost of the previous period, and the stability adjustment parameter.

[0022] Furthermore, in the aforementioned economic nonlinear model predictive control optimization problem, nonnegative relaxation variables are uniformly introduced for state constraints, terminal constraints, and stability constraints, and these variables are weighted to the objective function with penalty parameters to maintain the feasibility of the optimization problem under disturbance conditions.

[0023] Furthermore, a difference quadratic damping penalty term for the control variables is introduced into the objective function of the economic nonlinear model predictive control optimization proposition to suppress fluctuations in the optimal control sequence between adjacent time steps.

[0024] On the other hand, the present invention also provides a dynamic optimization system for plant-level load allocation of multi-module nuclear power units, including a memory and a processor. The memory is used to store a computer program, and the processor is used to implement the dynamic optimization method for plant-level load allocation of multi-module nuclear power units when the computer program is executed.

[0025] Furthermore, the aforementioned dynamic optimization method and system for plant-level load allocation in multi-module nuclear power units is applied to one of the following operating scenarios: A scenario involving the distribution of thermal power among modules of a nuclear steam supply system in a multi-module nuclear power unit; In the context of renewable energy grid integration, nuclear power units participate in grid peak shaving together with other power generation units. In combined heat and power (CHP) applications, nuclear power units are used for multi-load coordinated distribution between power supply load and heating load.

[0026] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention identifies the thermal and hydraulic parameters of each nuclear steam supply system module online through a dynamic parameter estimator, quantifies the differences in heat exchange performance between modules, and implements unbalanced load allocation accordingly, allocating more power output tasks to modules with higher thermal efficiency, thereby improving the overall power generation efficiency of the unit under specified load demand.

[0027] (2) The present invention introduces an operational reliability index into the cost function of the multi-objective economic stage. In the scenario of unbalanced load distribution operation, it can prevent the module from deviating too far from the design operating condition and ensure the long-term reliable operation of the nuclear power unit. At the same time, it applies constraints on key state variables to the discrete control model, so that the dynamic optimization is solved under the premise of strictly meeting the nuclear safety constraints, thereby ensuring the system safety of the multi-module nuclear power unit.

[0028] (3) The present invention introduces stability inequality constraints in the economic nonlinear model predictive control optimization problem, which forces the stability potential function to decrease along the time sequence. This constraint does not depend on the specific mathematical properties of the controlled unit model. Under the condition of bounded parameter disturbance, it provides input to state actual stability guarantee for the closed-loop system and has universality. Attached Figure Description

[0029] Figure 1 This is a flowchart illustrating the dynamic optimization method for plant-level load allocation of multi-module nuclear power units provided in an embodiment of the present invention.

[0030] Figure 2 This is a schematic diagram of the closed-loop control structure and method of the plant-level load allocation dynamic optimization method provided in the embodiments of the present invention.

[0031] Figure 3 This is a schematic diagram illustrating the principle of rolling time-domain parameter estimation and economic nonlinear model predictive control provided in an embodiment of the present invention.

[0032] Figure 4 The curves represent the estimation results of various thermal-hydraulic parameters during the dynamic optimization of plant-level load allocation provided in this embodiment of the invention.

[0033] Figure 5 The curves showing the changes in key output variables of each nuclear steam supply system module during the dynamic optimization of plant-level load allocation provided in this embodiment of the invention are shown.

[0034] Figure 6 The curves showing the changes in various indicators of the multi-objective economic stage cost during the dynamic optimization of plant-level load allocation provided in this embodiment of the invention are shown. Detailed Implementation

[0035] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described below are intended to facilitate the understanding of the present invention and do not constitute any limitation thereof.

[0036] This invention addresses the technical problem that existing plant-level load allocation methods for multi-module nuclear power units struggle to simultaneously maximize economic benefits, identify online differences in heat transfer performance between modules, and ensure robust closed-loop stability. It provides a dynamic optimization method and system for plant-level load allocation in multi-module nuclear power units. A steady-state optimizer provides a long-term economic optimal objective, a dynamic parameter estimator quantifies performance differences between modules online, and an economical nonlinear model predictive controller performs dynamic optimization under strict constraints while ensuring stability. These three components form an information closed loop through parameter estimation transmission, reference setpoint issuance, and decreasing stability potential function constraints. Ultimately, this achieves safe, stable, and efficient dynamic optimization of load allocation for multi-module nuclear power units under conditions of performance differences between modules.

