Reactor load tracking control method and system fused with disturbance compensation

Abstract

The invention discloses a DC-NGPC reactor load tracking control method and system fused with disturbance compensation, and the system comprises a nonlinear disturbance observer which is used for calculating a nonlinear disturbance estimation value of a reactor system according to the speed of a control rod and state feedback information outputted by the reactor system; the nonlinear generalized predictive controller based on disturbance compensation is used for providing a predictive control law of reactor load tracking control, and the predictive control law is used for calculating the speed of a control rod according to a power track provided by the outside, state feedback information output by a reactor system and a nonlinear disturbance estimated value calculated by the nonlinear disturbance observer; wherein the control rod speed is provided for the reactor system after being subjected to rod speed amplitude limiting, so as to track and control the load of the reactor system. The disturbance observed quantity obtained through estimation is introduced into the nonlinear generalized predictive controller, dynamic compensation of disturbance is effectively achieved, and the robustness of the whole system is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to a reactor load tracking control method and system. BACKGROUND

[0002] As a clean energy, nuclear energy is gradually becoming an indispensable key force in the global energy production system, and its share in the total power generation in some countries is also increasing, which means that more and more nuclear power plants need to participate in peak shaving to alleviate the pressure of power grid dispatching, which requires nuclear reactors to have load tracking capability. Load tracking operation refers to the flexible adjustment of the output power of the generator set according to the changes in the demand of the power grid, which is crucial for improving the peak shaving capability and operational stability of the power grid. For nuclear power plants, the goal of load tracking is to ensure safe operation and achieve dynamic matching and coordination of power generation capacity and power grid load demand by accurately regulating the thermal power output of the nuclear reactor.

[0003] However, as a complex system with strong coupling, time-varying and highly nonlinear characteristics, nuclear power plants also face problems such as external disturbances during long-term operation. In recent years, in view of the characteristics of this system, the design of the nuclear reactor load tracking controller has become a research hotspot that has attracted widespread attention, and researchers have proposed a variety of control methods.

[0004] Among them, proportional-integral-derivative (PID) control is widely used in the core power control of pressurized water reactor nuclear power plants due to its mature characteristics, but the traditional control strategy often fails to achieve satisfactory control results, as it does not consider the disturbance factors that may occur during system operation and cannot suppress disturbances. Therefore, advanced control methods such as fuzzy control, adaptive control, sliding mode control and neural network control have been gradually introduced and applied in this field. In addition, predictive control has attracted in-depth research by scholars due to its advantage of being able to make rolling predictions of future system behavior.

[0005] However, most of the above predictive control strategies are based on the linearization model of the system for prediction. Since high-order nonlinear terms are ignored when linearizing the nonlinear system, the resulting linear model is only an approximate description of the original nonlinear system. If the model deviation is large, it may adversely affect the control performance. In order to ensure control effectiveness, the linearized reactor model often needs to be updated according to the actual operating state, which will increase the real-time calculation burden and thus reduce the response speed of the control system. In order to overcome the limitations brought by the above linearization model, the research on nonlinear generalized predictive control based on continuous models has emerged, which can effectively handle complex nonlinear systems with constraints.

[0006] In addition, in the reactor power load tracking control, system disturbance can significantly affect the control performance of the controller. Due to the strong nonlinearity, parameter time-varying and multivariable coupling characteristics of the nuclear reactor itself, when the controller does not consider the external disturbance existing in the system, the core power response will deviate, thereby reducing the tracking accuracy and robustness of the controller. If the disturbance of the system is not effectively observed and compensated, the system may not respond to load changes in time, affecting the operation efficiency and safety of the nuclear power plant. Therefore, in order to guarantee the control performance, the observation and compensation of the disturbance are particularly important in the load tracking control.

