A load margin calculation method based on neural network and quadratic fitting

Abstract

This invention discloses a load margin calculation method based on neural networks and quadratic fitting, comprising: inputting the operating parameters of the initial operating point of the power system into a pre-trained neural network model to obtain a preliminary estimate of the load margin; using the preliminary estimate of the load margin as a benchmark, selecting multiple load parameter points, using another neural network model to obtain the target node voltage amplitude corresponding to each load parameter point, performing quadratic curve fitting, and calculating a quadratic value based on the vertex coordinates of the fitted quadratic curve; inputting the operating parameters of the initial operating point and the quadratic value of the load margin into other neural network models to obtain error correction coefficients, and correcting the quadratic value to obtain the final load margin; the system is used to execute this method. This invention deeply integrates the strong interpretability of theoretical laws with the rapid characteristics of data-driven methods, realizing a fast load margin calculation method that combines high accuracy and high interpretability.

Description

Technical Field

[0001] This invention relates to the field of voltage stability margin calculation in power systems, and specifically to a load margin calculation method based on neural networks and quadratic fitting. Background Technology

[0002] As is well known, load margin is an important indicator for measuring the distance between the operating state of a power system and the static voltage collapse point, and it is of great significance for online voltage stability assessment.

[0003] Continuous power flow algorithms are a classic method for calculating load margins, but they require multiple iterations, resulting in computational inefficiencies when solving load margin problems in large-scale power systems. To improve computational efficiency, recent literature has proposed load margin calculation methods based on neural networks. While these methods offer advantages in terms of speed, they suffer from insufficient interpretability and difficulty in guaranteeing computational accuracy.

[0004] Existing theoretical research indicates that near the voltage collapse point of a saddle-node bifurcation, the relationship between load parameters and node voltage amplitude can be approximated as a quadratic curve. This theoretical principle has been used to study rapid load margin calculation methods. However, how to combine this theoretical principle with efficient data-driven methods to propose a calculation method that is fast, accurate, and well-interpretable remains a pressing technical challenge.

[0005] In conclusion, developing a load margin calculation method that can balance computational efficiency, accuracy, and interpretability is crucial for improving the safe and stable operation of the power grid. Summary of the Invention

[0006] The technical problem this invention aims to solve is to provide a load margin calculation method based on neural networks and quadratic fitting, addressing the aforementioned issues in existing technologies. This method deeply integrates theoretical principles with the rapid characteristics of data-driven approaches, achieving fast load margin calculation that is both efficient and highly accurate, while also being highly interpretable. In this invention, the load margin is represented by the distance from the initial operating point to the voltage collapse point.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the method of the present invention includes the following steps: S1. Preliminary calculation of load margin: Input the operating parameters of the power system at the initial operating point into the pre-trained neural network model for preliminary calculation of load margin to obtain a preliminary estimate of the load margin. S2. Secondary calculation of load margin based on function fitting: Based on the preliminary estimated value, select multiple load parameter points, use a pre-trained node voltage amplitude calculation neural network model to obtain the target node voltage amplitude corresponding to each load parameter point, perform quadratic curve fitting based on the multiple load parameter points and their corresponding target node voltage amplitudes, and calculate the secondary calculated value of load margin according to the vertex coordinates of the quadratic curve. S3. Error Correction: Input the operating parameters of the initial operating point and the secondary calculated value of the load margin into the pre-trained error correction neural network model to obtain the error correction coefficient. Then, use the error correction coefficient to correct the secondary calculated value of the load margin to obtain the final load margin. The neural network model for the preliminary calculation of load margin in step S1 is a feedforward neural network, and the mapping relationship between its input and output can be expressed as follows: ( , , , , → ; Among them, input items This represents a vector consisting of the active power injected by the PV and PQ nodes at the initial operating point. This represents a vector consisting of changes in active power injection at PV and PQ nodes. This represents a vector consisting of the reactive power injected by the PQ node at the initial operating point; This represents a vector consisting of the changes in reactive power injection at nodes PQ; This represents a vector consisting of the voltage magnitudes of the PV nodes and the slack node at the initial operating point; output term This indicates the load margin.

[0008] The neural network model for calculating the node voltage amplitude in step S2 is a feedforward neural network, and the mapping relationship between its input and output can be expressed as follows: (λ, , , , , → ; Where λ is the load parameter, The target node voltage amplitude.

