System weak point identification method and system for forced oscillation

Abstract

The invention discloses a system weak point identification method and system for forced oscillation, and the method comprises the steps: collecting the time series data of the rotor angle, angular velocity and voltage phase / frequency of a generator of a power system based on a PMU, and constructing a measurement matrix and a time derivative matrix after preprocessing the collected data; constructing a feature matrix, solving a coefficient matrix, obtaining a state transition matrix and an input matrix from the coefficient matrix, and extracting to obtain a system dynamic equation; calculating a sensitivity matrix to represent the influence of the input on the system state; defining an output matrix, and calculating an influence matrix; quantifying the total contribution of each input to oscillation based on the sensitivity matrix and the influence matrix, and completing the recognition of the system weak point; the method can extract the dynamic equation of the system without depending on specific parameter information of the power system, identifies the weak point of the system through quantitative analysis, and improves the simplicity and reliability of the method.

Description

Technical Field

[0001] This invention belongs to the field of power system analysis technology, and in particular relates to a method and system for identifying weak points in systems subject to forced oscillations. Background Technology

[0002] Forced oscillations are common low-frequency oscillations in power systems, typically caused by external periodic disturbances, such as periodic fluctuations in generator mechanical power. Forced oscillations not only affect the stability of the power system but can also damage system equipment and even trigger large-scale power outages. Therefore, timely identification of weaknesses in the system is crucial for preventing and controlling forced oscillations.

[0003] Traditional forced oscillation analysis methods primarily rely on the physical models and parameter information of power systems, analyzing the dynamic response of the system by establishing differential equations or state-space models. For example, methods based on energy functions and modal analysis, while able to explain the oscillation mechanism to some extent, typically require detailed system parameters and have high computational complexity, making them difficult to apply rapidly in large-scale practical power systems. Furthermore, traditional analysis methods often struggle to quantitatively assess the contribution of each node to the oscillation, resulting in insufficient accuracy and reliability in identifying weak points.

[0004] In recent years, with the widespread application of Wide Area Measurement Systems (WAMS) and Phasor Measurement Units (PMUs), real-time data acquisition for power systems has become more convenient. Data-driven methods have gradually become a research hotspot. These methods, by analyzing real-time system data, can extract the dynamic characteristics of a system without relying on detailed system parameters. However, existing data-driven methods still suffer from insufficient interpretability and high computational complexity when identifying system weaknesses. For example, while machine learning-based forced oscillation analysis methods can train models with large amounts of data, their results often lack clear physical meaning, making it difficult to provide intuitive decision support for power system dispatchers.

[0005] Therefore, there is an urgent need for a method that can quantitatively analyze the weaknesses of a power system without relying on specific power system parameters, in order to improve the simplicity and reliability of forced oscillation analysis. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide a method and system for identifying weak points in systems subject to forced oscillations that can improve the accuracy of identification.

[0007] Technical solution: The present invention provides a method for identifying weak points in a system subject to forced oscillation, comprising:

[0008] Step 1: Acquire generator rotor angle of the power system based on synchronous phasor measurement unit (PMU) angular velocity The data includes time series data of voltage phase / frequency, and a measurement matrix is ​​constructed after preprocessing the acquired data. and Time derivative matrix ;

[0009] Step 2: Construct the feature matrix Solve the coefficient matrix Obtain the state transition matrix from the coefficient matrix. and input matrix Thus, the system dynamic equations are extracted. :

[0010] ;

[0011] ;

[0012] in, As a disturbance source, it serves as the input;

[0013] Step 3: Calculate the sensitivity matrix It characterizes the influence of input on the system state;

[0014] ;

[0015] in, Each element Indicates input Regarding system status The impact, and represents the row and column coordinates of the matrix;

[0016] Step 4: Define the output matrix Calculate the influence matrix :

[0017] ;

[0018] in, This is the mapping matrix from system state to output. Each element Indicates input For output Contribution; set threshold ,like Greater than If so, then that point is a weak point in the local system;

[0019] Step 5: Quantize each input based on the sensitivity matrix and influence matrix. The total contribution to the oscillation is used to identify the weak points in the system.

