New energy power grid transient voltage trajectory online prediction method

Abstract

The invention discloses a new energy power grid transient voltage trajectory online prediction method, and belongs to the technical field of power system operation and maintenance. The invention provides a transient voltage track online prediction method based on the Kupman theory. The problems that a traditional method for obtaining a voltage track based on fault offline simulation to carry out transient voltage stability analysis is low in calculation efficiency and accuracy and is difficult to adapt to a current large-scale new energy grid-connected system are solved. According to the Kupman operator extraction method based on the Hankel matrix enhanced expansion dynamic mode decomposition method, the method is completely based on wide-area measurement data, system modeling is avoided, dimension expansion of the measurement data can be achieved through the Hankel matrix, the dependency of the method on the measurement data is reduced, and the method is suitable for large-scale popularization and application. The calculation efficiency and accuracy of the method are improved, and online prediction of the system voltage response trajectory is realized. The method is mainly used for online prediction of the transient voltage trajectory of the new energy power grid.

Description

Technical Field

[0001] The invention belongs to the technical field of power system operation and maintenance. Background Art

[0002] With the continuous expansion of my country's power grid and the rapid growth of power load, when an AC short circuit fault occurs in the new energy grid-connected system, it is very easy to cause transient voltage instability or even collapse accidents. Due to the rapid occurrence and development of the accident, the difficulty of transient voltage stability analysis and control has increased significantly. The traditional transient voltage stability analysis method is generally based on the offline solution of the voltage operation trajectory of the system model, combined with the practical voltage stability criterion in the "National Grid Company Safety and Stability Calculation Regulations" that is often used in engineering to achieve transient voltage stability assessment. With the large-scale new energy grid connection, it is more difficult to solve the differential algebraic equations containing the dynamic operation of various power electronic equipment to obtain the system operation trajectory. Moreover, after the actual system is disturbed, due to the different flow operation modes, fault locations and the high uncertainty of new energy equipment, the occurrence and development of the system transient voltage instability are different, resulting in the traditional method of transient voltage stability analysis based on system modeling through offline simulation of anticipated faults to obtain the voltage trajectory. The calculation efficiency and accuracy are reduced, and it is difficult to apply to the current large-scale new energy grid-connected system. The above problems need to be solved urgently. Summary of the invention

[0003] The purpose of the present invention is to solve the problem that the traditional method of transient voltage stability analysis based on fault offline simulation to obtain voltage trajectory has low computational efficiency and accuracy and is difficult to adapt to the current large-scale new energy grid-connected system. The present invention provides an online prediction method for transient voltage trajectory of new energy power grid.

[0004] The method for online prediction of transient voltage trajectory of new energy power grid comprises the following steps:

[0005] Step 1: After the failure of the new energy grid, the voltage response data of the busbar in the power system to which the new energy grid is connected is obtained based on the vector measurement unit, and continuous time series data matrices X and Y are constructed according to the voltage response data;

[0006] Step 2: Construct the corresponding Hankel matrix based on X and Y and Said and are the Hankel matrices constructed for the i-th row of data in X and Y respectively; i = 1, 2, ... m;

[0007] Step 3: For all Hankel matrices, the Hankel matrix enhanced extended dynamic mode decomposition method is used to perform modal decomposition and extract the Koopman operator approximation matrix K;

[0008] Step 4: Perform eigendecomposition on the extracted Koopman operator approximation matrix K to obtain the voltage response prediction trajectory

[0009] Among them, λ i″′ is the matrix formed by the i′′th row in the Koopman eigenvalue matrix λ, ζ i″′ is the matrix formed by the i′′ column in the right eigenvector ζ, ψ i″′ (x) is the eigenfunction of the i′′-th Koopman mode, and M is the total number of Koopman modes.

[0010] Preferably,

[0011]

[0012] x(c i ,t i′ ) is the i-th measurement point c on the busbar of the power system to which the new energy grid is connected i At the i′th sampling time t i′ The voltage response data, x(c i ,t i″ ) is the i-th measurement point c on the busbar of the power system to which the new energy grid is connected i At the i″th sampling time t i″ Voltage response data, i = 1, 2, ... m, i' = 1, 2, ... k-1, i" = 2, ... k, t l From t1 to t k-1 A sampling moment in between.

[0013] Preferably,

[0014]

[0015] p and q are the columns and rows of the Hankel matrix, respectively, and both are less than k-1.