[0009] Step S2 specifically includes: S21. Using the preliminary estimated value as the midpoint, select two values ​​that are less than and greater than the midpoint to form three load parameter points; S22. Combine the three load parameter points with the operating parameters of the initial operating point, and input them into the node voltage amplitude calculation neural network model to obtain three corresponding target node voltage amplitudes; S23. Using the target node voltage amplitudes corresponding to the three obtained load parameter points, a quadratic function is fitted by solving a system of linear equations. =f( )=α 2 +β The coefficients α, β, and γ of +γ; S24. According to the formula = The secondary calculated value of the load margin is obtained.

[0010] The error correction neural network model described in step S3 is a feedforward neural network, and the mapping relationship between its input and output can be expressed as follows: ( , , , , →ε; Where ε is the error correction coefficient, its calculation formula is: ε= ; in, This represents the true load margin, calculated using the traditional continuous power flow method.

[0011] The specific calculation formula for correcting the secondary calculated value of the load margin using the error correction coefficient in step S3 is as follows: ; in, This is the final estimated load margin value.

[0012] Before inputting data into any of the neural network models in steps S1-S3, the input data is normalized; after obtaining the output data of the neural network, the output data is denormalized.

[0013] This invention also provides a load margin calculation system based on neural networks and quadratic fitting, for implementing the aforementioned load margin calculation method based on neural networks and quadratic fitting, comprising: The load margin preliminary calculation module is configured to process the input initial operating parameters using the load margin preliminary calculation neural network model and output a preliminary estimate of the load margin. The load margin secondary calculation module calculates the secondary value of the load margin based on the preliminary estimated value, using the node voltage amplitude calculation neural network model and quadratic curve fitting method. The error correction module is configured to perform error compensation on the secondary calculated value based on the error correction neural network model and output the final load margin.

[0014] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described method for calculating load margin based on neural networks and quadratic fitting.

[0015] The present invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the above-described method for calculating load margin based on neural networks and quadratic fitting.

[0016] Compared with the prior art, the advantages of the present invention are as follows: Significant improvements in computational efficiency: Compared to traditional continuous power flow calculation methods, this invention completely avoids the complex and time-consuming iterative solution process. By utilizing a trained neural network and combining it with fast quadratic curve fitting operations, the computation time is reduced by orders of magnitude compared to traditional methods, and the correlation between computation time and system size is significantly weakened, which can meet the requirements of online analysis for large-scale power systems.

[0017] Breakthroughs have been achieved in computational accuracy and interpretability: Since theoretical analysis shows that quadratic curves can approximate the changes in load parameters with node voltage amplitude near the voltage collapse point of a saddle-node bifurcation, a quadratic calculation based on quadratic function fitting is introduced, giving this invention excellent interpretability and generalization ability. This invention introduces an error correction neural network specifically designed to compensate for errors generated in the quadratic fitting process. This design allows for fine-tuning based on theoretically sound function fitting using data-driven methods, improving the computational accuracy of the method under various operating conditions. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating an embodiment of the present invention. Detailed Implementation

[0019] The present invention will be further described below with reference to the accompanying drawings and specific preferred embodiments, but this does not limit the scope of protection of the present invention.

[0020] like Figure 1 As shown, the technical solution adopted in this embodiment includes the following steps: S1. Preliminary calculation of load margin: Input the operating parameters of the power system at the initial operating point into the pre-trained neural network model for preliminary calculation of load margin to obtain a preliminary estimate of the load margin. S2. Secondary calculation of load margin based on function fitting: Based on the preliminary estimated value, select multiple load parameter points, use a pre-trained node voltage amplitude calculation neural network model to obtain the target node voltage amplitude corresponding to each load parameter point, perform quadratic curve fitting based on the multiple load parameter points and their corresponding target node voltage amplitudes, and calculate the secondary calculation value of load margin according to the vertex coordinates of the fitted quadratic curve. Compared to traditional continuous power flow calculation methods, this embodiment completely avoids the complex and time-consuming iterative solution process. By utilizing a trained neural network and combining it with fast quadratic curve fitting operations, the calculation time is reduced by orders of magnitude compared to traditional methods, and the correlation between calculation time and system size is significantly weakened, which can meet the requirements of online analysis for large-scale power systems.

[0021] Meanwhile, compared with the pure neural network "black box" model, this embodiment introduces a quadratic function fitting step based on theoretical laws. This step constructs a quadratic curve with clear meaning through the data points output by the neural network, and performs a quadratic calculation of the load margin by finding the vertex of the curve. This process not only effectively improves the accuracy of the calculation results, but also makes the logic of the entire calculation process clear and greatly enhances the interpretability of the method.