[0020] Furthermore, Step 1 includes: for the system having 1 generator, each generator has Sampling points at various times, based on generator rotor angles acquired by the PMU. and angular velocity Calculate the deviations of rotor angle and angular velocity near the steady-state operating point. and Construct a measurement matrix :

[0021] , ;

[0022] Then the measurement matrix for:

[0023] ;

[0024] in, and Indicates the first The generator at time The rotor angle and angular velocity, and Indicates the first The generator at time The rotor angle deviation value and angular velocity deviation value, and Indicates the first Rotor angle and angular velocity of the generator under steady state;

[0025] Measurement Matrix The dimension is ,in Indicates the number of state variables;

[0026] Next, the measurement matrix is ​​calculated. Time derivative:

[0027]

[0028]

[0029] in, The time sampling interval;

[0030] Then the time derivative matrix for:

[0031] ;

[0032] Time derivative matrix The dimension is also , and measurement matrix The dimensions are consistent.

[0033] Furthermore, the construction of the feature matrix described in Step 2 include:

[0034] Select a set of candidate functions, including constant terms, linear terms, polynomial terms, and trigonometric function terms with known forced oscillation frequencies;

[0035] Constructing the feature matrix :

[0036]

[0037] in, and These are rotor angle deviation and angular velocity deviation, respectively. This is the forced oscillation frequency; Indicates a point in time; and The first The generator rotor angle deviation and angular velocity deviation; the feature matrix dimension is 2r corresponds to the linear terms of r generators, including and , Corresponding to The sine and cosine terms of the candidate forced oscillation frequencies, i.e. and 1 corresponds to the constant term. This represents the number of time sampling points.

[0038] Furthermore, the solution of the coefficient matrix described in Step 2 include:

[0039] Initialize the coefficient matrix The initial values ​​are obtained by using the sequential threshold least squares method:

[0040] ;

[0041] in, Characteristic matrix The false reversal;

[0042] Introducing a threshold ,right Perform sparsification:

[0043] ;

[0044] The coefficient matrix is ​​updated gradually through iterative optimization. Until it converges.

[0045] Furthermore, the state transition matrix described in Step 2 and input matrix The format is as follows:

[0046] State transition matrix and input matrix We obtain this from the partition coefficient matrix Ξ:

[0047] State transition matrix A: Takes the portion of the corresponding linear term in Ξ;

[0048] Input matrix B: Take the portion of Ξ corresponding to the trigonometric function terms.

[0049] Furthermore, the output matrix described in Step 4 It is a mapping matrix from system state to output. The system output variable is set as the node voltage deviation, and the output matrix is... Defined as:

[0050] ;

[0051] in, It is the number of system state variables. It is the number of system output variables. , indicating the first The state variable is the first... The contribution of each output variable.

[0052] Furthermore, Step 5 includes:

[0053] Calculate the values ​​of each input source based on the sensitivity matrix and influence matrix. Total contribution to oscillations:

[0054]

[0055] Analyze each input source Total contribution to oscillations Size, set threshold ,like Greater than If the node containing the input source is identified, then the identification of the system's weak point is complete.

[0056] Based on the same inventive concept, the present invention also provides a system for identifying weak points in a system subject to forced oscillation, comprising:

[0057] The acquisition module is used to acquire the generator rotor angle of the power system based on the synchronous phasor measurement unit (PMU). angular velocity The data includes time series data of voltage phase / frequency, and a measurement matrix is ​​constructed after preprocessing the acquired data. and Time derivative matrix ;

[0058] The feature matrix module is used to construct the feature matrix. Solve the coefficient matrix Obtain the state transition matrix from the coefficient matrix. and input matrix Thus, the system dynamic equations are extracted. :

[0059]

[0060]

[0061] in, As a disturbance source, it serves as the input;

[0062] The sensitivity matrix module is used to calculate the sensitivity matrix. It characterizes the influence of input on the system state;

[0063]

[0064] in, Each element Indicates input Regarding system status The impact, and represents the row and column coordinates of the matrix;

[0065] The influence matrix module is used to define the output matrix. Calculate the influence matrix :

[0066]

[0067] in, This is the mapping matrix from system state to output. Each element Indicates input For output Contribution; set threshold ,like Greater than If so, then that point is a weak point in the local system;

[0068] The identification module is used to quantize each input source based on the sensitivity matrix and the influence matrix. The total contribution to the oscillation is used to identify the weak points in the system.

[0069] Based on the same inventive concept, the present invention also provides a computing device, comprising: one or more processors, one or more memories, and one or more programs, the programs being stored in the memory and configured to be executed by the processor, wherein when the programs are loaded onto the processor, they implement the steps of the system vulnerability identification method for forced oscillations as described in any of the preceding claims.

[0070] Based on the same inventive concept, the present invention also provides a storage medium storing a computer program, the computer program including program instructions, which, when executed by a processor, cause the processor to perform the steps of the system vulnerability identification method for forced oscillations as described in any of the preceding claims.