[0037] This invention uses a multi-module high-temperature gas-cooled reactor nuclear power unit (adopting a "two-reactor-one-machine" system structure) as a typical example to illustrate the implementation process of the proposed dynamic optimization method for plant-level load allocation in multi-module nuclear power units. The multi-module high-temperature gas-cooled reactor nuclear power unit consists of two identical nuclear steam supply system modules (NSSS modules) on the nuclear island side. Each NSSS module comprises a high-temperature gas-cooled reactor, a steam generator, and a main helium blower, among other equipment. Helium is used as the primary coolant for heat exchange between the reactor and the steam generator. The superheated steam generated by the two NSSS modules is uniformly mixed in the turbine inlet pipeline on the conventional island side to form main steam, which is used to drive the turbine for power generation. The conventional island side also includes secondary loop fluid network equipment such as a condenser, deaerator, and feedwater pumps.

[0038] like Figure 1 As shown in the embodiment, a dynamic optimization method for plant-level load allocation in a multi-module nuclear power unit is provided, and the implementation steps are as follows: S1. Establish a continuous-time mechanism model for a multi-module nuclear power unit and discretize it in the time domain to construct a discrete estimation model and a discrete control model respectively.

[0039] In this embodiment, for the reactor, steam generator, control rod system, and main helium blower on the nuclear island side of the multi-module high-temperature gas-cooled reactor nuclear power unit, as well as the steam header, turbine generator, and feedwater pump on the conventional island side, a continuous-time mechanism model of the entire plant in the form of a system of differential-algebraic equations is established based on the concept of block partitioning and lumped parameter modeling, and is uniformly denoted as: , In the formula, Indicates continuous time; , and These represent the state variables, control variables, and uncertain parameters of the unit under the plant-level load distribution operation scenario, respectively. To uniformly describe the dynamic characteristic function of the unit, the following types of equations should be included: mass, energy and momentum conservation equations describing the basic conservation of the system; neutron kinetic equations describing the nuclear fission chain reaction; thermo-hydraulic equations describing the heat transfer and flow processes in the primary and secondary loops; property calculation equations describing the thermophysical properties of the working fluids in the primary and secondary loops; and turbine-generator joint dynamic equations describing the work done by the main steam expansion and the output of electrical energy.

[0040] Taking the multi-module high-temperature gas-cooled reactor nuclear power unit as an example, its key state variables include the reactor relative thermal power of each NSSS module, the reactor outlet hot helium temperature, the steam generator outlet superheated steam temperature, and the main steam pressure before the turbine; its control variables include the reactor inlet helium flow rate of each NSSS module, the reactor external reactivity introduced by the control rods, the steam generator inlet feedwater flow rate, and the main steam regulating valve opening; its disturbance variables include the reactor inlet helium pressure and the steam generator inlet feedwater temperature of each NSSS module; its uncertain parameters include the reactor helium leakage rate of each NSSS module and the heat transfer coefficient of the secondary subcooling section of the steam generator.

[0041] Furthermore, the control variables input into the continuous-time mechanism model are set as zero-order hold-offs at any discrete sampling time step, and the system of differential-algebraic equations between adjacent discrete time steps is implicitly solved, thereby obtaining the discrete-time mechanism model of the unit: , In the formula, For discrete time step index, , and Representing discrete time steps Discrete state variables, control variables, and uncertain parameters at the location. This represents the discrete-time mechanism model of the unit.

[0042] In the implicit solution process, the finite element orthogonal collocation method is used to discretize the system of differential-algebraic equations between adjacent discrete time steps in the time domain. The discrete-time mechanism model will be used to construct a discrete estimation model in the estimation time domain and a discrete control model in the prediction time domain, both based on the current time step. The uncertain parameters at the current time step and the sequence of control variables along the prediction time domain are used as decision variables for optimization. At this point, the time domain estimation of dynamic parameter estimation is denoted as... Its corresponding historical sampling window contains A set of discrete time steps, i.e. The prediction time domain of the economic nonlinear model predictive control is denoted as... Its corresponding future predictive control involves A set of discrete time steps, i.e. .