[0007] In order to improve the accuracy and anti-disturbance of the reactor core load tracking, a new control strategy is needed to be provided, which can realize load tracking and disturbance compensation control at the same time, enhance the suppression ability of the control system to the disturbance, and improve the robustness of the whole system. SUMMARY

[0008] The purpose of the present application is to provide a DC-NGPC reactor load tracking control method and system fusing disturbance compensation, by introducing a nonlinear disturbance observer, using the state information of the system to obtain the disturbance observation value, and then applying the disturbance observation value to the nonlinear generalized predictive controller to realize disturbance compensation control, thereby enhancing the robustness of the control system.

[0009] To this end, the present application provides a DC-NGPC reactor load tracking control system fusing disturbance compensation, comprising: a nonlinear disturbance observer, configured to calculate a nonlinear disturbance estimation value of the reactor system according to the control rod speed and the state feedback information output by the reactor system; a nonlinear generalized predictive controller based on disturbance compensation, configured to provide a predictive control law for the reactor load tracking control, the predictive control law being configured to calculate the control rod speed according to the power trajectory provided by the outside, the state feedback information output by the reactor system, and the nonlinear disturbance estimation value calculated by the nonlinear disturbance observer; wherein the control rod speed is provided to the reactor system after being limited in amplitude, so as to track the load of the reactor system.

[0010] According to another aspect of the present application, a DC-NGPC reactor load tracking control method fusing disturbance compensation is provided, comprising the following steps: S1, estimating a nonlinear disturbance observation value of the reactor system according to the control rod speed and the state information output by the reactor system; S2, providing a nonlinear generalized predictive control law for the reactor load tracking control, the predictive control law being configured to calculate the control rod speed according to the power trajectory provided by the outside, the state feedback information output by the reactor system, and the nonlinear disturbance estimation value calculated by the nonlinear disturbance observer; S3, the control rod speed is provided to the reactor system after being limited in amplitude, so as to track the load of the reactor system.

[0011] The present application is directed to the problem of disturbance in reactor predictive control, and the nonlinear disturbance observer is introduced innovatively. The observer can effectively estimate the disturbance amount by using the state information of the system, and provide reliable basis for the subsequent compensation control. And the disturbance observation quantity estimated by the nonlinear disturbance observer is introduced into the nonlinear generalized predictive controller, and the dynamic compensation of the disturbance is effectively realized. The fusion control strategy significantly enhances the disturbance suppression ability of the control system, and improves the robustness of the whole system.

[0012] In addition to the purposes, features and advantages described above, the present application has other purposes, features and advantages. The present application will be further described below with reference to the drawings. BRIEF DESCRIPTION OF DRAWINGS

[0013] The drawings accompanying the specification of this application form a part thereof, serve to provide further understanding of the application, and together with the description of the application, explain the application. The drawings do not constitute an undue limitation on the scope of the application. In the drawings: Figure 1 is a structural block diagram of the fusion disturbance compensation DC-NGPC reactor load tracking control system of the present application; Figure 2 shows the estimated curve of the step disturbance applied in the reactor disturbance experiment; Figure 3 shows the control effect of reactor load tracking under the traditional PID control strategy with step disturbance applied; Figure 4 shows the control effect of reactor load tracking under the NGPC control strategy with step disturbance applied; Figure 5 shows the control effect of reactor load tracking under the DC-NGPC+NDO control strategy of the present application with step disturbance applied; Figure 6 shows the trajectory tracking error under the three control strategies of PID, NGPC and DC-NGPC+NDO; Figure 7 shows the estimated curve of the sinusoidal disturbance applied in the reactor disturbance experiment; Figure 8 shows the control effect of reactor load tracking under the traditional PID control strategy with sinusoidal disturbance applied; Figure 9 shows the control effect of reactor load tracking under the NGPC control strategy with sinusoidal disturbance applied; Figure 10 shows the control effect of reactor load tracking under the DC-NGPC+NDO control strategy of the present application with sinusoidal disturbance applied; Figure 11The trajectory tracking errors under the three control strategies of PID, NGPC and DC-NGPC+NDO are shown. DETAILED DESCRIPTION

[0014] The present application will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0015] The model adopted by the present application is a dynamic model of a pressurized water reactor system, which is composed of a neutron kinetics equation, a thermal-hydraulic equation and a reactivity equation. In order to facilitate the design of the control system, these equations are subsequently written in a nonlinear state space form.

