Thermal power generating unit linear model identification method based on Koopman operator
Through the linear model identification method of thermal power sets based on Koopman operator, the problems of large calculation burden and low prediction accuracy in dynamic modeling of thermal power sets are solved, and higher prediction accuracy and lower calculation burden are achieved.
Patent Information
- Application Number
- CN202411671723.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-21
- Publication Date
- 2025-03-25
AI Technical Summary
When dynamic modeling in thermal power units is performed in the prior art, it is difficult to effectively reduce the computational burden and shorten the calculation time, while improving prediction accuracy and identification accuracy.
The linear model identification method of thermal power sets based on Koopman operator is used to collect input-output data, construct new states and improvement functions, construct data matrix, set optimization problems, and solve the optimal delay using the least squares solution and mutual correlation coefficient. Finally, the original state is extracted using the EDMD correction method of the projection matrix.
It achieves higher prediction accuracy, reduces calculation burden and shortens calculation time, and is more in line with actual measurement results.
Smart Images
Figure CN119689846A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a modeling method suitable for a coordinated control system of a thermal power unit, in particular to a linear model identification method of a thermal power unit based on a Koopman operator. Background Art
[0002] The coordinated control system of thermal power units includes the control of steam temperature and pressure on the boiler side. In the context of thermal power units being responsible for frequency and peak regulation of the power grid, the operating conditions of thermal power units need to vary over a wide range, which poses a challenge to the control of steam temperature and pressure on the boiler side, and further affects subsequent emissions such as desulfurization and denitrification.
[0003] At present, control algorithms represented by model predictive control, Smith prediction, state feedback control, etc. are replacing traditional PID (i.e. proportional integral differential) control, and have played an important role in improving the quality of steam temperature and pressure control. However, this type of control algorithm requires modeling of the controlled process, and the dynamic characteristics of thermal power units under different loads are significantly different.
[0004] In response to the above problems, the prior art has studied the dynamic modeling methods of the controlled objects of thermal power units from different angles. When studying the model predictive control problem of nonlinear systems, one prior art is to obtain the Wiener model, bilinear model, etc. of the nonlinear system, and design a nonlinear model predictive controller based on this model; another prior art is to linearize the nonlinear model. The earliest research on model predictive control was based on linear systems, so the model predictive control theory of linear systems is relatively complete, which also makes the linearization of nonlinear models into linear system models the mainstream solution for predictive control theory research. Commonly used system-based linearization methods include local linearization and feedback linearization. Generally speaking, the model predictive controller designed for nonlinear systems needs to solve non-convex optimization problems at each sampling moment, which has a heavy solution burden and a long calculation time, which has also become a shortcoming of model predictive control in practical applications. Summary of the invention
[0005] In order to solve the technical problems existing in the above-mentioned prior art, the present invention provides a linear model identification method for thermal power units based on the Koopman operator, which can reduce the computational burden, shorten the computational time, and improve the prediction accuracy and identification accuracy.
[0006] According to one aspect of the present invention, a method for identifying a linear model of a thermal power plant based on a Koopman operator is provided, which comprises the following steps:
[0007] (1) collecting input-output data of a system to be identified, wherein the system to be identified is a thermal power unit;
[0008] (2) constructing a new state of the system to be identified based on the collected input-output data and selecting a lifting function, and constructing a data matrix using the new state and the lifting function to set the optimization problem to be solved and the parameters to be optimized;
[0009] (3) Solve the matrix of the system to be identified using the least squares method and solve the optimal delay based on the mutual correlation coefficient;
[0010] (4) Use the EDMD correction method based on the projection matrix to extract the original state of the system to be identified.
[0011] In the above-mentioned method for identifying a linear model of a thermal power plant based on the Koopman operator, the method further includes the following steps: (5) performing open-loop prediction using the identification model.
[0012] In the above-mentioned method for identifying a linear model of a thermal power plant based on the Koopman operator, in step (2), the new state is defined as the following formula:
[0013]
[0014] Among them, n d is the time delay, is the parameter to be optimized, u and y are the input data and output data of the system to be identified respectively, and k is the running time step of the system to be identified.
[0015] In the above-mentioned method for identifying a linear model of a thermal power plant based on the Koopman operator, in step (2), the selected lifting function is expressed as the following formula:
[0016]
[0017] Among them, the radial basis function parameters Follows uniform distribution, n y is the dimension of the output data y of the system to be identified, N rbf is the number of radial basis functions used.
