A Power Grid Transient Stability Judgment Method Based on the Maximum Lyapunov Exponential Probability Distribution Criterion

Abstract

A power grid transient stability discrimination method based on the maximum Lyapunov exponent probability distribution criterion utilizes a phasor measurement unit (PMU) to uniformly monitor and collect the phase angles of the voltage at each generator terminal in real time, and calculates the generator power angle trajectory. Based on the generator power angle trajectory, the power angle MLE trajectory is calculated. The probability distribution is fitted using a diffusion kernel density estimation method to obtain the MLE probability density function. Sampling is performed within the MLE range to calculate the probability distribution characteristics of the power angle MLE trajectory. A transient stability discrimination model is constructed and trained using a random forest algorithm. During real-time discrimination, the generator power angle trajectory is calculated based on the generator terminal voltage phase angle data collected by the PMU, and the probability distribution characteristics of the power angle MLE trajectory are calculated and input into the transient stability discrimination model to obtain the system transient stability discrimination result. This invention enhances the feature representation capability of the maximum Lyapunov exponent, improves the overall discrimination accuracy of transient stability, and reduces the risk of misjudgment and missed judgment.

Description

Technical Field

[0001] This invention belongs to the field of power system analysis, specifically relating to real-time power grid transient stability determination based on PMU response observation. Background Technology

[0002] With the rapid development of the national economy, the demand for electricity in society continues to increase, the installed capacity of new energy sources such as photovoltaic and wind power has further increased, and the commissioning of high-voltage direct current transmission channels has led to the gradual formation of a highly electronic AC / DC hybrid power grid. After fault disturbances, the dynamic behavior of the power system becomes more complex, and accurate judgment of the stability of the power system is of great significance for the safe operation of the system and emergency decision-making and control.

[0003] The maximum Lyapunov exponent is an indicator that characterizes the dynamic behavior of complex systems. When a transient fault occurs in a system, if the maximum Lyapunov exponent of the generator power angle is consistently negative at the end of the response, the system can transition to a stable equilibrium point and maintain transient stability; otherwise, it becomes unstable. Although this criterion applies under most operating conditions, under critical operating conditions, there may be situations where the generator power angle increases slowly in some areas, the maximum Lyapunov exponent is positive, but the system remains stable. In this case, the criterion fails, leading to misjudgments of system stability. Summary of the Invention

[0004] The purpose of this invention is to address the aforementioned problems by proposing a power grid transient stability discrimination method based on the probability distribution criterion of the maximum Lyapunov exponent. This method enhances the feature representation capability of the maximum Lyapunov exponent, reduces its limitations, uses the probability distribution characteristics of the maximum Lyapunov exponent within a time window as the stability discrimination criterion, and achieves real-time transient stability discrimination based on the random forest algorithm, thereby improving the accuracy of transient stability discrimination.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for determining the transient stability of a power grid based on the maximum Lyapunov exponent probability distribution criterion is characterized by the following steps:

[0007] Step 1: Use the phasor measurement unit (PMU) in the power system wide area measurement system to uniformly monitor and collect the phase angle of the voltage at each generator terminal in real time. After data collection, the data is transmitted to the power system monitoring center through a distributed communication network to obtain the real-time phase angle data of the generator terminal voltage. The generator terminal voltage phase angle is compared with the reference generator to calculate the generator power angle and the generator power angle trajectory formed by the generator power angle at the connection time. At the same time, all generator power angle trajectories are saved to the historical power angle trajectory data.

[0008] Step 2: Based on the generator power angle trajectory obtained in Step 1, calculate the real-time maximum Lyapunov exponent (MLE) of the power angle trajectory to obtain the power angle MLE trajectory;

[0009] Step 3: Combine the MLE trajectory of the power angle within the time period with the diffusion kernel density estimation method to fit the probability distribution of the MLE trajectory and obtain the MLE probability density function f. MLE ;

[0010] Step 4: Based on the MLE probability density function f obtained in Step 3 MLE N samples were uniformly sampled within the range of MLE values. S Next, sort the values ​​in ascending order. calculate probability density at As a probability distribution feature of the MLE trajectory at the power angle;