[0022] S3. Error Correction: Input the operating parameters of the initial operating point and the secondary calculated value of the load margin into the pre-trained error correction neural network model to obtain the error correction coefficient. Then, use the error correction coefficient to correct the secondary calculated value of the load margin to obtain the final load margin. This embodiment introduces an error correction neural network specifically designed to compensate for errors generated during the secondary fitting process. This design can improve the computational accuracy of the method under various operating conditions.

[0023] In a specific application example, the neural network model for the preliminary calculation of load margin in step S1 is a feedforward neural network; the mapping relationship between its input and output can be expressed as: ( , , , , → ; Among them, input items This represents a vector consisting of the active power injected by the PV and PQ nodes at the initial operating point. This represents a vector consisting of changes in active power injection at PV and PQ nodes. This represents a vector consisting of the reactive power injected by the PQ node at the initial operating point; This represents a vector consisting of the changes in reactive power injection at nodes PQ; This represents a vector consisting of the voltage magnitudes of the PV nodes and the slack node at the initial operating point; output term This indicates the load margin.

[0024] In a specific application example, the neural network model for calculating the node voltage amplitude in step S2 is a feedforward neural network, and the mapping relationship between its input and output can be expressed as follows: (λ, , , , , → ; Where λ is the load parameter, The target node voltage amplitude.

[0025] In a specific application example, step S2 specifically includes: S21. Using the preliminary estimated value as the midpoint, select two values ​​that are less than and greater than the midpoint to form three load parameter points; In this embodiment, the preliminary estimate obtained in step S1 is defined as follows: Using it as a reference, select the one closest to of and and order = , , and satisfy < < ; S22. Combine the three load parameter points with the operating parameters of the initial operating point, and input them into the node voltage amplitude calculation neural network model to obtain three corresponding target node voltage amplitudes; In this embodiment, respectively ( , , , , ), ( , , , , , ), ( , , , , , The neural network model is calculated by inputting the node voltage amplitude to obtain the corresponding voltage amplitude. , , ; S23. Using the target node voltage amplitudes corresponding to the three obtained load parameter points, a quadratic function is fitted by solving a system of linear equations. =f( )=α 2 +β The coefficients α, β, and γ of +γ; In this embodiment, the three load parameter points and their corresponding target node voltage amplitudes are ( , ), ( , ), ( , Substituting the above quadratic function, we obtain the system of linear equations: = ; Its analytical solution is: =A -1 Λ; Where A = Λ= ; S24. According to the formula =f(V )= The secondary calculation value of the load margin is obtained, where V It is a quadratic function =f( )=α 2 +β The x-coordinate of the vertex of +γ.

[0026] In this embodiment, after S23 is completed, according to the quadratic function f( The property of f( When the maximum value is reached, the node voltage amplitude is: V = ; Substitute it into the fitting function f( The secondary calculated value of the load margin obtained in step S2 is obtained. The analytical expression is obtained as follows: =f(V )= .

[0027] In a specific application example, the error correction neural network model described in step S3 is a feedforward neural network, and the mapping relationship between its input and output can be expressed as: ( , , , , →ε; Where ε is the error correction coefficient, its calculation formula is: ε= ; in, This represents the true load margin, calculated using the traditional continuous power flow method.

[0028] In a specific application example, the specific calculation formula for correcting the secondary calculated value of the load margin using the error correction coefficient in step S3 is as follows: ; in, To obtain the final corrected load margin estimate.

[0029] In a specific application example, before inputting data into any of the neural network models in steps S1-S3, the input data is normalized; after obtaining the output data of the neural network, the output data is denormalized.

[0030] This embodiment also includes a load margin calculation system based on neural networks and quadratic fitting, used to implement the above-mentioned load margin calculation method based on neural networks and quadratic fitting, including: The load margin preliminary calculation module is configured to process the input initial operating parameters using the load margin preliminary calculation neural network model and output a preliminary estimate of the load margin. The load margin secondary calculation module is configured to calculate the secondary value of the load margin based on the preliminary estimated value, using the node voltage amplitude calculation neural network model and the quadratic curve fitting method. The error correction module is configured to perform error compensation on the secondary calculated value based on the error correction neural network model and output the final load margin.

[0031] This embodiment also includes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described method for calculating load margin based on neural networks and quadratic fitting.

[0032] This embodiment also includes a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the above-described method for calculating load margin based on neural networks and quadratic fitting.