[0016] Preferably, in step 3, for all Hankel matrices, a Hankel matrix enhanced extended dynamic mode decomposition method is used to perform modal decomposition, and the implementation method of extracting the Koopman operator approximation matrix K includes:

[0017] First, define the scale factor

[0018] αj is the jth scaling factor, is the Hankel matrix at the jth measurement point The matrix formed by the last row of ; is the Hankel matrix at the first measurement point The matrix formed by the last row; ||·|| is the Euclidean norm of the required matrix;

[0019] Secondly, using the Hankel matrix constructed at all measurement points and all proportional factors, construct the modified continuous time series data matrix X' and Y', and use the observation function Map X' and Y' to the observation space to get the data matrix X lift and Y lift ;

[0020]

[0021] Among them, X lift and Y lift They are all data matrices with 4q rows and mp columns, where p and q are the columns and rows of the Hankel matrix respectively;

[0022] Finally, according to the Koopman operator theory, there exists And Perform linear deformation processing to obtain Y lift =KX lift +r(x); define the loss function J, minimize the residual term r(x) by solving the least squares optimization, and extract the Koopman operator approximation matrix K; where, is the Koopman operator.

[0023] Preferably,

[0024] ΔV n is the difference matrix between matrix Y and matrix X.

[0025] Preferably,

[0026] X lift.n and Y lift.n are the matrices formed by the nth row of the matrix after X' and Y' are mapped to the observation space, r(X lift.n ) is X lift.n The corresponding residual term.

[0027] Preferably, the implementation of step 4, performing eigendecomposition on the extracted Koopman operator approximation matrix K to obtain the voltage response prediction trajectory f(x) includes:

[0028] First, the extracted Koopman operator approximation matrix K is subjected to eigendecomposition to obtain K = wλζ, where w is the left eigenvector;

[0029] Secondly, according to the right eigenvector ζ and the observation function Get the eigenfunction of the i″′th Koopman mode ze ″′ is the matrix formed by the i′′th column in the right eigenvector ζ;

[0030] Finally, according to the Koopman eigenvalue matrix λ, the right eigenvector ζ and the eigenfunctions of all Koopman modes, the voltage response prediction trajectory is obtained:

[0031] λi ″′ is the matrix formed by the i′′-th row in the Koopman eigenvalue matrix λ.

[0032] An online prediction device for transient voltage trajectory of a new energy power grid comprises a storage device, a processor, and a computer program stored in the storage device and executable on the processor. The processor executes the computer program to implement the online prediction method for transient voltage trajectory of a new energy power grid.

[0033] A computer-readable storage device stores a computer program, and when the computer program is executed, the online prediction method for transient voltage trajectory of a new energy power grid is implemented.

[0034] The beneficial effects brought by the present invention are:

[0035] The present invention proposes an online prediction method for transient voltage trajectory of new energy power grid. A Koopman operator extraction method based on Hankel matrix enhanced extended dynamic mode decomposition method is proposed. This method is completely based on wide-area measurement data, avoiding system modeling, and can achieve dimension expansion of measurement data through Hankel matrix, reduce the dependence of the proposed method on measurement data, improve the calculation efficiency and accuracy of the method, and realize online prediction of system voltage response trajectory, so it has high practical application value.

[0036] The method of the present invention can accurately obtain the Koopman operator approximation matrix through a relatively short measurement time window (i.e., the size of X and Y), thereby ensuring the accuracy of transient voltage trajectory prediction. At the same time, the proposed method has good measurement noise robustness, can be adapted to practical engineering applications, and provides certain technical support for subsequent transient voltage stability analysis and control. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a flowchart of the online prediction method for transient voltage trajectory of the new energy power grid described in the present invention.