[0016] The reactor kinetics equation is generally expressed by a multi-group delayed neutron group. Since the point reactor kinetics equation of the multi-group delayed neutron has high computational complexity, the present application simplifies the multi-group delayed neutron into an equivalent model of a single-group delayed neutron to reduce the computational amount of the equation. The simplified kinetics equation is as follows:

[0017] (1)

[0018] (2)

[0019] wherein, is a relative neutron density, is a relative delayed neutron precursor density, is a total reactivity, is a delayed neutron fraction, is a prompt neutron generation time, is a delayed neutron precursor decay constant.

[0020] According to the law of conservation of energy, the thermal-hydraulic equation of the coolant and the fuel is as follows:

[0021] (3)

[0022] (4)

[0023] wherein, is an average temperature of the fuel rod, is a coolant outlet temperature, is a coolant inlet temperature, is a fuel power fraction, is a heat transfer coefficient of the fuel and the coolant, is a fuel heat capacity, is a coolant heat capacity. P0 is a rated power of the reactor, is a relative neutron density, and M is a mass flow heat capacity of the coolant.

[0024] The total reactivity in a nuclear reactor is generally considered to be composed of the reactivity change caused by control rod displacement, and the temperature effect of fuel temperature and coolant temperature. Therefore, the reactivity equation can be expressed as:

[0025] (5)

[0026] (6)

[0027] where, is the total reactivity, is the control rod integral value, is the fuel temperature coefficient, is the coolant temperature coefficient, is the overall reactivity value of the control rod, is the control rod speed. is the coolant outlet temperature, is the coolant inlet temperature, is the average temperature of the fuel rod, is the initial steady-state fuel temperature.

[0028] In combination with equations (1)-(6), the pressurized water reactor system model can be presented in the form of a nonlinear equation as follows:

[0029] (7)

[0030] The state variable of the system is defined as , the control rod speed is the input of the nonlinear state space model of the nuclear reactor system, i.e. , the output variable is , and the total disturbance of the system is . Then equation (7) can be further expressed in a nonlinear state space form:

[0031] (8)

[0032] In the equation,

[0033] , , .

[0034] For the nonlinear reactor system considering disturbance, the DC-NGPC predictive control law designed by the present application to meet the minimum performance index is:

[0035] (9)

[0036] In the equation, , , respectively the reference trajectory and its 1st and 2nd derivatives, is the disturbance compensation gain. is expressed as Lie derivative along is expressed as is expressed as Lie derivative along Lie derivative along Lie derivative along

[0037] With the control law, the controller can achieve good load tracking effect. As can be seen from equation (9), the system disturbance has been considered in the predictive control law. Therefore, in order to obtain the complete predictive control law and improve the robustness of the system, the value of the disturbance amount is needed.

[0038] In the reactor power load tracking control, the system disturbance will significantly affect the control performance of the controller. Due to the strong nonlinearity, parameter time-varying and multivariable coupling characteristics of the nuclear reactor itself, when the controller does not consider the external disturbance existing in the system, the core power response will deviate, thereby reducing the tracking accuracy and robustness of the controller.

[0039] Especially when using model predictive control, sliding mode control and other model-based control methods, the disturbance often causes the accumulation of prediction error, further affecting the controller's judgment of future behavior, leading to the deviation of control decision from the optimal. If the disturbance of the system is not effectively observed and compensated, the system may not respond to load changes in real time, affecting the operation efficiency and safety of the nuclear power plant. Therefore, in order to ensure the control performance, the observation and compensation of the disturbance are particularly important in the load tracking control.

[0040] The key to improving the anti-disturbance performance of the reactor core power predictive control system lies in enhancing the robustness of the nonlinear generalized predictive controller. Therefore, based on the nuclear reactor dynamics model, the nonlinear disturbance observer is introduced to realize effective estimation and compensation of external disturbance, thereby ensuring the dynamic response performance of the system.