[0033] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0034] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating load margin based on neural networks and quadratic fitting, characterized in that, Includes the following steps: S1. Preliminary calculation of load margin: Input the operating parameters of the power system at the initial operating point into the pre-trained neural network model for preliminary calculation of load margin to obtain a preliminary estimate of the load margin. S2. Secondary calculation of load margin based on function fitting: Based on the preliminary estimated value, select multiple load parameter points, use a pre-trained node voltage amplitude calculation neural network model to obtain the target node voltage amplitude corresponding to each load parameter point, perform quadratic curve fitting based on the multiple load parameter points and their corresponding target node voltage amplitudes, and calculate the secondary calculated value of load margin according to the vertex coordinates of the quadratic curve. S3. Error Correction: Input the operating parameters of the initial operating point and the secondary calculated value of the load margin into the pre-trained error correction neural network model to obtain the error correction coefficient. Then, use the error correction coefficient to correct the secondary calculated value of the load margin to obtain the final load margin.

2. The load margin calculation method based on neural networks and quadratic fitting according to claim 1, characterized in that, The neural network model for the preliminary calculation of load margin in step S1 is a feedforward neural network, and the mapping relationship between its input and output can be expressed as follows: ( , , , , )→ ； Among them, input items This represents a vector consisting of the active power injected by the PV and PQ nodes at the initial operating point. This represents a vector consisting of changes in active power injection at PV and PQ nodes. This represents a vector consisting of the reactive power injected by the PQ node at the initial operating point; This represents a vector consisting of the changes in reactive power injection at nodes PQ; This represents a vector consisting of the voltage magnitudes of the PV nodes and the slack node at the initial operating point; output term This indicates the load margin.

3. The load margin calculation method based on neural networks and quadratic fitting according to claim 2, characterized in that, The neural network model for calculating the node voltage amplitude in step S2 is a feedforward neural network, and the mapping relationship between its input and output can be expressed as follows: (l, , , , , )→ ; Where λ is the load parameter, The target node voltage amplitude.

4. The load margin calculation method based on neural networks and quadratic fitting according to claim 3, characterized in that, Step S2 specifically includes: S21. Using the preliminary estimated value of the load margin as the midpoint, select two values ​​that are less than and greater than the midpoint to form three load parameter points; S22. Combine the three load parameter points with the operating parameters of the initial operating point, and input them into the node voltage amplitude calculation neural network model to obtain three corresponding target node voltage amplitudes; S23. Using the target node voltage amplitudes corresponding to the three obtained load parameter points, a quadratic function is fitted by solving a system of linear equations. =f( )=α 2 +β The coefficients α, β, and γ of +γ; S24. According to the formula = The secondary calculated value of the load margin is obtained.

5. The load margin calculation method based on neural networks and quadratic fitting according to claim 4, characterized in that, The error correction neural network model described in step S3 is a feedforward neural network, and the mapping relationship between its input and output can be expressed as follows: ( , , , , )→ε; Where ε is the error correction coefficient, its calculation formula is: e= ; in, This represents the true load margin, calculated using the traditional continuous power flow method.

6. The load margin calculation method based on neural networks and quadratic fitting according to claim 5, characterized in that, The specific calculation formula for correcting the secondary calculated value of the load margin using the error correction coefficient in step S3 is as follows: ； in, To obtain the final corrected load margin estimate.

7. The load margin calculation method based on neural networks and quadratic fitting according to claim 6, characterized in that, Before inputting data into any of the neural network models in steps S1-S3, the input data is normalized; after obtaining the output data of the neural network, the output data is denormalized.

8. A load margin calculation system based on neural networks and quadratic fitting, used to implement the load margin calculation method based on neural networks and quadratic fitting as described in any one of claims 1 to 7, characterized in that, include: The load margin preliminary calculation module is configured to process the input initial operating parameters using the load margin preliminary calculation neural network model and output a preliminary estimate of the load margin. The load margin secondary calculation module is configured to calculate the secondary value of the load margin based on the preliminary estimated value, using the node voltage amplitude calculation neural network model and the quadratic curve fitting method. The error correction module is configured to perform error compensation on the secondary calculated value based on the error correction neural network model and output the final load margin.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the load margin calculation method based on neural networks and quadratic fitting as described in any one of claims 1 to 7.

10. A computer program product, characterized in that, The method includes a computer program that, when executed by a processor, implements the steps of the load margin calculation method based on neural networks and quadratic fitting as described in any one of claims 1 to 7.

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