[0038] Figure 2 This is the wiring diagram of the Nordic system; G1 to G20 represent the 1st to 20th generators, Figure 2 The remaining numbers in are the busbar numbers;

[0039] Figure 3 This is the system voltage trajectory prediction result diagram under stable conditions; among them, Figure 3 a is a comparison diagram of the time domain simulation trajectory and the predicted trajectory of bus 1 in the system under stable conditions. Figure 3b is a comparison diagram between the time domain simulation trajectory and the predicted trajectory of bus 2 in the system under stable conditions;

[0040] Figure 4 This is the system voltage trajectory prediction result diagram under instability; among them, Figure 4 a is a comparison diagram of the time domain simulation trajectory and the predicted trajectory of bus 1 in the system under instability. Figure 4 b shows the comparison between the time domain simulation trajectory and the predicted trajectory of bus 2 in the system under the unstable condition. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0043] Specific implementation method 1. Combination Figure 1 As shown, the online prediction method for transient voltage trajectory of the new energy power grid described in this embodiment includes the following steps:

[0044] Step 1: After the failure of the new energy grid, the voltage response data of the busbar in the power system to which the new energy grid is connected is obtained based on the vector measurement unit, and continuous time series data matrices X and Y are constructed according to the voltage response data;

[0045] Step 2: Construct the corresponding Hankel matrix based on X and Y and Said and are the Hankel matrices constructed for the i-th row of data in X and Y respectively; i = 1, 2, ... m;

[0046] Step 3: For all Hankel matrices, the Hankel matrix enhanced extended dynamic mode decomposition method is used to perform modal decomposition and extract the Koopman operator approximation matrix K;

[0047] Step 4: Perform eigendecomposition on the extracted Koopman operator approximation matrix K to obtain the voltage response prediction trajectory

[0048] Among them, λ i″′ is the matrix formed by the i′′th row in the Koopman eigenvalue matrix λ, ζ i″′ is the matrix formed by the i′′ column in the right eigenvector ζ, ψi″′ (x) is the eigenfunction of the i′′-th Koopman mode, and M is the total number of Koopman modes.

[0049] In this embodiment, a Koopman operator extraction method based on the Hankel matrix enhanced extended dynamic mode decomposition method is proposed. This method is completely based on wide-area measurement data, avoids system modeling, and can achieve dimensionality expansion of measurement data through the Hankel matrix, thereby reducing the dependence of the proposed method on measurement data, improving the calculation efficiency and accuracy of the method, and realizing online prediction of the system voltage response trajectory, and thus has high practical application value.

[0050] Furthermore, the construction of continuous time series data matrices X and Y, and the construction of the corresponding Hankel matrix based on X and Y are given. and The specific expression of:

[0051]

[0052]

[0053] x(c i ,t i′ ) is the i-th measurement point c on the busbar of the power system to which the new energy grid is connected i At the i′th sampling time t i′ The voltage response data, x(c i ,t i″ ) is the i-th measurement point c on the busbar of the power system to which the new energy grid is connected i At the i″th sampling time t i″ Voltage response data, i = 1, 2, ... m, i' = 1, 2, ... k-1, i" = 2, ... k, t l From t1 to t k-1 a sampling time between; p and q are the columns and rows of the Hankel matrix, respectively, and both are less than k-1.

[0054] Furthermore, in step 3, for all Hankel matrices, the Hankel matrix enhanced extended dynamic mode decomposition method is used to perform modal decomposition, and the implementation method of extracting the Koopman operator approximation matrix K includes:

[0055] First, define the scale factor

[0056] αj is the jth scaling factor, is the Hankel matrix at the jth measurement point The matrix formed by the last row of ; is the Hankel matrix at the first measurement point The matrix formed by the last row; ||·|| is the Euclidean norm of the required matrix;

[0057] Secondly, using the Hankel matrix constructed at all measurement points and all proportional factors, construct the modified continuous time series data matrix X' and Y', and use the observation function Map X' and Y' to the observation space to get the data matrix X lift and Y lift ;

[0058]

[0059] Among them, X lift and Y lift They are all data matrices with 4q rows and mp columns, where p and q are the columns and rows of the Hankel matrix respectively;

[0060] Finally, according to the Koopman operator theory, there exists And Perform linear deformation processing to obtain Y lift =KX lift +r(x); define the loss function J, minimize the residual term r(x) by solving the least squares optimization, and extract the Koopman operator approximation matrix K; where, is the Koopman operator.

[0061] In this preferred embodiment, a Koopman operator extraction method based on the Hankel matrix enhanced extended dynamic mode decomposition method is proposed. This method is completely based on wide-area measurement data, avoids system modeling, and can achieve dimensionality expansion of measurement data through the Hankel matrix, thereby reducing the dependence of the proposed method on measurement data and improving the calculation efficiency and accuracy of the method.

[0062] Furthermore, ΔV n is the difference matrix between matrix Y and matrix X.