[0011] Step 5: Combining the generator power angle trajectory from Step 1 and the corresponding power angle MLE trajectory calculated in Step 2, calculate the probability distribution characteristics of the power angle MLE trajectory according to Step 4, and use the probability distribution characteristics of the power angle MLE trajectory as a new feature set of power angle MLE probability distribution; based on the new feature set of power angle MLE probability distribution and the corresponding transient stability label, if the label is 0, it indicates that the power grid is transiently stable under historical operating conditions, and if it is 1, it indicates that the power grid is transiently unstable. Using the probability distribution characteristics of the power angle MLE trajectory in the new feature set of power angle MLE probability distribution as input and the corresponding transient stability label as output, a transient stability discrimination model is constructed and trained using the random forest algorithm with strong nonlinear fitting ability.

[0012] Step Six: Based on the transient stability discrimination model trained in Step Five, given the generator power angle trajectory obtained in Step One at the current time, calculate the corresponding power angle MLE trajectory according to Step Two, and then calculate the probability distribution characteristics of the power angle MLE trajectory according to Step Three and Step Four. Input the probability distribution characteristics of the power angle MLE trajectory into the transient stability discrimination model obtained in Step Five, and output the transient stability label of the system at the current time. If it is 0, it indicates that the system is transiently stable at the current time; if it is 1, the system is transiently unstable.

[0013] The formula for calculating the MLE trajectory of the work angle obtained in step two is as follows:

[0014]

[0015] In the formula: Let kΔt be the power angle MLE of the i-th generator at time kΔt, where k is a positive integer greater than N, N is the initial point for calculation (N is a positive integer), Δt is the time interval for the PMU to monitor the phase angle of the generator terminal voltage, and kΔt represents the time at which the generator power angle MLE is calculated. Let be the generator power angles of the i-th generator in the system at times hΔt, (h-1)Δt, (k+h)Δt, and (k+h-1)Δt, respectively, where h is the time counter and takes a positive integer value within [1, N]. When the initial point N is 1, equation (1) simplifies to:

[0016]

[0017] In the formula: the meanings of each parameter are consistent with those in formula (1). These are the generator power angle trajectories of the i-th generator at time Δt, 0Δt, kΔt, and (k+1)Δt, respectively.

[0018] The probability distribution of the work angle MLE trajectory obtained in step two is fitted using the diffusion kernel density estimation method to obtain the MLE probability density function. The specific calculation process is as follows:

[0019] Samples of the MLE trajectory of the work angle within a given time period The total number of samples is N m Based on the diffusion kernel density estimation theory, the MLE probability density function f of the work angle MLE trajectory is... MLE (m;t) is represented as:

[0020]

[0021]

[0022] In the formula: For Gaussian kernel function, Let m be the set of all real numbers, m be the possible values ​​of the angle of effort MLE, and t be the value derived from the sample. The determined parameters, where subscript 'a' represents the sample. The count of t. The calculation of t is carried out according to the following process:

[0023] ① Construct two iterative estimators as shown in equations (4) and (5):

[0024]

[0025] In the formula: j is the round number for calculation, ||f MLE (j) || 2 Let be the norm of the MLE probability density function calculated in the j-th round. Gaussian kernel function The 2jth derivative, m a ,m k for In the sample, the subscripts a and k represent the sample. The count, Let t be the optimal value of parameter t obtained from the calculation in the j-th round;

[0026]

[0027] In the formula: Let ||f| be the optimal estimate of parameter t obtained in the j-th round of calculation. MLE (j+1) || 2 Let be the norm of the MLE probability density function calculated in the (j+1)th round;

[0028] ②Assuming the MLE follows a normal distribution, calculate the sample variance σ 2 As The initial value is set to the number of calculations, l = 5;

[0029] ③ with Substituting the initial value into equation (4) to calculate ||f MLE (l+2) || 2 That is, in equation (4), let j = l + 2 for calculation, and then ||f MLE (l+2) || 2 Substituting into equation (5) yields the following results: The initial value is corrected to And let l = l-1;

[0030] ④ Repeat step ③ until you get the result. As The initial value;

[0031] ⑤ Substituting the initial value into equation (4) to calculate ||f MLE (2) || 2 Then calculate

[0032] t * This is the optimal estimate of parameter t in equation (3);

[0033] ⑥ Order The initial value is t * Set l = 5, and repeat steps ③-⑤ as one round until there is a gap of t between two rounds of iteration. * The change is less than 10 -6 At this time, let t = t in equation (3) * That is, the probability density function of MLE is f as shown in equation (3). MLE (m;t).

