Hydraulic turbine governing system identification method with time delay link

Abstract

This application discloses an identification method for a turbine-controlled system with time-delay elements, comprising: establishing an identification model of a fractional-order time-delay state-space model of the turbine-controlled system based on the system matrix; and constructing an identification process based on the identification model using the Adam algorithm based on Kalman filtering (KF). This application establishes a fractional-order time-delay state-space model for turbine-controlled systems with time-delay elements, using turbine torque as the input data and turbine flow rate as the output data. Unlike common integer-order models, this invention establishes a fractional-order model to describe the system, which can more accurately describe the actual system.

Description

Technical Field

[0001] This application belongs to the field of industrial control technology, specifically relating to a method for identifying a water turbine regulating system with time delay. Background Technology

[0002] In recent years, the installed capacity of hydropower units has been continuously increasing, exhibiting dynamic characteristics during transitions such as startup, grid connection, and load adjustment. To ensure power supply quality and operational safety, the requirements for their control systems have become more stringent. The turbine regulating system, as the core of the hydropower unit's control, typically employs a simple, easy-to-implement, and highly reliable PID controller. However, the turbine regulating system itself is a complex system exhibiting time-varying, uncertain, and nonlinear characteristics. Coupled with the mechanical delay inherent in hydraulic servo systems, traditional PID parameter tuning methods are insufficient to meet the control requirements of turbine regulating systems containing time-delay elements. Therefore, how to tune the PID parameters of a turbine regulating system with time-delay elements has become one of the key challenges in improving control performance.

[0003] To address this, many scholars have studied the control performance of turbine regulation systems, using algorithms such as improved atomic search optimization, improved fuzzy particle swarm optimization, and improved gravity search. These proposed algorithms demonstrate good control performance and improve system dynamics, but none have considered the time delay problem inherent in turbine regulation systems. Summary of the Invention

[0004] This application provides a method for identifying a turbine control system with time delay to solve the above-mentioned technical problems.

[0005] To solve the above-mentioned technical problems, one technical solution adopted in this application is: a method for identifying a turbine regulating system containing a time-delay element, comprising:

[0006] S1. Based on the system matrix, establish an identification model for the fractional-order time-delay state-space model of the turbine regulating system;

[0007] S2. Based on the identification model, construct the identification process of Adam algorithm based on Kalman filter (KF).

[0008] Furthermore, the method in step S1 includes:

[0009] Based on formulas (1)-(2), the fractional-order time-delay state-space model is obtained; where formulas (1)-(2) are:

[0010] , , , (1)

[0011] (2);

[0012] in, It is the system's state vector. It is a system input signal. As intermediate variables; matrix , , and It is the system matrix; polynomial factor , , These are the parameters to be estimated; The order is Fractional difference operator.

[0013] Furthermore, based on formula (3), the fractional-order discrete state-space equations defined by Greenwald-Letnikov are obtained; where formula (3) is:

[0014] (3);

[0015] Where k is the k-th sample, and h is the sampling interval equal to 1, defined as follows: .

[0016] Furthermore, based on formula (4), the identification model is obtained; where formula (4) is:

[0017] (4);

[0018] in, It is the system output signal. It is a function with a mean of 0 and a variance of . White noise; It is the information vector of the system.

[0019] Furthermore, the method in step S2 includes:

[0020] S21. Initialize the parameters of the identification model and determine the number of iterations;

[0021] S22. Based on the turbine torque and turbine flow rate, acquire input and output data;

[0022] S23. Construct an estimate of the information vector from the state vectors in the input and output data;

[0023] S24. Based on the estimated value of the information vector, calculate the first moment estimate and the first bias correction, and at the same time calculate the second moment estimate and the second bias correction;

[0024] S25. Based on the first moment estimation, the first bias correction, the second moment estimation, and the second bias correction, obtain the parameter vector estimate;

[0025] S26. Determine if the maximum number of loops has been reached; if not, repeat the above steps; if yes, output the identification result.

[0026] Furthermore, the method in step S23 includes:

[0027] Based on formulas (5)-(8), the estimated values ​​of the information vector are obtained. Among them, formulas (5)-(8) are:

[0028] (5);

[0029] (6);

[0030] (7);

[0031] (8).

[0032] Furthermore, the method in step S24 includes:

[0033] Based on formulas (9)-(10), the first-order moment estimate is obtained. and first deviation correction Among them, formulas (9)-(10) are:

[0034] (9);

[0035] (10);

[0036] Based on formulas (11)-(12), the second-order moment estimate is obtained. and the second deviation correction Among them, formulas (11)-(12) are:

[0037] (11);

[0038] (12).

[0039] Furthermore, the method in step S25 includes:

[0040] Based on formula (13), the parameter vector estimate is obtained; where formula (13) is:

[0041] (13);

[0042] in, These are the estimated values ​​for the parameter vector.