[0041] When estimating the disturbance in the nuclear reactor control system, let the disturbance estimation value be , the disturbance estimation error be , and assume that the disturbance is bounded and slowly changing, that is, .

[0042] For the nonlinear model of the nuclear reactor (see equation (7)), the nonlinear disturbance observer designed by the present application is as follows:

[0043] (10)

[0044] wherein, is the state variable inside the observer, and , is the nonlinear function to be designed for the observer, is the gain of the observer, is the integral of in the first equation, and is the integral of in the first equation, and represents the value at the last time, and

[0045] (11)

[0046] From equation (8), we have:

[0047] (12)

[0048] Stability analysis of the nonlinear disturbance observer is performed, and a Lyapunov function is assumed as:

[0049] (13)

[0050] Taking the derivative of equation (13) and combining equation (12), we have:

[0051] (14)

[0052] According to the Lyapunov stability criterion, as long as a suitable is selected to make , the observer is asymptotically stable. Finally, substituting the estimated disturbance into equation (9), we have:

[0053] (15)

[0054] As can be seen from equation (15), the control strategy realizes the fusion of nonlinear generalized predictive control and nonlinear disturbance observer, has the ability to estimate unknown disturbances in the system in real time, can reconstruct the disturbance signal from the state and output of the system and introduce it into the control loop for compensation, significantly reduces the influence of disturbances on the prediction accuracy, and enhances the robustness and anti-interference ability of the controller.

[0055] The DC-NGPC+NDO control system designed in the application is shown in Figure 1 In the figure, is the relative neutron density; is the overall reactivity value of the control rod; is the prompt neutron generation time; is the prediction time domain; , , These are the reference trajectory and its first and second derivatives, respectively. To control the speed of the rod; These are the state variables inside the observer; For observer gain; The nonlinear function to be designed for the observer; This is an estimate of the interference; ; For disturbance compensation gain; , for along Lie derivative, for along The second-order Lie derivative.

[0056] For safety reasons, the operating speed of the control rod assembly is mechanically limited, i.e., rod speed limiter. For example, in a certain reactor, the maximum speed of the control rods is 72 steps per minute, and the reactor core height is approximately 3.7 meters. The control rod assembly requires approximately 300 steps to move from bottom to top. Therefore, it can be obtained that... The scope is:

[0057] (Unit: m / s)

[0058] Among them, values ​​greater than the upper limit are taken as the upper limit, and values ​​less than the lower limit are taken as the lower limit.

[0059] To verify the feasibility of the proposed nonlinear generalized predictive control strategy that integrates a nonlinear perturbation observer, the sampling time in the simulation was... The value is 0.0001, predicting the time domain. The value is 0.0006, and other reactor parameters are shown in Table 1.

[0060] Table 1. Reactor Model Parameter Table

[0061] Considering the complexity of reactor disturbances, this experiment uses both step and sinusoidal signals to represent the disturbances, and two sets of experiments were conducted to verify the feasibility of the proposed control strategy. The total system disturbance is... Add to state variables Above, that is, adding perturbations to the first four channels of the state vector, and As shown in equation (16).

[0062] (16)

[0063] I. Step Disturbance Compensation

[0064] The expected trajectory set in this example is: The power change characteristics, when the disturbance is a step signal, the specific disturbance parameters are shown in Table 2.

[0065] Table 2. Step Disturbance Parameters

[0066] The observer's gain is set to The perturbation values ​​observed by NDO are as follows Figure 2 As shown, NDO can quickly estimate disturbances and perform compensation.

[0067] Table 3. L2 Norm of Trajectory Tracking Error for Three Control Strategies

[0068] When the load tracking controller of a nuclear power plant reactor does not consider system disturbances, significant deviations may occur during actual operation. This is primarily manifested in the output power failing to accurately track the grid load demand, thus reducing the response accuracy and stability of the control system. Furthermore, the accumulation of disturbances may lead to large overshoot or steady-state errors during system operation, and even reduce the safety margin, affecting the safe and stable operation of the reactor. Therefore, this invention conducted simulation tests on PID, NGPC, and DC-NGPC+NDO control strategies respectively, and compared the control effects of the three strategies in the face of disturbances.