[0043] Furthermore, the finite element orthogonal configuration method employs differentiated configuration schemes in the dynamic parameter estimator and the economic nonlinear model predictive controller. In this embodiment, the discrete estimation model corresponding to the dynamic parameter estimator uses 10 finite element units to construct historical sampling windows, with one Gauss-Radau configuration point located at the end of each finite element unit; similarly, the discrete control model corresponding to the economic nonlinear model predictive controller uses 10 finite element units to construct future prediction windows, with three Gauss-Radau configuration points set within each finite element unit. The physical basis for this differentiated configuration is that the control input sequence within the estimation window consists of known historical measurements, thus a lower-order configuration accuracy is sufficient to characterize its dynamic behavior; while the control input sequence within the control window represents the decision variables to be optimized, requiring a higher-order configuration accuracy to support the solution quality of the predictive optimization.

[0044] S2. Using the discrete estimation model as the state recursion equation constraint, establish a dynamic parameter estimation optimization proposition and apply the first constraint; based on the power generation efficiency index, operation reliability index and load matching index, establish a multi-objective economic stage cost function, and use the discrete control model as the state prediction equation constraint to apply the second constraint.

[0045] like Figure 2 As shown, the performance differences between modules are first quantified online using a dynamic parameter estimator. Specifically, as... Figure 3 As shown, in the control cycle At this point, using the discrete estimation model as the state recursion equation constraint, the dynamic parameter estimator, based on the input-output measurement data within the historical time window, solves the following dynamic parameter estimation optimization problem: , , , , , , , In the formula, The estimation time domain for dynamic parameter estimation. , and These represent the first and second samples within the historical sampling window. Estimated state variables, estimated output variables, and predicted residuals at each time step; Indicates the first Actual measurement data at each time step; This represents the vector of thermal-hydraulic parameters to be estimated. This represents the prior mean of the parameter; and These are the measurement noise covariance matrix and the prior parameter covariance matrix, respectively. and These are the state transition function and output function of the discrete estimation model, respectively. and These are the feasible region constraint of the state variable and the allowable set constraint of the parameter to be estimated, which together constitute the first constraint.

[0046] In the embodiment, the objective function of the dynamic parameter estimation optimization problem includes two terms. The first term is the sum of the quadratic forms obtained by inverse weighting of the measurement noise covariance matrix of the predicted residuals, which is used to reflect the degree of fit of the model to historical observation data. The second term is the quadratic form obtained by inverse weighting of the parameter prior covariance matrix of the deviation between the estimated value of the parameter to be estimated and its prior mean, which is used to reflect the confidence level of the parameter prior information.

[0047] Furthermore, the parameter prior covariance matrix The system can be refreshed online in each control cycle based on the inverse of the simplified Hessian matrix at the optimal solution of the problem in the previous cycle, thereby achieving recursive updating of parameter prior information and adaptive estimation.

[0048] In this embodiment of the invention, the thermal-hydraulic parameter to be estimated is the helium leakage rate of the reactor primary loop. The heat transfer coefficient of the secondary subcooling section of the steam generator is included in the online estimation as a global parameter that does not change over time; It is included in the online estimation as a local parameter that varies with the operating conditions.

[0049] Next, regarding the optimization objective of plant-level load allocation for multi-module nuclear power units, this embodiment of the invention sets a multi-objective economic stage cost function consisting of three factors: power generation efficiency, operational reliability, and load matching degree. Its overall form is as follows: , In the formula, , , These are the weighting coefficients for the three indicators. For power generation efficiency indicators, For operational reliability indicators, This is a load matching index.

[0050] The power generation efficiency index Defined as the unit's electrical power output The negative value of the ratio of the sum of the products of the relative thermal power and the rated power of each NSSS module, i.e.: , In the formula, The total number of NSSS modules, in this embodiment =2; For the first The reactor relative thermal power of each NSSS module; This represents the rated power of the reactor module. This specification aims to maximize the actual power generation efficiency of the unit and is equivalently constructed to minimize its negative value.