[0063] Furthermore, by setting the loss function J, the Koopman operator approximation matrix K is obtained by minimizing J, and the nonlinear Koopman operator Linearization improves the accuracy and feasibility of the method of the present invention, specifically:

[0064]

[0065] X lift.n and Y lift.n are the matrices formed by the nth row of the matrix after X' and Y' are mapped to the observation space, r(X lift.n ) is X lift.n The corresponding residual term.

[0066] Furthermore, in step 4, the extracted Koopman operator approximation matrix K is subjected to eigendecomposition to obtain the voltage response prediction trajectory f(x), and the implementation method includes:

[0067] First, the extracted Koopman operator approximation matrix K is subjected to eigendecomposition to obtain K=wλζ, where λ is the Koopman eigenvalue matrix, w is the left eigenvector, and ζ is the right eigenvector;

[0068] Secondly, according to the right eigenvector ζ and the observation function Get the eigenfunction of the i″′th Koopman mode ζ i″′ is the matrix formed by the i′′th column in the right eigenvector ζ;

[0069] Finally, according to the Koopman eigenvalue matrix λ, the right eigenvector ζ and the eigenfunctions of all Koopman modes, the voltage response prediction trajectory is obtained:

[0070] λ i″′ is the matrix formed by the i′′-th row in the Koopman eigenvalue matrix λ.

[0071] In this preferred embodiment, a method for obtaining the voltage response prediction trajectory f(x) is provided. By calculating the Koopman operator approximation matrix K, the eigenfunction of the Koopman mode is obtained, thereby realizing the transient voltage trajectory prediction completely based on the measured data.

[0072] Specific implementation method 2: An online prediction device for transient voltage trajectory of a new energy power grid includes a storage device, a processor, and a computer program stored in the storage device and executable on the processor. The processor executes the computer program to implement the online prediction method for transient voltage trajectory of a new energy power grid as described in specific implementation method 1.

[0073] Specific implementation method three: a computer-readable storage device, wherein the storage device stores a computer program, wherein when the computer program is executed, the online prediction method for transient voltage trajectory of a new energy power grid as described in specific implementation method one is implemented.

[0074] Verification test:

[0075] The effects of the present invention are further described with reference to the embodiments, specifically:

[0076] like Figure 2 The Nordic system shown simulates the following operating conditions:

[0077] Working condition a: When the load bus 1 is connected to 100% induction motor load, a three-phase short circuit fault occurs in the line between bus 4032 and 4044 in the system near bus 4032 at 1 second. After the fault lasts for 100ms, the line is tripped and the fault is cleared;

[0078] Working condition b: When the load bus 1 is connected to 100% induction motor load, a three-phase short circuit fault occurs in the system line 4032-4044 near the bus 4032 at 1 second. After the fault lasts for 200ms, the line is tripped and the fault is cleared;

[0079] The voltage trajectory of the new energy grid transient voltage is predicted online using the method for online prediction of the voltage trajectory of the new energy grid described in the present invention. First, the voltage amplitude of each load bus in the area after the fault is measured, and a 0.5s analysis window is set (i.e., the size of the constructed matrices X and Y is determined). The prediction results of the key bus voltage trajectory are as follows: Figure 3 and Figure 4 As shown (taking bus 1 and bus 2 as examples). The root mean square error values ​​of the method of the present invention are statistically analyzed, and the results are listed in Table 1. Table 1 shows the root mean square error values ​​of the voltage trajectory prediction results of bus 1 to bus 6.

[0080] Table 1 Root mean square error results of the method of the present invention

[0081]

[0082] Table 1 shows the root mean square error results of the method of the present invention under different operating conditions. For the tested buses 1 to 6, under the two operating conditions a and b, the root mean square errors of the trajectory prediction using the present invention are all less than 0.005, indicating that the method of the present invention has high accuracy in transient voltage trajectory prediction. Therefore, the feasibility and effectiveness of the method of the present invention in predicting transient voltage trajectory in power systems can be further verified by the root mean square error results and trajectory prediction results.