[0069] Figure 3 , Figure 4 and Figure 5 The control effects of the above control methods are demonstrated. From the trajectory tracking results, it can be seen that the PID, NGPC, and DC-NGPC+NDO control strategies can basically achieve trajectory tracking. The PID and NGPC control strategies can effectively track the desired power level, especially during the rise and fall phases, with rapid response and smooth control without significant overshoot. However, when the system experiences disturbances, the control becomes less effective. Figure 3 and Figure 4 It is evident that the control accuracy of PID and NGPC deteriorates, making it difficult to suppress the effects of disturbances. Figure 5 The trajectory tracking effect of the DC-NGPC+NDO control strategy proposed in this invention is demonstrated. It not only effectively achieves load tracking, but also achieves good results in disturbance suppression, enabling the reactor to have good control performance under complex operating conditions.

[0070] Figure 6The trajectory tracking errors of three control strategies are shown. It can be seen that the PID control strategy produces a large deviation. The NGPC control strategy shows good control performance in the early stages, but its error increases significantly when the system is disturbed, failing to achieve good trajectory tracking. In contrast, the DC-NGPC+NDO control strategy proposed in this invention also exhibits good control performance when the system is disturbed, with its tracking error generally kept within a small range. The three control strategies are constructed in the form of error vectors, and their L2 norms are shown in Table 3. The L2 norms of the error vectors also confirm the differences in trajectory tracking performance among the control strategies.

[0071] II. Sine Disturbance Compensation

[0072] The expected trajectory set in this example is: When the disturbance is a sinusoidal signal, its specific parameters are shown in Table 4.

[0073] Table 4. Sinusoidal Disturbance Parameter Table

[0074] Observer gain set to , Figure 7 The results of the nonlinear disturbance observer's (NDO) estimation of the disturbance are shown. It can be seen that the NDO can accurately and quickly estimate the disturbance dynamically and feed the estimated value back to the controller for real-time compensation, effectively improving the system's disturbance rejection capability and control stability.

[0075] Figure 8 , Figure 9 and Figure 10 The control effects of three control strategies—PID, NGPC, and DC-NGPC+NDO—are demonstrated when facing sinusoidal disturbances. The trajectory tracking results show that all three strategies can basically achieve target trajectory tracking. However, from... Figure 8 and Figure 9 The magnified view clearly shows that both PID and NGPC exhibit significant oscillations under perturbation, indicating limited perturbation suppression capabilities. In contrast, Figure 10 The demonstrated DC-NGPC+NDO control strategy not only achieves precise load tracking, but also exhibits strong robustness under disturbance conditions, effectively improving the reactor's control performance under complex operating conditions.

[0076] Table 5. L2 Norm of Trajectory Tracking Error for Three Control Strategies

[0077] Figure 11This paper compares the errors of three control strategies in trajectory tracking under sinusoidal disturbance conditions. It can be seen that the PID control strategy exhibits a large tracking deviation and low accuracy throughout the overall control process. While the NGPC control strategy shows relatively stable overall control performance, its tracking error is still significantly higher than that of DC-NGPC+NDO due to the presence of disturbances. In contrast, the proposed DC-NGPC+NDO control strategy maintains high control accuracy even under disturbances, with its tracking error consistently remaining within a small range, fully demonstrating superior disturbance suppression capability and system robustness.

[0078] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A DC-NGPC reactor load tracking control system with integrated disturbance compensation, characterized in that, include: The nonlinear disturbance observer is used to calculate the nonlinear disturbance estimate of the reactor system based on the control rod velocity and the state feedback information output by the reactor system. A disturbance-compensated nonlinear generalized predictive controller is used to provide the predictive control law for reactor load tracking control. This predictive control law calculates the control rod velocity based on the power trajectory provided by the external environment, the state feedback information output by the reactor system, and the nonlinear disturbance estimate calculated by the nonlinear disturbance observer. The control rod speed is provided to the reactor system after being limited to track and control the reactor system load.