[0034] The transient stability refers to the transient work angle stability.

[0035] The generator power angle refers to the difference in terminal phase angle between the generator and the reference generator.

[0036] The training of the transient stability discrimination model relies on the new feature set of the power angle MLE probability distribution constructed by the historical power angle trajectory data saved in step one through steps two, three, four and five. The real-time discrimination of transient stability relies on the probability distribution features of the power angle MLE trajectory calculated by the generator power angle trajectory in step one through steps two, three and four.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] The method of this invention can fully consider various complex working conditions, including critical working conditions. It uses the diffusion kernel density estimation method to fit the probability distribution of the power angle MLE trajectory, and obtains the probability distribution features of the power angle MLE trajectory by sampling based on the MLE probability density function, thereby improving the feature representation ability of the maximum Lyapunov exponent. Furthermore, based on the probability distribution features, a stability discrimination model is constructed using the random forest algorithm to perform real-time transient stability discrimination of the system, thereby improving the overall discrimination accuracy of transient stability and reducing the risk of misjudgment and missed judgment. Attached Figure Description

[0039] Figure 1 The flowchart shows the power grid transient stability discrimination method based on the maximum Lyapunov exponent probability distribution criterion.

[0040] Figure 2 This is a schematic diagram of the computing scenario described in an embodiment of the present invention.

[0041] Figure 3 These are typical stable, unstable, and critical work angle trajectories.

[0042] Figure 4 These are typical MLE trajectories corresponding to stable, unstable, and critical work angle trajectories.

[0043] Figure 5 This represents the MLE probability distribution within a typical 0.2-second time window at the end of stable, unstable, and critical work angle trajectories. Detailed Implementation

[0044] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] like Figure 1 As shown in the embodiment of the present invention, the power grid transient stability discrimination method based on the maximum Lyapunov exponent probability distribution criterion includes the following steps: Step 1: Using the phasor measurement unit (PMU) in the power system wide-area measurement system, the phase angles of the voltages at the generator terminals of each generator in the power system are monitored and collected in real time. The generator terminal voltage phase angles are compared with those of a reference generator to obtain the generator power angle and the generator power angle trajectory formed by the generator power angles at the connection time. This embodiment uses transient simulation data under a simplified main grid typical operation mode in a certain region of China as the research object. The network structure is shown in [reference needed]. Figure 2 It comprises 197 nodes, 24 renewable energy power plants, and 4 DC transmission lines. The transient simulation software used is PSD-BPA developed by the China Electric Power Research Institute Co., Ltd., with transient faults set to various fault types including N-1, N-2, N-3, and DC faults, as covered in the power system safety guidelines. After simulation, using the system's slack node as the reference generator, the power angle trajectories of the remaining 15 generators during the transient process are calculated. Typical stable, unstable, and critical generator power angle trajectories are shown below. Figure 3 As shown.

[0046] Step Two: Based on the generator power angle trajectory obtained in Step One, calculate the real-time maximum Lyapunov exponent of the power angle trajectory to obtain the power angle MLE trajectory. Typical power angle MLE trajectories under stable, unstable, and critically stable conditions are shown below. Figure 4 As shown. Figure 4 This indicates that the power angle MLE trajectory may interweave under the three typical operating conditions, affecting the determination of transient stability.

[0047] Step 3: Combining the power angle MLE trajectory within 0.2 seconds of the transient final stage, the probability distribution of the power angle MLE trajectory is fitted using the diffusion kernel density estimation method to obtain the MLE probability density function. The probability distributions of the power angle MLE trajectory under typical stable, unstable, and critically stable conditions are as follows: Figure 5 As shown. Figure 5This indicates that after fitting the probability distribution of the work angle MLE trajectory, different working conditions can be significantly distinguished, and the feature representation ability of the maximum Lyapunov exponent is enhanced.

[0048] Step 4: Based on the MLE probability density function obtained in Step 3, uniformly sample 1000 times within the MLE value range [-2,2], and sort the sampled values ​​from smallest to largest. Calculate the probability density at the sampled values ​​as the probability distribution feature of the MLE trajectory.

