A data-driven economic model predictive control method for nonlinear power systems

Abstract

The application provides a data-driven economic model predictive control method of a nonlinear power system, and belongs to the technical field of power system control. The method of the application firstly linearizes the system by adopting a Koopman operator method, combines the Koopman operator theory with a neural network, obtains the system matrix by using a least square method, and updates the neural network parameters according to errors by adopting a gradient descent method; after the system linearization is completed, an economic model predictive controller based on data driving is adopted to control the system, the optimization target is solved to obtain the optimal control amount at each sampling period, so that the minimum operation cost demand is obtained. The economic model predictive control is adopted in the application, the economic model predictive control can combine the economic optimization and the process control of the power system, realizes the transient optimization and the real-time control of the system to improve the control performance of the system, and can process the constraints in the power system and has good stability and robustness.

Description

Technical Field

[0001] This invention relates to a data-driven economic model predictive control method for nonlinear power systems, belonging to the field of power system control technology. Background Technology

[0002] In recent years, the energy crisis and environmental pollution have increasingly drawn attention. Wind, solar, and other renewable energy sources are relatively environmentally friendly and possess vast resource reserves, making them a potential mainstay in the global energy transition. Therefore, related technologies for new energy power generation systems are developing rapidly. However, with the increasing demands on power generation system control, several problems urgently need to be addressed. First, most new energy power generation systems exhibit strong nonlinearity. Second, in new energy power generation systems, the controller's task is not only to meet the system's control requirements and ensure normal operation, but also to consider economic optimization and improve system efficiency. Finally, the safe and stable operation of new energy power generation systems is crucial, subject to very strict constraints and stringent stability requirements within the power system.

[0003] Against this backdrop, a data-driven economic model predictive control algorithm provides a novel power system control method. Economic model predictive control combines economic optimization and process control of the power system, achieving transient optimization and real-time control to improve system performance. It can handle constraints in the power system and exhibits good stability and robustness. For system nonlinearity, dynamic system construction based on Koopman theory constructs an approximate linear model of the system based on system measurement data. Therefore, the Koopman operator can effectively utilize system data in the smart grid, and the resulting linearized system model can be perfectly applied to economic model predictive control. Summary of the Invention

[0004] Technical problem: The technical problem that this invention aims to solve and the objective it seeks to achieve.

[0005] This invention aims to solve the problem that strong nonlinear elements exist in new energy power generation systems, making it impossible to use linear control methods for control optimization. Nonlinear elements can cause great difficulties in control and have a certain impact on the stability of the system. Therefore, this invention uses a data-driven economic model prediction algorithm to linearize the nonlinear system, and then uses the economic model prediction method to directly predict and optimize the economic benefits of the system, thereby achieving the optimal system cost loss.

[0006] Technical solution: The complete technical means and methods of this invention.

[0007] This invention proposes a data-driven economic model predictive control method for nonlinear power systems, aiming to solve nonlinear problems and control stability issues in new energy power generation systems. Based on Koopman theory, economic model predictive control can provide an accurate linearized dynamic model of the system based on system data, improving the economic efficiency and safety of system operation.

[0008] A data-driven economic model-based predictive control method includes the following steps:

[0009] The nonlinear system is approximated as a linear time-invariant system using the Koopman operator method:

[0010] ;

[0011] In the formula The matrix is ​​the state matrix. For the control matrix, For the output matrix, For system status, The system state at the next moment. For system control variables, This is the system output;

[0012] use Let represent the state at the next moment. Then the state and input of the nonlinear system are as follows:

[0013] ;

[0014] in, These represent the system's state vector, the state vector at the next moment, and the system's control vector, respectively. By collecting data from the dynamic system, the following extended data matrix is ​​obtained:

[0015] ;

[0016] in It is the linear space state after transformation by the Koopman neural network. and Let represent the system state after the transformation and the system state at the next moment, respectively. Then, the state-space equation of the system is obtained by using the linear least squares method:

[0017] ;

[0018] in It is the Frobenius norm. The two optimization problems above can be solved to obtain the system dynamic matrix under the linear system state. , and Therefore, through the above transformation, the system has achieved linearization.

[0019] The neural network also needs to be trained during each linearization process. The purpose of training is to make the function... Approximating nonlinear systems, due to It is a complex function, therefore it requires system-level data processing. Multiple revisions were made.