[0071] Beneficial effects: Compared with existing technologies, this invention extracts the dynamic equations of the system based on real-time PMU data in a data-driven manner, without relying on specific parameter information of the power system. It can be quickly and easily applied to actual power systems, and is especially suitable for forced oscillation analysis of large-scale complex power grids. By calculating the sensitivity matrix and influence matrix, this invention can quantitatively analyze the contribution of each input source to the oscillation and accurately identify local and global weak points in the system. Compared with traditional qualitative analysis methods, this invention provides more accurate weak point identification results, which helps power system dispatchers formulate targeted control strategies. Attached Figure Description

[0072] Figure 1 This is a flowchart of a method according to an embodiment of the present invention. Detailed Implementation

[0073] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0074] As attached Figure 1 As shown, the system weakness identification method for forced oscillation in this embodiment includes:

[0075] Step 1: Acquire generator rotor angle of the power system based on synchronous phasor measurement unit (PMU) angular velocity The data includes time series data of voltage phase / frequency, and a measurement matrix is ​​constructed after preprocessing the acquired data. and Time derivative matrix ;

[0076] Step 2: Construct the feature matrix Solve the coefficient matrix Obtain the state transition matrix from the coefficient matrix. and input matrix Thus, the system dynamic equations are extracted. :

[0077] ;

[0078] ;

[0079] in, As a disturbance source, it serves as the input;

[0080] Step 3: Calculate the sensitivity matrix It characterizes the influence of input on the system state;

[0081] ;

[0082] in, Each element Indicates input Regarding system status The impact, and represents the row and column coordinates of the matrix;

[0083] Step 4: Define the output matrix Calculate the influence matrix :

[0084] ;

[0085] in, This is the mapping matrix from system state to output. Each element Indicates input For output Contribution; set threshold ,like Greater than If so, then that point is a weak point in the local system;

[0086] Step 5: Quantize each input based on the sensitivity matrix and influence matrix. The total contribution to the oscillation is used to identify the weak points in the system.

[0087] Specifically, Step 1: The power system in this embodiment adopts an IEEE 9-bus system, which includes 9 buses, 3 generators, and 9 branches. A synchronous phasor measurement unit (PMU) is installed on each generator node of the IEEE 9-bus system to collect the generator's rotor angle (…). ), angular velocity ( The data consisted of time-series data of voltage phase and frequency. The time interval for acquiring the time-series data was 0.02 seconds (50Hz sampling frequency), and the acquisition duration was 10 seconds.

[0088] Based on the generator rotor angle and angular velocity data acquired by the PMU, the deviation value near the steady-state operating point is calculated. and Construct a measurement matrix :

[0089]

[0090]

[0091] in, and Indicates the first The generator at time The rotor angle and angular velocity, and Indicates the first The rotor angle and angular velocity of the generator in steady state. , .

[0092]

[0093] in, and Indicates the first The generator at time The rotor angle and angular velocity, and Indicates the first The rotor angle and angular velocity of the generator in steady state. , =500.

[0094]

[0095]

[0096] in, The time sampling interval is denoted as .

[0097] Time derivative matrix :

[0098]

[0099] in, , .

[0100] Step 2: Construct the feature matrix Solve the coefficient matrix Extract the system dynamic equations.

[0101] The candidate function set is selected, including constant terms, linear terms, polynomial terms, and trigonometric function terms with known forced oscillation frequencies. The forced oscillation frequency of the system is then determined. ,but

[0102]

[0103] Constructing the feature matrix :

[0104]

[0105] Where 2r corresponds to the linear terms of r generators, including Δδ and Δω, and 2n corresponds to the sine and cosine terms of n candidate forced oscillation frequencies, i.e. and 1 corresponds to the constant term.

[0106] Here r=3, n=1, therefore, the dimension of the feature matrix is ​​500×9.

[0107] Initialize the coefficient matrix The initial values ​​are obtained by using the sequential threshold least squares method:

[0108]

[0109] in, Characteristic matrix The false reversal;

[0110] Introducing a threshold For the coefficient matrix Perform sparsification:

[0111] ;

[0112] The coefficient matrix is ​​updated gradually through iterative optimization. Until it converges.

[0113] If r=3 and n=1, then the coefficient matrix The dimension is 9×6. Based on the coefficient matrix Ξ obtained from the solution, matrices A and B are extracted:

[0114] State transition matrix A: Take the part of the corresponding linear terms in Ξ (rows 2 to 7, dimension 6×6);

[0115] Input matrix B: Take the portion of the trigonometric function terms in Ξ (rows 8 to 9, dimension 2×6) and transpose it.