[0049] Step 5: Combining the generator power angle trajectory from Step 1 and the corresponding power angle MLE trajectory calculated in Step 2, calculate the probability distribution characteristics of the power angle MLE trajectory according to Step 4, and use these characteristics as a new feature set for the power angle MLE probability distribution. Using the probability distribution characteristics of the power angle MLE trajectory in this new feature set as input and the corresponding transient stability label as output, construct and train a transient stability discrimination model using the random forest algorithm. Model training is implemented using Python and the open-source toolkit Scikit-learn.

[0050] Step Six: Based on the transient stability discrimination model trained in Step Five, given the generator power angle trajectory obtained in Step One at the current moment, calculate the corresponding power angle MLE trajectory according to Step Two. Then, calculate the probability distribution characteristics of the power angle MLE trajectory according to Steps Three and Four, input the probability distribution characteristics of the power angle MLE trajectory into the transient stability discrimination model obtained in Step Five, and output the transient stability discrimination result of the system at the current moment. In this embodiment, 1000 unstable operating condition samples and 1000 stable operating condition samples were randomly selected to test the transient stability discrimination method proposed in this application. At the same time, the discrimination effect of the traditional maximum Lyapunov exponent criterion was compared and tested. The results are shown in Table 1. The test results show that the method proposed in this application can effectively improve the overall discrimination accuracy of transient stability and reduce the risk of misjudgment and missed judgment.

[0051] Table 1

[0052] Traditional maximum Lyapunov exponent criterion 84.8 7.2 25.7 The transient stability determination method proposed in this application 96.8 3.5 2.8

[0053] Finally, it should be noted that the above description is merely one embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining the transient stability of a power grid based on the maximum Lyapunov exponent probability distribution criterion, characterized in that, Includes the following steps: Step 1: Use the phasor measurement unit (PMU) in the power system wide area measurement system to uniformly monitor and collect the phase angle of the voltage at the generator terminals of each generator in the power system in real time. After data collection, the data is transmitted to the power system monitoring center through a distributed communication network to obtain the real-time phase angle data of the generator terminals. The generator terminal voltage phase angle is compared with the reference generator to obtain the generator power angle and the generator power angle trajectory formed by the generator power angle at the connection time. At the same time, all generator power angle trajectories are saved to the historical power angle trajectory data. Step 2: Based on the generator power angle trajectory obtained in Step 1, calculate the real-time maximum Lyapunov exponent of the power angle trajectory to obtain the power angle MLE trajectory; Step 3: Combine the MLE trajectory of the power angle within the time period with the diffusion kernel density estimation method to fit the probability distribution of the MLE trajectory and obtain the MLE probability density function f. MLE ; Step 4: Based on the MLE probability density function f obtained in Step 3 MLE N samples were uniformly sampled within the range of MLE values. S Then, sort the values ​​in ascending order to m. S1 ,m S2 ,...,m SNS Calculate m S1 ,m S2 ,...,m SNS The probability density f at point MLE (m S1 ),f MLE (m S2 ),...,f MLE (m SNS This serves as a probability distribution characteristic of the MLE trajectory at the power angle; Step 5: Combining the generator power angle trajectory from Step 1 and the corresponding power angle MLE trajectory calculated in Step 2, calculate the probability distribution characteristics of the power angle MLE trajectory according to Step 4, and use the probability distribution characteristics of the power angle MLE trajectory as a new feature set of power angle MLE probability distribution; based on the new feature set of power angle MLE probability distribution and the corresponding transient stability label, if the label is 0, it indicates that the power grid is transiently stable under historical operating conditions, and if it is 1, it indicates that the power grid is transiently unstable. Using the probability distribution characteristics of the power angle MLE trajectory in the new feature set of power angle MLE probability distribution as input and the corresponding transient stability label as output, a transient stability discrimination model is constructed and trained using the random forest algorithm with strong nonlinear fitting ability. Step Six: Based on the transient stability discrimination model trained in Step Five, given the generator power angle trajectory obtained in Step One at the current time, calculate the corresponding power angle MLE trajectory according to Step Two, and then calculate the probability distribution characteristics of the power angle MLE trajectory according to Step Three and Step Four. Input the probability distribution characteristics of the power angle MLE trajectory into the transient stability discrimination model obtained in Step Five, and output the transient stability label of the system at the current time. If it is 0, it indicates that the system is transiently stable at the current time; if it is 1, the system is transiently unstable.