[0083] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims

1. An online prediction method for transient voltage trajectory of a new energy power grid, characterized in that: The method comprises the following steps: Step 1: After the failure of the new energy grid, the voltage response data of the busbar in the power system to which the new energy grid is connected is obtained based on the vector measurement unit, and continuous time series data matrices X and Y are constructed according to the voltage response data; Step 2: Construct the corresponding Hankel matrix based on X and Y and Said and are the Hankel matrices constructed for the i-th row of data in X and Y respectively; i = 1, 2, ... m; Step 3: For all Hankel matrices, the Hankel matrix enhanced extended dynamic mode decomposition method is used to perform modal decomposition and extract the Koopman operator approximation matrix K; Step 4: Perform eigendecomposition on the extracted Koopman operator approximation matrix K to obtain the voltage response prediction trajectory Among them, λ i″′ is the matrix formed by the i′′th row in the Koopman eigenvalue matrix λ, ζ i″′ is the matrix formed by the i′′ column in the right eigenvector ζ, ψ i″′ (x) is the eigenfunction of the i′′-th Koopman mode, and M is the total number of Koopman modes.

2. The online prediction method for transient voltage trajectory of a new energy power grid according to claim 1 is characterized in that: x(c i ,t i′ ) is the i-th measurement point c on the busbar of the power system to which the new energy grid is connected i At the i′th sampling time t i′ The voltage response data, x(c i ,t i″ ) is the i-th measurement point c on the busbar of the power system to which the new energy grid is connected i At the i″th sampling time t i″ Voltage response data, i = 1, 2, ... m, i' = 1, 2, ... k-1, i" = 2, ... k, t l From t1 to t k-1 A sampling moment in between.

3. The online prediction method for transient voltage trajectory of a new energy power grid according to claim 2 is characterized in that: p and q are the columns and rows of the Hankel matrix, respectively, and both are less than k-1.

4. The online prediction method for transient voltage trajectory of a new energy power grid according to claim 1 is characterized in that: Step 3: For all Hankel matrices, the Hankel matrix enhanced extended dynamic mode decomposition method is used to perform modal decomposition, and the implementation method of extracting the Koopman operator approximation matrix K includes: First, define the scale factor αj is the jth scaling factor, is the Hankel matrix at the jth measurement point The matrix formed by the last row of ; is the Hankel matrix at the first measurement point The matrix formed by the last row; ||·|| is the Euclidean norm of the required matrix; Secondly, using the Hankel matrix constructed at all measurement points and all proportional factors, construct the modified continuous time series data matrix X' and Y', and use the observation function Map X' and Y' to the observation space to get the data matrix X lift and Y lift ; Among them, X lift and Y lift They are all data matrices with 4q rows and mp columns, where p and q are the columns and rows of the Hankel matrix respectively; Finally, according to the Koopman operator theory, there exists And Perform linear deformation processing to obtain Y lift =KX lift +r(x); define the loss function J, minimize the residual term r(x) by solving the least squares optimization, and extract the Koopman operator approximation matrix K; where, is the Koopman operator.

5. The method for online prediction of transient voltage trajectory of new energy power grid according to claim 4 is characterized in that: ΔV n is the difference matrix between matrix Y and matrix X.

6. The online prediction method for transient voltage trajectory of a new energy power grid according to claim 1 is characterized in that: X lift.n and Y lift.n are the matrices formed by the nth row of the matrix after X' and Y' are mapped to the observation space, r(X lift.n ) is X lift.n The corresponding residual term.

7. The online prediction method for transient voltage trajectory of a new energy power grid according to claim 1 is characterized in that: Step 4: Performing eigendecomposition on the extracted Koopman operator approximation matrix K to obtain the voltage response prediction trajectory f(x) includes: First, the extracted Koopman operator approximation matrix K is subjected to eigendecomposition to obtain K = wλζ, where w is the left eigenvector; Secondly, according to the right eigenvector ζ and the observation function Get the eigenfunction of the i″′th Koopman mode ζ i″′ is the matrix formed by the i′′th column in the right eigenvector ζ; Finally, according to the Koopman eigenvalue matrix λ, the right eigenvector ζ and the eigenfunctions of all Koopman modes, the voltage response prediction trajectory is obtained: λ i″′ is the matrix formed by the i′′′-th row in the Koopman eigenvalue matrix λ.

8. An online prediction device for transient voltage trajectory of a new energy power grid, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that: The processor executes a computer program to implement the online prediction method for transient voltage trajectory of a new energy power grid as described in any one of claims 1 to 7.

9. A computer-readable storage device storing a computer program, characterized in that: When the computer program is executed, the online prediction method for transient voltage trajectory of the new energy power grid is implemented as described in any one of claims 1 to 7.

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