[0116] Step 3: Calculate the sensitivity matrix :

[0117] The system state matrix has been extracted in Step 2. and input matrix Calculate the sensitivity matrix :

[0118]

[0119]

[0120] Each element Indicates input Regarding system status The impact.

[0121] Step 4: Influence Matrix Calculation and Local Weak Point Identification

[0122] Define the output matrix The system's output variable is set to the voltage deviation of each node, and the output matrix is... :

[0123]

[0124] in, , indicating the first The state variable is the first... The contribution of each output variable.

[0125]

[0126] Calculate the influence matrix

[0127]

[0128] Each element Indicates input For output Contributions;

[0129] Set threshold Due to the influence matrix Significantly greater than Then node 2 is a weak point in the local system;

[0130] Step 5: Quantize each input source Total contribution to oscillations:

[0131]

[0132] Analyze each input source Total contribution to oscillations Size, set threshold , Greater than If the input source is node 2, then the node is the weak point of the global system, thus completing the identification of the weak point of the system.

[0133] This concludes the identification of weak points in a system designed for forced oscillations.

[0134] Based on the same inventive concept, this embodiment also provides a system for identifying weak points in a system subject to forced oscillation, comprising:

[0135] The acquisition module is used to acquire the generator rotor angle of the power system based on the synchronous phasor measurement unit (PMU). angular velocity The data includes time series data of voltage phase / frequency, and a measurement matrix is ​​constructed after preprocessing the acquired data. and Time derivative matrix ;

[0136] The feature matrix module is used to construct the feature matrix. Solve the coefficient matrix Obtain the state transition matrix from the coefficient matrix. and input matrix Thus, the system dynamic equations are extracted. :

[0137]

[0138]

[0139] in, As a disturbance source, it serves as the input;

[0140] The sensitivity matrix module is used to calculate the sensitivity matrix. It characterizes the influence of input on the system state;

[0141]

[0142] in, Each element Indicates input Regarding system status The impact, and represents the row and column coordinates of the matrix;

[0143] The influence matrix module is used to define the output matrix. Calculate the influence matrix :

[0144]

[0145] in, This is the mapping matrix from system state to output. Each element Indicates input For output Contribution; set threshold ,like Greater than If so, then that point is a weak point in the local system;

[0146] The identification module is used to quantize each input source based on the sensitivity matrix and the influence matrix. The total contribution to the oscillation is used to identify the weak points in the system.

[0147] Based on the same inventive concept, this embodiment also provides a computing device, including: one or more processors, one or more memories, and one or more programs, the programs being stored in the memory and configured to be executed by the processor, the programs being loaded onto the processor to implement the steps of the system vulnerability identification method for forced oscillations according to any of the preceding claims.

[0148] Based on the same inventive concept, this embodiment also provides a storage medium storing a computer program, the computer program including program instructions, which, when executed by a processor, cause the processor to perform the steps of the system vulnerability identification method for forced oscillations as described in any of the preceding claims.

[0149] The above embodiments are merely preferred embodiments of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications and improvements made to the technical solutions based on the technical concepts proposed in the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for identifying weak points in a system subject to forced oscillations, characterized in that, include: Step 1: Acquire generator rotor angle of the power system based on synchronous phasor measurement unit (PMU) angular velocity The data includes time series data of voltage phase / frequency, and a measurement matrix is ​​constructed after preprocessing the acquired data. and Time derivative matrix ; Step 2: Construct the feature matrix Solve the coefficient matrix Obtain the state transition matrix from the coefficient matrix. and input matrix Thus, the system dynamic equations are extracted. : ； ； in, As a disturbance source, it serves as the input; Step 3: Calculate the sensitivity matrix It characterizes the influence of input on the system state; ； in, Each element Indicates input Regarding system status The impact, and represents the row and column coordinates of the matrix; Step 4: Define the output matrix Calculate the influence matrix : ； in, This is the mapping matrix from system state to output. Each element Indicates input For output Contribution; set threshold ,like Greater than If so, then that point is a weak point in the local system; Step 5: Quantize each input based on the sensitivity matrix and influence matrix. The total contribution to the oscillation is used to identify the weak points in the system.