[0018] In the above-mentioned method for identifying a linear model of a thermal power plant based on the Koopman operator, in step (2), the data matrix is constructed as follows:
[0019]
[0020] Among them, n ψ is the dimension of the lifting function, L is the total time step of the collected data, n uis the dimension of the input data u of the system to be identified, Ψ represents the data matrix constructed by a lifting function with a step size of L, Ψ' represents Ψ shifted backward for one moment, U represents the matrix of collected input data, and Y represents the matrix of collected output data.
[0021] In the above-mentioned method for identifying a linear model of a thermal power plant based on the Koopman operator, in step (2), the optimization problem to be solved is expressed as the following formula:
[0022]
[0023] Among them, A and B are the system matrix and input matrix of the system to be solved and identified, respectively, and C is the output matrix of the system to be solved and identified.
[0024] In the above-mentioned method for identifying a linear model of a thermal power plant based on the Koopman operator, in step (3), the matrix of the system to be identified is solved according to the least squares method, and the analytical solution is expressed as the following formula:
[0025]
[0026] in, represents the Moore–Penrose generalized inverse.
[0027] In the above-mentioned method for identifying a linear model of a thermal power plant based on the Koopman operator, in step (3), the method for solving the optimal time delay according to the mutual correlation coefficient includes:
[0028] Set input data u k And the output data y k The mutual correlation coefficient is expressed as follows:
[0029]
[0030] Based on the mutual correlation coefficient, a set of optimal time delays is obtained, and the set of optimal time delays is expressed as the following formula:
[0031]
[0032] Where S represents the maximum lag or maximum advance time step, and the correlation coefficient R uy (m) represents the correlation between the input data u and the output data y that are lagged or advanced by m time steps, D is the selected regional limit, and Δ is a random term used to reduce the interference of random factors.
[0033] In the above-mentioned method for identifying the linear model of a thermal power plant based on the Koopman operator, in step (4), the original state of the system to be identified extracted by the EDMD correction method based on the projection matrix is expressed as the following formula:
[0034]
[0035] Among them, the projection matrix I represents the unit matrix and 0 represents the zero matrix.
[0036] In the above-mentioned method for identifying a linear model of a thermal power plant based on the Koopman operator, in step (5), an open-loop prediction is performed by iterating the identification model represented by the following formula:
[0037]
[0038] y k+1 =Cψ(ξ k+1 ),
[0039] k=k+1.
[0040] Beneficial effects: The linear model identification method of a thermal power unit based on the Koopman operator of the present invention has higher prediction accuracy, is more consistent with actual measurement results, and can reduce the calculation burden and shorten the calculation time. BRIEF DESCRIPTION OF THE DRAWINGS
[0041] The above and other aspects, features and advantages of the embodiments of the present invention will become more apparent through the following description in conjunction with the accompanying drawings, in which:
[0042] Figure 1 is a flow chart of a method for identifying a linear model of a thermal power plant based on a Koopman operator according to an embodiment of the present invention;
[0043] Figure 2 is the input-output data of a 900MW thermal power unit (i.e., the system to be identified) according to an embodiment of the present invention;
[0044] Figure 3 It is a comparison chart of prediction results using the linear identification model of a thermal power unit based on the Koopman operator according to an embodiment of the present invention. DETAILED DESCRIPTION
[0045] Hereinafter, specific embodiments of the present invention will be described in detail with reference to the accompanying drawings. However, the present invention may be implemented in many different forms, and the present invention should not be construed as being limited to the specific embodiments set forth herein. On the contrary, these embodiments are provided to explain the principles of the present invention and their practical applications, so that other persons skilled in the art can understand the various embodiments of the present invention and various modifications suitable for specific intended applications.
[0046] As used herein, the term "including" and its variations represent open terms, meaning "including but not limited to". The terms "based on", "according to", etc. mean "based at least in part on", "based at least in part on". The terms "one embodiment" and "an embodiment" mean "at least one embodiment". The term "another embodiment" means "at least one other embodiment". The terms "first", "second", etc. may refer to different or the same objects. Other definitions may be included below, whether explicit or implicit. Unless the context clearly indicates otherwise, the definition of a term is consistent throughout the specification.
[0047] Figure 1 The present invention is a flowchart of a method for identifying a linear model of a thermal power plant based on a Koopman operator according to an embodiment of the present invention.
[0048] Reference Figure 1 In step S110, the input-output data (u k ,y k Here, the collected data does not need to include the internal state data of the system to be identified. Where u and y are the input data and output data of the system to be identified, respectively (for example, Figure 2 In the above equation, the input data is the feed water volume, and the output data is the main steam pressure), and the subscript k is the operating time step of the system to be identified.