[0020] System Matrix and By solving vectors arrive The linear least squares regression is used to obtain the system dynamic model. The accuracy of the system dynamic model obtained by the linear least squares regression algorithm is evaluated by constructing an error function. The actual data is compared with the data obtained by the estimated regression model, and the error between the two is expressed as the sum of squares:

[0021] ;

[0022] Regarding the obtained error Apply gradient descent to the function. On the neural network parameters, by adjusting the function Adjusting the parameters makes By gradually decreasing the size of the function and through repeated training and adjustments, the function can accurately transform the original system into a linear system in Koopman's invariant subspace, thus achieving precise linearization of the nonlinear system.

[0023] Regarding the design process of a data-driven economic model predictive controller, firstly, a generalized economic objective function is established based on the economic indicators and control requirements of the power system. Then, the optimization problem of the system is constructed by combining a data-driven linearized model. Finally, the overall algorithm flow and structural design are given.

[0024] In economic model predictive control, the objective function mainly includes two aspects: economic indicators for system optimization and process control indicators. The primary objectives are to improve the economic efficiency of the system operation (e.g., increasing the output power of a new energy power generation system and reducing system operating costs) and to ensure the stability and safety of the system operation (e.g., reducing large fluctuations in system state and frequent actions of actuators). The form of the objective function is no longer limited to a quadratic tracking function but can be written in a generalized form, such as nonlinear or nonconvex forms.

[0025] In optimizing the time domain Within this system, the overall objective function can be written as:

[0026] ;

[0027] in This represents the operating cost of the entire system, while This represents the impact of system state fluctuations on economic operation. Based on the system's linearization model, the economic model predictive controller will solve the following optimization problem in each sampling period:

[0028] ;

[0029] In the formula Original spatial state go through The state of the linear system after function mapping, It is the optimal control quantity obtained after solving the optimization problem. yes The optimal state of the system at a given time is determined by the system output matrix. Mapping the upgraded state back to the original space yields the original space state. .

[0030] As can be seen from the optimization problem above, the economic model forecasting controller, through... Solving optimization problems of linear systems in a coordinate system can greatly reduce the computational complexity of the controller and improve its real-time performance.

[0031] The Koopman-EMPC method for identification and optimal control of nonlinear power systems is mainly structured into two modules: a system identification module and an optimal control module. The system identification module primarily solves the linear model and trains the neural network. The economic model predictive control module mainly obtains the optimal control quantity for the nonlinear system through iterative optimization of the Koopman linear system.

[0032] Furthermore, in economic model predictive control, the objective function can be written in a more generalized form, such as a nonlinear or nonconvex form. Therefore, the system's objective function may exist... Therefore, traditional model predictive control stability analysis methods are not applicable to economic model predictive control, necessitating the development of new stability analysis methods. This invention uses dissipative theory and auxiliary objective functions to prove the asymptotic stability of the system under economic model predictive control.

[0033] Beneficial effects:

[0034] This invention linearizes the nonlinear components of a system by applying Koopman operator theory, resulting in a high-dimensional linear system model, which then enables the use of linear system control methods. Subsequently, economic model predictive control is employed for control optimization, directly linking the system state to its economic cost and allowing for direct optimization of the system's economic benefits to achieve the optimal system cost loss. Attached Figure Description

[0035] Figure 1 This refers to a data-driven economic model predictive control method based on Koopman theory.

[0036] Figure 2 This refers to the linearization process of a system based on the Koopman operator theory;

[0037] Figure 3 A structural diagram for predictive control stability analysis of economic models;

[0038] Figure 4 A block diagram of the Koopman-EMPC strategy for nonlinear power systems;

[0039] Figure 5 This is a schematic diagram of a point absorption wave energy converter.

[0040] Figure 6(a) shows the states of different linear models of wave energy converters. Predictive comparison;

[0041] Figure 6(b) shows the states of different linear models of wave energy converters. Predictive comparison;

[0042] Figure 7(a) shows the system state trajectories of EMPC strategies based on different linear models;

[0043] Figure 7(b) shows the input trajectories of EMPC strategies based on different linear models;

[0044] Figure 8(a) shows the power generation of wave energy converters based on different linear models;

[0045] Figure 8(b) shows the total energy acquired by wave energy converters based on different linear models. Detailed Implementation

[0046] This invention proposes a data-driven economic model predictive control method for nonlinear power systems, which will be further explained below with reference to the accompanying drawings.