[0051] The operational reliability indicators Defined as Key state variables Its process design value The sum of squares of the normalized deviations between the two norms (i.e. Norm penalty term form (hereinafter the same), that is: , The The norm penalty term provides a smooth, differentiable penalty effect near the process design values ​​of key state variables.

[0052] The load matching index Defined as the unit's electrical power output With the total load demand of the power grid The absolute value of the deviation between them is normalized to the total rated thermal power of the unit (i.e. Norm penalty term form (hereinafter the same), that is: , The Norm penalty terms have the exact penalty property: when their weighting coefficients... When the value of is greater than the infinite norm of the Lagrange multipliers at the optimal solution of the original constrained optimization problem, the penalty term is equivalent to […]. This is applied as a hard equality constraint to the optimization problem, thereby achieving accurate load matching.

[0053] Furthermore, using the discrete control model as the constraint for the state prediction equation, the safety boundary constraints of key state variables, the operational constraints of control variables, and the power operation constraints are applied as a second set of constraints to the discrete control model. The limits of the safety boundary constraints include at least one of the following: the safety limit for the relative thermal power of the reactor, the safety limit for the reactor outlet coolant temperature, the safety limit for the superheated steam temperature at the steam generator outlet, and the safety limit for the main steam pressure before the turbine.

[0054] The operational constraints are determined by the mechanical design, driving capability, and control logic of the actuator, and include at least one of the following: the adjustable range of coolant flow rate at the reactor inlet, the adjustable range of reactor external reactivity introduced by the control rods, the adjustable range of feedwater flow rate at the steam generator inlet, and the opening range of the main steam regulating valve.

[0055] The power operation constraints are determined by the reactor core reactivity management capability of the nuclear power unit, the thermal stress and temperature limit requirements of the fuel elements, and the coordinated operation requirements of each NSSS module. They include at least one of the following: load change rate limit (upper and lower bounds of the derivative of the unit's electrical power output with respect to time), single load adjustment mileage limit (upper bound of the absolute value of the cumulative change in the unit's electrical power output during a single load adjustment event), minimum stable operating power limit for a single module (lower bound of the relative thermal power of each NSSS module), and relative thermal power imbalance limit between each NSSS module (upper bound of the absolute value of the pairwise difference in relative thermal power between each module).

[0056] S3. Solve the nonlinear programming problem with the multi-objective economic stage cost function as the objective and the nuclear power unit steady-state equation and the second constraint as the constraint during the power grid dispatch cycle. Obtain the steady-state optimal operating point of each module as the reference set point and send it to the economic nonlinear model predictive controller.

[0057] In each power grid dispatch cycle, a nonlinear programming problem is solved with the multi-objective economic stage cost function as the objective and the steady-state equations of the multi-module nuclear power unit and the above-mentioned operational constraints as constraints. Figure 2 ): , , , In the formula, and Let represent the feasible regions of the state variables and control variables, respectively. The obtained This refers to the steady-state optimal operating point of each module of the nuclear power unit within the current scheduling cycle, and is used as a reference setpoint to be sent to the downstream economic nonlinear model predictive controller.

[0058] The objective function of the steady-state optimization problem adopts the same mathematical form and weight setting as the multi-objective economic stage cost function established in S2, so that the solution of the steady-state optimal operating point and the solution of dynamic optimization share the same multi-objective economic index system. The execution cycle of solving the nonlinear programming problem is synchronized with the power grid dispatch cycle, usually on the order of hours; the execution cycles of the rolling time-domain parameter estimation in S4 and the solution of the economic nonlinear model predictive control optimization proposition with stability inequality constraints in S4 are synchronized with the unit control cycle, usually on the order of seconds.

[0059] S4. In each control cycle, the estimated values ​​of the thermal and hydraulic parameters of each module are identified online through dynamic parameter estimation. After fixing the parameter estimates, an economical nonlinear model with stability inequality constraints is constructed to predict and solve the control optimization problem. The first step control quantity is then applied to the nuclear power unit.