2. The power grid transient stability discrimination method based on the maximum Lyapunov exponent probability distribution criterion according to claim 1, characterized in that, The formula for calculating the MLE trajectory of the work angle obtained in step two is as follows: In the formula: Let kΔt be the power angle MLE of the i-th generator at time kΔt, where k is a positive integer greater than N, N is the initial point for calculation (N is a positive integer), Δt is the time interval for the PMU to monitor the phase angle of the generator terminal voltage, and kΔt represents the time at which the generator power angle MLE is calculated. Let be the generator power angles of the i-th generator in the system at times hΔt, (h-1)Δt, (k+h)Δt, and (k+h-1)Δt, respectively, where h is the time counter and takes a positive integer value within [1, N]. When the initial point N is 1, equation (1) simplifies to: In the formula: the meanings of each parameter are consistent with those in formula (1). These are the generator power angle trajectories of the i-th generator at time Δt, 0Δt, kΔt, and (k+1)Δt, respectively.

3. The power grid transient stability discrimination method based on the maximum Lyapunov exponent probability distribution criterion according to claim 1, characterized in that, The probability distribution of the work angle MLE trajectory obtained in step two is fitted using the diffusion kernel density estimation method to obtain the MLE probability density function. The specific calculation process is as follows: Samples of the MLE trajectory of the work angle within a given time period The total number of samples is N m Based on the diffusion kernel density estimation theory, the MLE probability density function f of the work angle MLE trajectory is... MLE (m;t) is represented as: In the formula: For Gaussian kernel function, Let m be the set of all real numbers, m be the possible values ​​of the angle of effort MLE, and t be the value derived from the sample. The determined parameters, where subscript 'a' represents the sample. The counting of t; the calculation of t is carried out according to the following process: ① Construct two iterative estimators as shown in equations (4) and (5): In the formula: j is the round number for calculation, ||f MLE (j) || 2 Let be the norm of the MLE probability density function calculated in the j-th round. Gaussian kernel function The 2jth derivative, m a ,m k for In the sample, the subscripts a and k represent the sample. The count, Let t be the optimal value of parameter t obtained from the calculation in the j-th round; In the formula: Let ||f| be the optimal estimate of parameter t obtained in the j-th round of calculation. MLE (j+1) || 2 Let be the norm of the MLE probability density function calculated in the (j+1)th round; ②Assuming the MLE follows a normal distribution, calculate the sample variance σ 2 As initial value, Let the number of calculations be l = 5; ③ with Substituting the initial value into equation (4) to calculate ||f MLE (l+2) || 2 That is, in equation (4), let j = l + 2 for calculation, and then ||f MLE (l+2) || 2 Substituting into equation (5) yields the following results: The initial value is corrected to And let l = l-1; ④ Repeat step ③ until you get the result. As The initial value; ⑤ Substituting the initial value into equation (4) to calculate ||f MLE (2) || 2 Then calculate t * This is the optimal estimate of parameter t in equation (3); ⑥ Order The initial value is t * Set l = 5, and repeat steps ③-⑤ as one round until there is a gap of t between two rounds of iteration. * The change is less than 10 -6 At this time, let t = t in equation (3) * That is, the probability density function of MLE is f as shown in equation (3). MLE (m;t).

4. The power grid transient stability discrimination method based on the maximum Lyapunov exponent probability distribution criterion according to claim 1, characterized in that, The transient stability refers to the transient work angle stability.

5. The power grid transient stability discrimination method based on the maximum Lyapunov exponent probability distribution criterion according to claim 1, characterized in that, The generator power angle refers to the difference in terminal phase angle between the generator and the reference generator.

6. The power grid transient stability discrimination method based on the maximum Lyapunov exponent probability distribution criterion according to claim 1, characterized in that, The training of the transient stability discrimination model relies on the new feature set of the power angle MLE probability distribution constructed by the historical power angle trajectory data saved in step one through steps two, three, four and five. The real-time discrimination of transient stability relies on the probability distribution features of the power angle MLE trajectory calculated by the generator power angle trajectory in step one through steps two, three and four.

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