[0047] A data-driven economic model predictive control method for nonlinear power systems includes the following steps:

[0048] Consider a deep learning-based Koopman system linearization framework, such as... Figure 2 As shown, this invention considers approximating the nonlinear system as a linear time-invariant system as follows:

[0049] ;

[0050] In the formula The matrix is ​​the state matrix. For the control matrix, For the output matrix, For system status, The system state at the next moment. For system control variables, This is the system output. The following uses... Let represent the state at the next moment. Then the state and input of the nonlinear system are as follows:

[0051] ;

[0052] in, These represent the system's state vector, the state vector at the next moment, and the system's control vector, respectively. By collecting data from the dynamic system, the following extended data matrix is ​​obtained:

[0053] ;

[0054] in It is the linear space state after transformation by the Koopman neural network. and Let represent the system state after the transformation and the system state at the next moment, respectively. Then, the state-space equation of the system can be obtained using the linear least squares method:

[0055] ;

[0056] in This is the Frobenius norm. The two optimization problems above can be solved to obtain the system dynamics matrix under linear system conditions. , and Therefore, through the above transformation, the system has achieved linearization.

[0057] To improve the accuracy of the model after linearization, the neural network needs to be trained during each linearization process. The purpose of training is to make the function... Approximating nonlinear systems. Because... It is a complex function, therefore it requires system-level data processing. Multiple revisions were made.

[0058] System Matrix and By solving vectors arrive The linear least squares regression model is used to obtain the system dynamic model. This invention evaluates the accuracy of the system dynamic model obtained by the linear least squares regression algorithm by constructing an error function. The actual data is compared with the data obtained from the estimated regression model, and the error between the two is expressed as the sum of squares:

[0059] ;

[0060] Regarding the obtained error Apply gradient descent to the function. On the neural network parameters, by adjusting the function Adjusting the parameters makes The function gradually decreases. After multiple training and adjustments, the function can accurately transform the original system into a linear system in the Koopman invariant subspace, achieving precise linearization of the nonlinear system.

[0061] Regarding the design process of a data-driven economic model predictive controller, firstly, a generalized economic objective function is established based on the economic indicators and control requirements of the power system. Then, the optimization problem of the system is constructed by combining a data-driven linearized model. Finally, the overall algorithm flow and structural design are given.

[0062] In economic model predictive control, the objective function mainly includes two aspects: economic indicators for system optimization and process control indicators. The primary objectives are to improve the economic efficiency of the system operation (e.g., increasing the output power of a new energy power generation system and reducing system operating costs) and to ensure the stability and safety of the system operation (e.g., reducing large fluctuations in system state and frequent actions of actuators). The form of the objective function is no longer limited to a quadratic tracking function but can be written in a generalized form, such as nonlinear or nonconvex forms.

[0063] In optimizing the time domain Within this system, the overall objective function can be written as:

[0064] ;

[0065] in This represents the operating cost of the entire system, while This represents the impact of system state fluctuations on economic operation. Combining the system linearization model, the economic model predictive controller will solve the following optimization problem in each sampling period:

[0066] ;

[0067] In the formula Original spatial state go through The state of a linear system after function mapping, the system output matrix Mapping the upgraded state back to the original space yields the original space state. As can be seen from the above optimization problem, the economic model predictive controller, through... Solving optimization problems of linear systems in a coordinate system can greatly reduce the computational complexity of the controller and improve its real-time performance.

[0068] The Koopman-EMPC method for identification and optimal control of nonlinear power systems is mainly structured into two modules: a system identification module and an optimal control module. The system identification module primarily solves the linear model and trains the neural network. The economic model predictive control module mainly obtains the optimal control quantity for the nonlinear system through iterative optimization of the Koopman linear system.

[0069] Furthermore, in economic model predictive control, the objective function can be written in a more generalized form, such as a nonlinear or nonconvex form. Therefore, the system's objective function may exist... Therefore, traditional model predictive control stability analysis methods are not applicable to economic model predictive control, necessitating the development of new stability analysis methods. This invention uses dissipative theory and auxiliary objective functions to prove the asymptotic stability of the system under economic model predictive control. The stability analysis process is as follows: Figure 3 As shown, where It is the objective function under the optimal solution, since the original single objective function exists. Therefore, we construct an auxiliary single objective function to satisfy... It can be proven that it is asymptotically stable under the auxiliary objective function. The auxiliary objective function is defined as follows: During the process, it can be observed that the auxiliary objective function and the original objective function... The difference between them is constant. Therefore, the two objective functions have the same convergence and optimal solution, and it can be deduced that the system is asymptotically stable under the predictive control of the economic model.

[0070] For those skilled in the art, any changes, modifications, substitutions, and variations made to the embodiments without departing from the principles and spirit of the present invention, based on the teachings of the present invention, still fall within the protection scope of the present invention.

[0071] For example

[0072] Example 1:

[0073] This invention focuses on the theoretical implementation of mainstream new energy power generation systems, and conducts related research. For the control and optimization of small-scale single new energy systems, such as wave converter power generation systems, an economic model predictive control strategy based on the Koopman operator is adopted. The structure of the power generation system is as follows: Figure 5 As shown. The nonlinear mathematical model of the wave energy converter can be expressed as:

[0074] ;

[0075] in , and These represent the vertical positions of the surface buoy and the ocean waves, respectively. It is the mass of the floating buoy. For wave excitation force, For radiation force, It is a viscous force. For still water restoring force, This is the control input for the system.