[0060] Examples, such as Figure 4 As shown, in each control cycle The dynamic parameter estimator backtracks to obtain the most recent data from the distributed control system. Historical input-output measurement data for each sampling time step. The nonlinear programming solver is used to solve the dynamic parameter estimation optimization problem established in S2, obtaining the estimated thermal-hydraulic parameters of each NSSS module at the current time. ( Figure 2 ); the estimated value of the parameter The parameters are transmitted in real time to the economical nonlinear model predictive controller for online correction of the corresponding thermal-hydraulic parameters in its control model. This enables the economical nonlinear model predictive controller to make differentiated load allocation optimization decisions based on the actual heat exchange performance differences of each NSSS module.

[0061] Then, in each control cycle The economical nonlinear model predictive controller performs the following sub-steps: S4.1 Fix the thermo-hydraulic parameters in the discrete control model to the parameter estimates. .

[0062] S4.2 Based on Prediction Time Domain The cumulative cost of the inner tracking phase constructs a stability potential function. The cost of the tracking phase is defined as follows: , In the formula, and These represent the predicted state variables and predicted control variables in the prediction time domain, respectively. and These are the positive definite weight matrices corresponding to the state deviation and control deviation, respectively; and This is the steady-state reference setpoint. The stability potential function... The value of is specifically taken as the cumulative value of the tracking stage cost corresponding to the optimal control sequence obtained in the current control cycle along the prediction time domain: , In the formula, and They are respectively The optimal solution to the time-predictive control problem State prediction and control prediction at the step; For the deadline The truncated parameter perturbation sequence at time step; This represents the initial state of the system.

[0063] It should be noted that the stability potential function To simultaneously depend on the system's initial state The parameter perturbation sequence up to the current time step With time The path-dependent function differs from the traditional Lyapunov function, which only depends on the current state. Its function is to use the cumulative tracking error corresponding to the optimal control law of the current control cycle as a metric, and then construct the following stability constraints to ensure the stability of the closed-loop system.

[0064] S4.3 introduces stability inequality constraints to force the stability potential function to decrease along the time series: , In the formula, This is a stability adjustment parameter. and Each is the previous control cycle. The value of the stability potential function obtained at the location and the tracking stage cost of the actual state-control pair are related in... All constants are known during the solution process.

[0065] The above constraint is mathematically equivalent to: the cumulative cost of the tracking stage corresponding to the optimal control sequence of the current cycle should not exceed the decreasing threshold determined by the information of the previous cycle, thereby explicitly guaranteeing the temporal decreasing nature of the stability potential function. The stability adjustment parameter... The larger the value, the stricter the descent constraint, and the faster the system state approaches the steady-state reference setpoint; conversely, the smaller the value, the stricter the descent constraint, and the faster the system state approaches the steady-state reference setpoint. The smaller the value, the looser the descending constraint, allowing the system to have greater room for economic performance optimization while ensuring stability.

[0066] Furthermore, under nominal conditions, i.e., when there is no mismatch between the system and the model, the stability inequality constraint holds strictly in each control cycle; when parameter perturbations exist, the constraint may become invalid in stages, at which point the corresponding slack variables introduced in S4.4 become necessary. To maintain the feasibility of the optimization proposition, the degree of weakening of the decrease is limited by the boundedness of the perturbation norm.

[0067] S4.4 introduces non-negative relaxation variables for state constraints, terminal constraints, and stability constraints, and uses a sufficiently large penalty parameter. By applying weighted penalties to the objective function, a robust reconfiguration optimization proposition for economical nonlinear model predictive control is constructed: , , , , , , , , In the formula, ,and and As functions related to inequality constraints, they correspond to the safety boundary constraints for key state variables, and the inequality constraint functions related to the operational constraints and power operation constraints of control variables, respectively. The set of non-negative relaxed variables corresponding to the state variable safety boundary constraints, power operation constraints, terminal equality constraints (lower / upper bounds) and stability inequality constraints, with each subset exceeding 0; This is a penalty parameter. The penalty parameter... The value of is not less than the dual norm of the Lagrange multipliers at the optimal solution of the original economic nonlinear model predictive control problem.

[0068] During the initial control cycle of the system (i.e.) Since there is no value of the stability potential function from the previous control cycle and no cost of the actual tracking stage, the stability inequality constraint is ignored; from the second control cycle onwards, the stability inequality constraint is applied normally in the form described above.