[0049] In step S120, based on the collected input-output data (u k ,y k ) construct a new state of the system to be identified and select a lifting function, and use the new state and the lifting function to construct a data matrix to set the optimization problem to be solved and the parameters to be optimized.
[0050] Specifically, the new state ξ k It is defined as the following formula 1.
[0051]
[0052] Among them, n d is the delay, which is the parameter to be optimized. Here, the new state ξ k The definition is to convert the past n dThe output data at the kth moment is superimposed on the output data at the current kth moment, that is, the current new state ξ k Is to y k Joint representation to make full use of information from past time.
[0053] Furthermore, the selected lifting function ψ(ξ) is expressed as the following equation 2.
[0054]
[0055] Among them, the radial basis function parameters Follows uniform distribution. y is the dimension of the output data y of the system to be identified (where, since the input data u and output data y of the system to be identified are two arrays, the dimension here refers to the length of the array), N rbf is the number of radial basis functions used.
[0056] Furthermore, the data matrix is constructed as the following Equation 3, Equation 4, Equation 5 and Equation 6.
[0057]
[0058] Among them, n ψ is the dimension of the lifting function, and L is the total time step of the collected data. u is the dimension of the input data u of the system to be identified, Ψ represents the data matrix constructed by a lifting function with a step size of L, Ψ' represents Ψ shifted backward for one moment, U represents the matrix of collected input data, and Y represents the matrix of collected output data.
[0059] In addition, the optimization problem to be solved is expressed as the following Equation 7 and Equation 8.
[0060]
[0061] Among them, A and B are the system matrix and input matrix of the system to be solved and identified, respectively, and C is the output matrix of the system to be solved and identified.
[0062] In step S130, the matrix of the system to be identified is solved according to the least squares solution method, and the optimal delay is solved according to the mutual correlation coefficient.
[0063]
[0064] in, represents the Moore–Penrose generalized inverse.
[0065] Specifically, in step S130, the optimal delay is solved according to the mutual correlation coefficient. For the input data u and the output data y, the mutual correlation coefficient between the two is expressed as the following equation 11.
[0066]
[0067] Among them, S represents the maximum lag (or advance) time step, and the correlation coefficient R uy (m) represents the correlation between the input data u and the output data y delayed (or advanced) by m time steps. The set of optimal time delays is expressed as the following equation 12.
[0068]
[0069] Where D is the selected area limit, Δ is a random term used to reduce the interference of random factors, and the optimal delay is selected from the set of optimal delays. d Considering the actual situation, D=5 can be selected.
[0070] In step S140, the original state of the system to be identified is extracted using the EDMD correction method based on the projection matrix. The elements of the lifting function include the state itself, which conforms to the following formula 13.
[0071] Ψ(ξ)=[ξ β1(ξ) … β N (ξ)] T
[13]
[0072] Among them, β i represents any lifting function without a specified form, i = 1, 2, 3, ..., N. The original state of the system to be predicted (ie, the output at the next time k+1 after time k) can be expressed as the following equation 14.
[0073]
[0074] Among them, the projection matrix I represents the unit matrix, and the subscript below the 0 matrix represents n y (n d +1)×[n ψ -n y (n d +1)].
[0075] In step S150 , an open-loop prediction is performed using the identification model.
[0076] Specifically, the initial output data (i.e., the output data y at time k) and historical data are collected, the process control quantity (i.e., the input data u) is collected, and the following equations 15, 16, 17, and 18 are repeatedly executed in sequence.
[0077]
[0078] y k+1 =Cψ(ξ k+1 )
[17]
[0079] k=k+1
[18]
[0080] In the above equations 15, 16, 17 and 18, their meanings are respectively: construct a new state according to the output data sequence; predict the next time step lifting function according to the prediction equation; correct and extract the next time step state; time step iteration.
[0081] Figure 2 is the input-output data of a 900MW thermal power unit (i.e., the system to be identified) according to an embodiment of the present invention. The system identification model of the unit is performed using this data, and the open-loop prediction results obtained are as follows: Figure 3 As shown. Figure 3 In the measurement curve, the measured value curve refers to the actual input value and output value, that is, the corresponding Figure 2 The input-output data shown, the Koopman curve is the prediction result obtained based on the traditional Koopman method, the Koopman with correction curve (i.e., the corrected Koopman curve) is the prediction result obtained based on the method according to an embodiment of the present invention, and the built-in function tfest curve refers to the prediction result obtained based on the traditional transfer function identification method.
[0082] from Figure 3 It can be found that the identification method according to the embodiment of the present invention has higher prediction accuracy, is more consistent with the actual measurement results, and can reduce the calculation burden and shorten the calculation time.