2. The method for identifying weak points in a system subject to forced oscillations according to claim 1, characterized in that, Step 1 includes: for the system having 1 generator, each generator has Sampling points at various times, based on generator rotor angles acquired by the PMU. and angular velocity Calculate the deviations of rotor angle and angular velocity near the steady-state operating point. and Construct a measurement matrix : ， ； Then the measurement matrix for: ； in, and Indicates the first The generator at time The rotor angle and angular velocity, and Indicates the first The generator at time The rotor angle deviation value and angular velocity deviation value, and Indicates the first Rotor angle and angular velocity of the generator under steady state; Measurement Matrix The dimension is ,in Indicates the number of state variables; Next, the measurement matrix is ​​calculated. Time derivative: ； ； in, The time sampling interval; Then the time derivative matrix for: ； Time derivative matrix The dimension is also , and measurement matrix The dimensions are consistent.

3. The method for identifying weak points in a system subject to forced oscillations according to claim 1, characterized in that, Step 2 describes the construction of the feature matrix. include: Select a set of candidate functions, including constant terms, linear terms, polynomial terms, and trigonometric function terms with known forced oscillation frequencies; Constructing the feature matrix : ； in, and These are rotor angle deviation and angular velocity deviation, respectively. This is the forced oscillation frequency; Indicates a point in time; and The first The generator rotor angle deviation and angular velocity deviation; the feature matrix dimension is 2r corresponds to the linear terms of r generators, including and , Corresponding to The sine and cosine terms of the candidate forced oscillation frequencies, i.e. and 1 corresponds to the constant term. This represents the number of time sampling points.

4. The method for identifying weak points in a system subject to forced oscillation according to claim 1, characterized in that, Step 2 involves solving the coefficient matrix. include: Initialize the coefficient matrix The initial values ​​are obtained by using the sequential threshold least squares method: ； in, Characteristic matrix The false reversal; Introducing a threshold ,right Perform sparsification: ； The coefficient matrix is ​​updated gradually through iterative optimization. Until it converges.

5. The method for identifying weak points in a system subject to forced oscillations according to claim 1, characterized in that, The state transition matrix mentioned in Step 2 and input matrix The format is as follows: State transition matrix and input matrix We obtain this from the partition coefficient matrix Ξ: State transition matrix A: Takes the portion of the corresponding linear term in Ξ; Input matrix B: Take the portion of Ξ corresponding to the trigonometric function terms.

6. The method for identifying weak points in a system subject to forced oscillation according to claim 1, characterized in that, The output matrix mentioned in Step 4 It is a mapping matrix from system state to output. The system output variable is set as the node voltage deviation, and the output matrix is... Defined as: ； in, It is the number of system state variables. It is the number of system output variables. , indicating the first The state variable is the first... The contribution of each output variable.

7. The method for identifying weak points in a system subject to forced oscillations according to claim 1, characterized in that, Step 5 includes: Calculate the values ​​of each input source based on the sensitivity matrix and influence matrix. Total contribution to oscillations: ； Analyze each input source Total contribution to oscillations Size, set threshold ,like Greater than If the node containing the input source is identified, then the identification of the system's weak point is complete.

8. A system for identifying weak points in a system subjected to forced oscillations, characterized in that, include: The acquisition module is used to acquire the generator rotor angle of the power system based on the synchronous phasor measurement unit (PMU). angular velocity The data includes time series data of voltage phase / frequency, and a measurement matrix is ​​constructed after preprocessing the acquired data. and Time derivative matrix ; The feature matrix module is used to construct the feature matrix. Solve the coefficient matrix Obtain the state transition matrix from the coefficient matrix. and input matrix Thus, the system dynamic equations are extracted. : ； ； in, As a disturbance source, it serves as the input; The sensitivity matrix module is used to calculate the sensitivity matrix. It characterizes the influence of input on the system state; ； in, Each element Indicates input Regarding system status The impact, and represents the row and column coordinates of the matrix; The influence matrix module is used to define the output matrix. Calculate the influence matrix : ； in, This is the mapping matrix from system state to output. Each element Indicates input For output Contribution; set threshold ,like Greater than If so, then that point is a weak point in the local system; The recognition module is used to quantize each input based on the sensitivity matrix and the influence matrix. The total contribution to the oscillation is used to identify the weak points in the system.

9. A computing device, characterized in that, include: One or more processors, one or more memories, and one or more programs, said programs being stored in the memory and configured to be executed by the processor, said programs, when loaded onto the processor, implementing the steps of the system vulnerability identification method for forced oscillations according to any one of claims 1 to 7.

10. A storage medium, characterized in that, The storage medium stores a computer program, which includes program instructions that, when executed by a processor, cause the processor to perform the steps of the system vulnerability identification method for forced oscillations according to any one of claims 1 to 7.

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