[0069] S4.5 The interior point method or sequential quadratic programming method is used as the nonlinear programming solver to solve the reconstruction optimization problem online. A hot start strategy based on the historical best solution is adopted between adjacent control cycles, and the best solution of the previous cycle is used as the initial guess of the solution process of the next cycle to shorten the online solution time.

[0070] S4.6 Extract the first-step control quantity from the obtained optimal control sequence and apply it to the corresponding actuator of the multi-module nuclear power unit.

[0071] S4.7 To suppress drastic fluctuations in the optimal control sequence between adjacent time steps, this embodiment of the invention further introduces a difference quadratic form vibration suppression penalty term for the control variables into the objective function of the reconstruction optimization problem:

[0072] In the formula, It is a symmetric positive semi-definite weight matrix. The vibration suppression penalty term helps extend the service life of the nuclear power unit's actuators.

[0073] S5. Continuously monitor the load demand change signals issued by the power grid dispatching layer, and update the reference setpoint as needed; otherwise, continue to recursively execute the parameter estimation and predictive control steps.

[0074] Waiting for the multi-module nuclear power unit to transition to the next control cycle The steady-state optimizer continuously monitors load demand change signals issued by the power grid dispatching layer. When the change signal exceeds a preset threshold, it returns to S3 to resolve the steady-state multi-objective optimization problem to update the reference setpoint and initiate a new round of rolling optimization; otherwise, the dynamic parameter estimator and the economic nonlinear model predictive controller sequentially execute parameter estimation and predictive control steps at the current reference setpoint. Within each control cycle, the parameter estimation and predictive control steps are executed once each, continuously advancing the closed-loop optimization of load allocation through the aforementioned rolling mechanism.

[0075] On the other hand, the embodiment also provides a dynamic optimization system for plant-level load allocation of multi-module nuclear power units, including a memory and a processor. The memory is used to store a computer program, and the processor is used to implement the dynamic optimization method for plant-level load allocation of multi-module nuclear power units when the computer program is executed.

[0076] To verify the feasibility and effectiveness of the dynamic optimization method and system for plant-level load allocation of multi-module nuclear power units provided by this invention, the specific implementation methods of this invention are further described below with reference to a set of simulation data. This invention embodiment builds a closed-loop simulation system based on a dynamic modeling platform. The specific implementation parameter settings for each component in the closed-loop simulation system are as follows: The simulation step size of the nuclear power unit dynamic simulator is 2 seconds; the dynamic simulator is subjected to zero-mean Gaussian state disturbance and measurement noise in each simulation step; the reactor helium leakage rate of the two NSSS modules is set to different values ​​(0.105 for NSSS module 1 and 0.1 for NSSS module 2), thus forming the difference in heat transfer performance between the modules; Multi-objective weighting coefficients of steady-state optimizer , , The values ​​are set to 1, 0.1, and 10 respectively; the sampling period of the dynamic parameter estimator is 2 seconds, the estimation time domain is 20 seconds, and the discrete estimation model contains 10 finite elements, each containing one Gauss-Radau configuration point located at the end of the finite element; the thermal-hydraulic parameters to be estimated include the reactor helium leakage rate of the dual NSSS module. Heat transfer coefficient of the secondary subcooling section of the steam generator The sampling period of the economical nonlinear model predictive controller is 2 seconds, the prediction time domain is 20 seconds, and the discrete control model contains 10 finite element methods, each containing 3 Gauss-Radau collocation points; stability adjustment parameters. It was set to 0.05.

[0077] The initial operating conditions used in this embodiment are as follows: both NSSS modules are operating at 75% of their rated power. Under steady-state conditions, the reactor outlet hot helium temperature of each module is 734.37°C, the superheated steam temperature at the steam generator outlet is 571°C, the main steam pressure before the turbine is 13.24 MPa, and the unit's electrical power output is approximately 136.79 MW. At this time, the controller is not aware in advance of the differences in thermo-hydraulic parameters between the two NSSS modules; these differences must be identified online by the dynamic parameter estimator in S4.