2. The DC-NGPC reactor load tracking control system with integrated disturbance compensation according to claim 1, characterized in that, The reactor system is a pressurized water reactor system.

3. The DC-NGPC reactor load tracking control system with integrated disturbance compensation according to claim 2, characterized in that, The state variables of the reactor system are: , The relative neutron density, For the relatively slow-emitting neutron precursor nuclear density, It is the average temperature of the fuel rods. It is the coolant outlet temperature. For the integral value of the control rod, To control the rod speed, i.e. As the input to the nonlinear state-space model of the nuclear reactor system, the output variable is The total disturbance of the system is The nonlinear state-space expression of the nonlinear equations of the pressurized water reactor system model is as follows: ； in, For nonlinear functions of the reactor system, , .

4. The DC-NGPC reactor load tracking control system with integrated disturbance compensation according to claim 3, characterized in that, The expression for the nonlinear disturbance observer is as follows: ； in, For the perturbation estimation of the observer, Let be the state variable inside the observer, and have , for The integral, and This represents the state variables inside the observer at the previous moment. The nonlinear function to be designed for the observer, For observer gain, for The derivative of .

5. The DC-NGPC reactor load tracking control system with integrated disturbance compensation according to claim 4, characterized in that, The formula for calculating the predictive control law of the nonlinear generalized predictive controller is as follows: ； in, The relative neutron density; To control the overall reactivity value of the rod; For the instantaneous neutron generation time; For prediction in the time domain; , , These are the load reference trajectory and its first and second derivatives, respectively; For disturbance compensation gain, ; , for along Lie derivative, for along The second-order Lie derivative, Represented as along Lie derivative, Represented as Along Find the derivative of Lie and then follow along Find the derivative of Lie.

6. A DC-NGPC reactor load tracking control method incorporating disturbance compensation, characterized in that, Includes the following steps: S1. Estimate the nonlinear disturbance observations of the reactor system based on the control rod velocity and the state information output by the reactor system. S2. Provides a nonlinear generalized predictive control law for reactor load tracking control. This predictive control law is used to calculate the control rod velocity based on the power trajectory provided by the outside world, the state feedback information output by the reactor system, and the nonlinear disturbance estimate calculated by the nonlinear disturbance observer. S3. The control rod speed is provided to the reactor system after being limited to track and control the reactor system load.

7. The DC-NGPC reactor load tracking control method with integrated disturbance compensation according to claim 6, characterized in that, The reactor system is a pressurized water reactor system.

8. The DC-NGPC reactor load tracking control method with integrated disturbance compensation according to claim 7, characterized in that, The state variables of the reactor system are: , The relative neutron density, For the relatively slow-emitting neutron precursor nuclear density, It is the average temperature of the fuel rods. It is the coolant outlet temperature. For the integral value of the control rod, To control the speed of the rod As the input to the nonlinear state-space model of the nuclear reactor system, the output variable is The total disturbance of the system is The nonlinear state-space expression of the nonlinear equations of the pressurized water reactor system model is as follows: ； in, For nonlinear functions of the reactor system, , .

9. The DC-NGPC reactor load tracking control method with integrated disturbance compensation according to claim 8, characterized in that, The formula for calculating the observed value of the nonlinear disturbance is as follows: ； in, For the perturbation estimation of the observer, Let be the state variable inside the observer, and have , for The integral, and This represents the state variables inside the observer at the previous moment. The nonlinear function to be designed for the observer, For observer gain, for The derivative of .

10. The DC-NGPC reactor load tracking control method with integrated disturbance compensation according to claim 9, characterized in that, The formula for calculating the predictive control law is as follows: ； in, The relative neutron density; To control the overall reactivity value of the rod; For the instantaneous neutron generation time; For prediction in the time domain; , , These are the load reference trajectory and its first and second derivatives, respectively; For disturbance compensation gain, ; , for along Lie derivative, for along The second-order Lie derivative, Represented as along Lie derivative, Represented as Along Find the derivative of Lie and then follow along Find the derivative of Lie.

Images