[0043] The beneficial effects of this application are as follows: This application establishes a fractional-order time-delay state-space model for a turbine-controlled system with time-delay components. Turbine torque is used as the input data of the turbine-controlled system, and turbine flow rate is used as the output data. Unlike common integer-order models, this invention establishes a fractional-order model to describe the system, which can more accurately describe the actual system. As shown in the figure, the algorithm can effectively identify the model parameters. This application uses Kalman filtering (KF) for state estimation and the Adam algorithm for parameter identification. Compared to the stochastic gradient descent algorithm, the Adam algorithm adaptively adjusts the learning rate and introduces a momentum mechanism, improving the convergence speed. The Adam algorithm can better identify time-delay systems with higher accuracy and smaller estimation errors. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating an embodiment of the method for identifying a turbine regulating system with time delay elements according to this application;

[0045] Figure 2 yes Figure 1 A flowchart illustrating an embodiment of step S2;

[0046] Figure 3 This is a schematic diagram of a turbine regulating system containing a time delay element, according to an embodiment of the method for identifying a turbine regulating system containing a time delay element of this application.

[0047] Figure 4 This is an overall flowchart of the Adam algorithm based on Kalman filtering, an embodiment of the identification method for a water turbine regulating system with time delay in this application;

[0048] Figure 5 This is a general schematic diagram of the fractional-order time-delay state space of an embodiment of the water turbine regulating system identification method with time-delay elements of this application;

[0049] Figure 6 This is a schematic diagram illustrating the error between the identification parameters and the actual values ​​of an embodiment of the identification method for a turbine regulating system with time delay elements according to this application. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments.

[0051] Numerous specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways than those described herein, and therefore the invention is not limited to the specific embodiments disclosed in the following specification.

[0052] See Figure 1 , Figure 1 This is a schematic flowchart of an embodiment of the method for identifying a turbine regulating system with time delay elements according to this application. The method includes:

[0053] S1. Based on the system matrix, establish an identification model for the fractional-order time-delay state-space model of the turbine regulation system.

[0054] Specifically, a fractional-order time-delay state-space model of a hydro-turbine regulating system is established, and the general form of the fractional-order time-delay state-space model is given. It is a system input signal. It is the system output signal. It is a function with a mean of 0 and a variance of . White noise, It is the system's state vector. Using intermediate variables, we obtain the general form of the model:

[0055] , , , (1)

[0056] Consider a fractionally symmetrical system, i.e., a fractional order that is a multiple of the same basis and is known. The fractional-order discrete state-space model can then be expressed as:

[0057] (2);

[0058] Among them, matrix , , and It is the system matrix; polynomial factor , , These are the parameters to be estimated; The order is Fractional difference operator.

[0059] Solve for fractional derivatives using the Grünwald-Letnikov definition:

[0060] (14);

[0061] in The order is Fractional difference operator, Let t = kh be a function, where k is the k-th sample and h is the sampling interval equal to 1. Substituting it into formula (14), the fractional derivative is rewritten as:

[0062] (15);

[0063] According to formula (16):

[0064] (16);

[0065] Based on formula (3), the fractional discrete state-space equation based on the Greenwald-Laitnikov definition is obtained as follows:

[0066] (3);

[0067] Based on formula (4), the identification model of the fractional time-delay state-space model of the turbine regulating system is obtained:

[0068] (4);

[0069] In the above formula, It is the system's information vector, represented as:

[0070] ;

[0071] ;

[0072] ;

[0073] ;

[0074] in, Let the system's parameter vector be represented as:

[0075] ; ; ; ;

[0076] When the fraction order When the historical states are known, then the weighted sum of the historical states is used. For known terms, it is represented as:

[0077] ;

[0078] S2. Based on the identification model, construct the identification process of the Adam algorithm based on Kalman filtering.

[0079] For details, please refer to Figure 2 The method of step S2 includes:

[0080] S21. Initialize the parameters of the identification model and determine the number of iterations.

[0081] Specifically, initialize the parameters of the recognition model, given the number of iterations L, and let k=1. .

[0082] S22. Based on the turbine torque and turbine flow rate, acquire input and output data.

[0083] The turbine torque of the turbine regulating system is used as input data. The turbine flow rate is used as output data. Record data.

[0084] S23. Construct an estimate of the information vector from the input data and the state vector in the output data.

[0085] Specifically, the state vector in the information vector Replace with its estimated value Constructing an estimation of information vectors ;

[0086] (5);

[0087] (6);

[0088] (7);

[0089] (8).

[0090] S24. Based on the estimated value of the information vector, calculate the first moment estimate and the first bias correction, and simultaneously calculate the second moment estimate and the second bias correction.

[0091] Specifically, based on formulas (9)-(10), the first-order moment estimate is obtained. and first deviation correction Among them, formulas (9)-(10) are:

[0092] (9);

[0093] (10);

[0094] Based on formulas (11)-(12), the second-order moment estimate is obtained. and the second deviation correction Among them, formulas (11)-(12) are:

[0095] (11);

[0096] (12);

[0097] S25. Based on the first moment estimation, the first bias correction, the second moment estimation, and the second bias correction, obtain the parameter vector estimate;

[0098] Specifically, the parameter vector estimate is obtained based on formula (13); where formula (13) is:

[0099] (13);

[0100] S26. Determine if the maximum number of iterations has been reached; if not, repeat the above steps; if yes, output the identification result. .