[0078] During a certain scheduling cycle, the power grid issued a load demand command to increase the total power output of the generating units to 148.52 MW. The optimal load setting obtained through S4 steady-state multi-objective optimization is as follows: the reactor relative thermal power of NSSS module #1 is approximately 59.44% of its rated power, and the reactor relative thermal power of NSSS module #2 is 100% of its rated power. The physical basis for this unbalanced load distribution scheme is as follows: Figure 4 As shown, online parameter identification revealed that the reactor helium leakage rate of module 1#NSSS was relatively high, indicating a relatively weak ability of its coolant to carry heat from the core and reflector layer. Therefore, it was allocated a lower thermal power output. Module 2#NSSS, on the other hand, was allocated full power output, thereby maximizing the overall power generation efficiency of the unit. This unbalanced allocation scheme is significantly different from the traditional equal load allocation scheme.

[0079] like Figure 5 As shown, the dynamic optimization process can be roughly divided into three stages: rapid tracking, dynamic adjustment, and steady-state maintenance. During the simulation, the reactor power output and outlet hot helium temperature of the two NSSS modules can track the corresponding expected trajectories well, and the superheated steam temperature at the steam generator outlet and the main steam pressure in front of the turbine are maintained near their respective set values, indicating that the method can maintain closed-loop stability during the dynamic optimization process.

[0080] like Figure 6 As shown, the unit's power generation efficiency improved from 37.02% before optimization to approximately 38.15% under steady-state operation; the operational reliability and load matching indices both approached zero during the steady-state phase. The unit's final steady-state power output was approximately 149.29 MW, with a slight deviation of about 0.5% relative to the 148.52 MW load command issued by the grid, reflecting the aforementioned... Bounded penalty properties of norm penalty terms with finite weighted coefficients.

[0081] As can be seen from the above embodiments, the method proposed in this invention can accurately predict and coordinate the dynamics of multi-timescale nuclear power units, implement unbalanced load distribution based on the differences in heat transfer performance between modules to improve the economic performance of the unit, strictly ensure the safety and stability of unit operation, and maintain the feasibility of closed-loop optimization under disturbance conditions.

[0082] It should be noted that, when implementing the dynamic optimization method and system for plant-level load allocation of multi-module nuclear power units provided in the above embodiments, the division of the above functional modules should be used as an example. The functions can be allocated to different functional modules as needed, that is, the internal structure of the terminal or server can be divided into different functional modules to complete all or part of the above functions. Furthermore, the dynamic optimization method and system embodiments for plant-level load allocation of multi-module nuclear power units provided in the above embodiments belong to the same concept, and their specific implementation process is detailed in the method embodiments, which will not be repeated here.

[0083] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A dynamic optimization method for plant-level load allocation in multi-module nuclear power units, characterized in that, Includes the following steps: Step 1: Establish a continuous-time mechanism model for a multi-module nuclear power unit and discretize it in the time domain to construct a discrete estimation model and a discrete control model respectively; Step 2: Using the discrete estimation model as the state recursion equation constraint, establish a dynamic parameter estimation optimization proposition and apply the first constraint; establish a multi-objective economic stage cost function based on the power generation efficiency index, operation reliability index and load matching index, and apply the second constraint using the discrete control model as the state prediction equation constraint. Step 3: Solve the nonlinear programming problem with the multi-objective economic stage cost function as the objective and the nuclear power unit steady-state equation and the second constraint as the constraint during the power grid dispatch cycle. Obtain the steady-state optimal operating point of each module as the reference set point and send it to the economic nonlinear model predictive controller. Step 4: In each control cycle, the estimated values ​​of the thermal-hydraulic parameters of each module are identified online through dynamic parameter estimation. After fixing the parameter estimates, an economic nonlinear model with stability inequality constraints is constructed to predict and solve the control optimization problem. The first step control quantity is then applied to the nuclear power unit. Step 5: Continuously monitor the load demand change signals issued by the power grid dispatching layer, update the reference setpoint as needed, otherwise continue to recursively execute the parameter estimation and predictive control steps.

2. The dynamic optimization method for plant-level load allocation of multi-module nuclear power units according to claim 1, characterized in that, The first constraint includes: the feasible region constraint of the state variable and the allowable set constraint of the parameter to be estimated; The second constraint includes: safety boundary constraints for key state variables, operational constraints for control variables, and power operation constraints.