[0083] The terms "exemplary," "example," and the like used throughout this specification mean "used as an example, instance, or illustration" and do not mean "preferred" or "advantageous" over other embodiments. The detailed description includes specific details for the purpose of providing an understanding of the described techniques. However, these techniques can be implemented without these specific details. In some instances, in order to avoid obscuring the concepts of the described embodiments, well-known structures and devices are shown in block diagram form.
[0084] The optional implementation modes of the embodiments of the present invention are described in detail above in conjunction with the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above implementation modes. Within the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all belong to the protection scope of the embodiments of the present invention.
[0085] The above description of the contents of this specification is provided to enable any person of ordinary skill in the art to implement or use the contents of this specification. Various modifications to the contents of this specification will be apparent to those of ordinary skill in the art, and the general principles defined herein may be applied to other variations without departing from the scope of protection of the contents of this specification. Therefore, the contents of this specification are not limited to the examples and designs described herein, but are consistent with the widest range of principles and novel features disclosed herein.
Claims
1. A method for identifying a linear model of a thermal power unit based on the Koopman operator, characterized in that: The linear model identification method of a thermal power unit comprises the following steps: (1) collecting input-output data of a system to be identified, wherein the system to be identified is a thermal power unit; (2) constructing a new state of the system to be identified based on the collected input-output data and selecting a lifting function, and constructing a data matrix using the new state and the lifting function to set the optimization problem to be solved and the parameters to be optimized; (3) Solve the matrix of the system to be identified using the least squares method and solve the optimal delay based on the mutual correlation coefficient; (4) Use the EDMD correction method based on the projection matrix to extract the original state of the system to be identified.
2. The method for identifying a linear model of a thermal power plant based on Koopman operator according to claim 1, characterized in that: The thermal power unit linear model identification method further comprises the following steps: (5) Use the identification model for open-loop prediction.
3. The method for identifying a linear model of a thermal power plant based on Koopman operator according to claim 2, characterized in that: In step (2), the new state is defined as follows, Among them, n d is the time delay, is the parameter to be optimized, u and y are the input data and output data of the system to be identified respectively, and k is the running time step of the system to be identified.
4. The method for identifying a linear model of a thermal power plant based on Koopman operator according to claim 3, characterized in that: In step (2), the selected lifting function is expressed as follows, Among them, the radial basis function parameters Follows uniform distribution, n y is the dimension of the output data y of the system to be identified, N rbf is the number of radial basis functions used.
5. The method for identifying a linear model of a thermal power plant based on Koopman operator according to claim 4, characterized in that: In step (2), the data matrix is constructed as follows, Among them, n ψ is the dimension of the lifting function, L is the total time step of the collected data, n u is the dimension of the input data u of the system to be identified, Ψ represents the data matrix constructed by a lifting function with a step size of L, Ψ' represents Ψ shifted backward for one moment, U represents the matrix of collected input data, and Y represents the matrix of collected output data.
6. The method for identifying a linear model of a thermal power plant based on Koopman operator according to claim 5, characterized in that: In step (2), the optimization problem to be solved is expressed as follows: Among them, A and B are the system matrix and input matrix of the system to be solved and identified, respectively, and C is the output matrix of the system to be solved and identified.
7. The method for identifying a linear model of a thermal power plant based on Koopman operator according to claim 6, characterized in that: In step (3), the matrix of the system to be identified is solved by the least squares method, and the analytical solution is expressed as the following formula: in, represents the Moore–Penrose generalized inverse.
8. The method for identifying a linear model of a thermal power plant based on Koopman operator according to claim 7, characterized in that: In step (3), the method for solving the optimal delay according to the mutual correlation coefficient includes: Set input data u k And the output data y k The mutual correlation coefficient is expressed as follows: Based on the mutual correlation coefficient, a set of optimal time delays is obtained, and the set of optimal time delays is expressed as the following formula: Where S represents the maximum lag or maximum advance time step, and the correlation coefficient R uy (m) represents the correlation between the input data u and the output data y that are lagged or advanced by m time steps, D is the selected regional limit, and Δ is a random term used to reduce the interference of random factors.
9. The method for identifying a linear model of a thermal power plant based on Koopman operator according to claim 8, characterized in that: In step (4), the original state of the system to be identified extracted by the EDMD correction method based on the projection matrix is expressed as follows: Among them, the projection matrix I represents the unit matrix and 0 represents the zero matrix.
10. The method for identifying a linear model of a thermal power plant based on Koopman operator according to claim 9, characterized in that: In step (5), the open-loop prediction is performed by iteratively using the identification model represented by the following formula: y k+1 =Cψ(ξ k+1 ), k=k+1.