[0101] like Figure 3-5 As shown, in one embodiment, input data Output data for the turbine torque of the turbine regulating system. It is the flow rate of the water turbine.

[0102] Using the fractional-order time-delay state-space model mentioned above, the following model can be established for this embodiment:

[0103] ; ; ; ;

[0104] Consider fractional order =0.3, we can get: =-0.39, =-0.09, =-0.1, =-0.07, =-0.1, =-0.07, =-0.02, =0.03;

[0105] To facilitate the substitution of the parameters to be identified into the Adam algorithm, the parameters to be identified are grouped into a parameter vector. Let the parameters to be identified be as follows:

[0106]

[0107] Refer to step S2 for parameter identification. Several issues need to be considered when setting the data length L: If the data length is too short, the identification results will be unsatisfactory, leading to low identification accuracy; if the data length is too long, the computational load will be excessive.

[0108] The parameter identification results using the identification method for a turbine regulating system with time delay elements according to this embodiment are as follows: Figure 6 As shown in the figure. The method in this embodiment has high identification accuracy, small parameter identification error, and the estimated value of the parameter to be identified is very close to the true value. It also has high convergence accuracy, which shows that the identification method has good applicability to parameter identification of turbine control systems with time delay.

[0109] This application establishes a fractional-order time-delay state-space model for a turbine-controlled system with time-delay components. Turbine torque serves as the input data, and turbine flow rate as the output data. Unlike common integer-order models, this invention establishes a fractional-order model to describe the system, which can more accurately describe the actual system. As shown in the figure, the algorithm can effectively identify the model parameters.

[0110] This application uses Kalman filtering for state estimation and Adam algorithm for parameter identification. Compared with stochastic gradient algorithm, Adam algorithm adaptively adjusts the learning rate and introduces momentum mechanism to improve convergence speed. Adam algorithm can better identify time-delay systems and has higher identification accuracy, with smaller estimation error.

[0111] The above description is merely an embodiment of this application and does not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for identifying a turbine regulating system containing a time-delay element, characterized in that, include: S1. Based on the system matrix, establish an identification model for the fractional-order time-delay state-space model of the turbine regulating system; S2. Based on the identification model, construct the identification process of Adam algorithm based on Kalman filtering.

2. The method according to claim 1, characterized in that, The method of step S1 includes: Based on formulas (1)-(2), the fractional-order time-delay state-space model is obtained; wherein, formulas (1)-(2) are: ， ， ， （1） （2）； in, It is the system's state vector. It is a system input signal. As intermediate variables; matrix , , and It is the system matrix; polynomial factor , , These are the parameters to be estimated; Is the order of Fractional difference operator.

3. The method according to claim 2, characterized in that, Based on formula (3), the fractional-order discrete state-space equations defined by Greenwald-Letnikov are obtained; wherein, formula (3) is: （3）； Where k is the k-th sample, and h is the sampling interval equal to 1, defined as follows: .

4. The method according to claim 3, characterized in that, Based on formula (4), the identification model is obtained; wherein, formula (4) is: （4）； in, It is the system output signal. It is a function with a mean of 0 and a variance of . White noise; It is the information vector of the system.

5. The method according to claim 1, characterized in that, The method of step S2 includes: S21. Initialize the parameters of the identification model and determine the number of iterations; S22. Based on the turbine torque and turbine flow rate, acquire input and output data; S23. Construct an estimated value of the information vector from the input data and the state vector in the output data; S24. Based on the estimated value of the information vector, calculate the first moment estimate and the first bias correction, and simultaneously calculate the second moment estimate and the second bias correction; S25. Based on the first-order moment estimate, the first deviation correction, the second-order moment estimate, and the second deviation correction, obtain the parameter vector estimate; S26. Determine if the maximum number of loops has been reached; if not, repeat the above steps; if yes, output the identification result.

6. The method according to claim 5, characterized in that, The method of step S23 includes: Based on formulas (5)-(8), the estimated value of the information vector is obtained. ; where formulas (5)-(8) are: （5）； （6）； （7）； （8）。 7. The method according to claim 5, characterized in that, The method of step S24 includes: Based on formulas (9)-(10), the first-order moment estimate is obtained. and the first deviation correction ; where formulas (9)-(10) are: （9）； （10）； Based on formulas (11)-(12), the second-order moment estimate is obtained. and the second deviation correction ; where formulas (11)-(12) are: （11）； （12）。 8. The method according to claim 5, characterized in that, The method of step S25 includes: Based on formula (13), the estimated value of the parameter vector is obtained; wherein, formula (13) is: （13）； in, These are the estimated values ​​for the parameter vector.

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