3. The dynamic optimization method for plant-level load allocation of multi-module nuclear power units according to claim 1, characterized in that, Step 1 specifically includes: For nuclear power units with multiple nuclear steam supply system modules, a continuous-time mechanism model in the form of a system of differential-algebraic equations is established under the plant-level load distribution operation scenario; The continuous-time mechanism model is discretized in the time domain using the finite element orthogonal collocation method, and a discrete estimation model for estimating thermal-hydraulic parameters and a discrete control model for economic predictive control are constructed respectively. The discrete estimation model uses uncertain thermal-hydraulic parameters as decision variables, and the discrete control model uses a future sequence of control variables as decision variables.

4. The dynamic optimization method for plant-level load allocation of multi-module nuclear power units according to claim 1, characterized in that, Step 2 establishes a dynamic parameter estimation optimization proposition, including: combining the prior mean and covariance information of the thermal-hydraulic parameters to be estimated and the measurement noise covariance information to construct a dynamic parameter estimation optimization proposition in the form of maximum a posteriori probability estimation. The dynamic parameter estimation optimization proposition is expressed as: ， ， ， ， ， ， ， In the formula, The estimation time domain for dynamic parameter estimation. , and These represent the first and second samples within the historical sampling window. Estimated state variables, estimated output variables, and predicted residuals at each time step; Indicates the first Actual measurement data at each time step; This represents the vector of thermal-hydraulic parameters to be estimated. This represents the prior mean of the parameter; and These are the measurement noise covariance matrix and the prior parameter covariance matrix, respectively. and These are the state transition function and output function of the discrete estimation model, respectively. and These are the feasible region constraints for the state variables and the allowable set constraints for the parameters to be estimated, respectively.

5. The dynamic optimization method for plant-level load allocation of multi-module nuclear power units according to claim 1, characterized in that, The objective function of the dynamic parameter estimation optimization problem in step 2 includes: The quadratic term obtained by weighting the predicted residuals with the measurement noise covariance matrix is ​​used to reflect the degree of fit of the model to historical observation data; The quadratic term, obtained by weighting the deviation between the estimated value of the parameter to be estimated and its prior mean using the parameter prior covariance matrix, is used to reflect the confidence level of the parameter prior information.

6. The dynamic optimization method for plant-level load allocation of multi-module nuclear power units according to claim 1, characterized in that, The power generation efficiency index in step 2 is defined as the negative value of the ratio of the unit's electrical power output to the sum of the products of the relative thermal power and rated power of each module. The operational reliability index is defined as the sum of squared norms of the normalized deviations between key state variables and their process design values. The load matching index is defined as the absolute value of the deviation between the unit's electrical power output and the total load demand of the power grid, normalized to the unit's total rated thermal power.

7. The dynamic optimization method for plant-level load allocation of multi-module nuclear power units according to claim 1, characterized in that, In the economic nonlinear model predictive control optimization problem in step 4, the stability potential function is taken as the cumulative value of the tracking stage cost corresponding to the optimal control sequence of the current control cycle along the prediction time domain. The cost of the tracking phase is defined as the sum of the quadratic form of the deviation between the predicted state and the reference setpoint, and the quadratic form of the deviation between the predicted control variable and the corresponding control quantity of the reference setpoint.

8. The dynamic optimization method for plant-level load allocation of multi-module nuclear power units according to claim 7, characterized in that, The aforementioned economic nonlinear model predictive control optimization proposition also includes a stability inequality constraint, which states that the cumulative cost of the tracking stage corresponding to the optimal control sequence in the current period does not exceed the decreasing threshold determined in the previous period. The decreasing threshold is jointly determined by the value of the stability potential function in the previous period, the actual tracking stage cost in the previous period, and the stability adjustment parameter.

9. A dynamic optimization system for plant-level load allocation in a multi-module nuclear power unit, comprising a memory and a processor, wherein the memory is used to store computer programs, characterized in that, The processor is used to implement the dynamic optimization method for plant-level load allocation of multi-module nuclear power units as described in any one of claims 1-8 when executing the computer program.

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