[0076] The above system adopts an economic model predictive control strategy based on the Koopman operator, and the simulation sampling time is selected. The time is 0.1s, and the number of boundaries is... The value is 20, and the parameter matrix of the cost function is... and The number of radial basis functions The value is 400, and the center is randomly selected in a uniform distribution. In the simulation results, Figure 6 shows that under the same control input and fluctuation conditions, the state trajectory of the actual system is almost identical to that of the Koopman lifting linear model. However, for the linear system model using the fourth-order Runge-Kutta method, the state trajectory differs significantly from the actual system. Therefore, the proposed Koopman lifting linear model is more accurate than the Runge-Kutta linear model. Figure 7 shows that after adding system constraints, the system's state and input can operate smoothly within the constraints, and Figure 8 shows that the model based on Koopman theory is sufficiently accurate, and the output power of the proposed Koopman-EMPC method is greater than that of the locally linearized EMPC method. During the simulation time, the proposed Koopman-EMPC method achieves a 5.61% increase in energy compared to the locally linearized EMPC method. In summary, using the proposed Koopman-EMPC method, the system's state and input always operate within the constraints, and compared to traditional model predictive control, the output power of the system is significantly increased under economic model predictive control, resulting in a marked improvement in the system's economy.

Claims

1. A data-driven economic model predictive control method for nonlinear power systems, characterized in that, Includes the following steps: 1) System linearization: The system is linearized using the Koopman operator method. The Koopman operator theory is combined with the neural network, and the system matrix is ​​obtained using the least squares method. The neural network parameters are updated using the gradient descent method according to the error. The nonlinear mathematical model of the wave energy converter is expressed as: ； in , Represents the position of the surface buoy. It is the mass of the floating buoy. For wave excitation force, For radiation force, For viscous force, For still water restoring force, For system control input; 2) After the system is linearized, a data-driven economic model predictive controller is used to control the system. The optimal control quantity is obtained by solving the optimization objective in each sampling period to minimize the operating cost requirement. Specifically as follows: In optimizing the time domain The overall objective function of the system can be written as: ； in This represents the operating cost of the entire system, while This represents the impact of system state fluctuations on economic operation. Based on the system's linearization model, the economic model predictive controller will solve the following optimization problem in each sampling period: ； In the formula Original spatial state go through The state of the linear system after function mapping, It is the optimal control quantity obtained after solving the optimization problem, and the system outputs the matrix. Mapping the upgraded state back to the original space yields the original space state. .

2. The data-driven economic model predictive control method for nonlinear power systems according to claim 1, characterized in that, Step 1) specifically includes: Using the Koopman operator method, the nonlinear system is approximated as a linear time-invariant system as follows: ； In the formula The state matrix, For the control matrix, For the output matrix, For system status, The system state at the next moment. For system control variables, The system output is a state matrix. use Let represent the state at the next moment. Then the state and input of the nonlinear system are as follows: ； in, These represent the system's state vector, the state vector at the next moment, and the system's control vector, respectively. By collecting data from the dynamic system, the following extended data matrix is ​​obtained: ； in It is the linear space state after transformation by the Koopman neural network. and Let represent the system state after the transformation and the system state at the next moment, respectively. Then, the state-space equation of the system is obtained by using the linear least squares method: ； in It is the Frobenius norm. The above equation, when solved for the two optimization problems, yields the system dynamic matrix under linear system conditions. , and Therefore, through the above transformation, the system has achieved linearization.

3. The data-driven economic model predictive control method for nonlinear power systems according to claim 2, characterized in that, The neural network also needs to be trained during each linearization process. The purpose of training is to make the function... Approximating nonlinear systems, due to It is a complex function, therefore it requires system-level data processing. Multiple revisions were made; System Matrix and By solving vectors arrive The linear least squares regression is used to obtain the system dynamic model. The accuracy of the system dynamic model obtained by the linear least squares regression algorithm is evaluated by constructing an error function. The actual data is compared with the data obtained by the estimated regression model, and the error between the two is expressed as the sum of squares: ； Regarding the obtained error Apply gradient descent to the function. On the neural network parameters, by adjusting the function Adjusting the parameters makes By gradually decreasing the size of the function and through repeated training and adjustments, the function accurately transforms the original system into a linear system in Koopman's invariant subspace, thus achieving precise linearization of the nonlinear system.

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