Method for Locating Disturbance Sources of Forced Power Oscillation Based on KDE Transfer Entropy Causality Analysis

Abstract

The method for locating the disturbance source of forced power oscillation based on KDE transfer entropy causality analysis belongs to the technical field of power system operation and maintenance. By analyzing the causal relationship between the measurement signals of the disturbance source and non-disturbance source units during the forced power oscillation process of the system, the present invention realizes the location of the forced power disturbance source. The present invention uses the causality analysis method to solve the problem of locating the disturbance source of forced power oscillation, getting rid of the dependence on the system model and parameters, and can realize the fast online location of the forced oscillation disturbance source only based on the measurement data, effectively improving the location accuracy and location efficiency of the forced oscillation disturbance source.

Description

Technical Field

[0001] The invention belongs to the technical field of power system operation and maintenance, and in particular relates to a method for locating a forced power oscillation disturbance source based on KDE transfer entropy causal analysis. Background Art

[0002] Forced oscillation of power system is an oscillation phenomenon caused by continuous periodic disturbance. When the external disturbance frequency is close to the natural oscillation frequency of the system, it may cause resonance, seriously affecting the safety and stability of the power system. The characteristics of forced power oscillation include rapid onset, strong randomness, and rapid calming after the disturbance source is lost. Therefore, in the context of the expansion of the power grid and the widespread application of new energy, quickly and accurately locating the oscillation source is the key to suppressing forced oscillation.

[0003] There are two main types of forced power oscillation source positioning methods that are currently widely recognized: positioning methods based on physical mechanisms and positioning methods based on data-driven. The accuracy of methods based on physical mechanisms depends on the detailed models and parameters of the system, but in actual complex systems, it is often difficult to obtain these models and parameters, which limits the application of the methods. Data-driven methods have high requirements on the quality of input data. If there is noise, missing or outliers in the data, it will significantly affect the accuracy of disturbance source positioning.

[0004] In recent years, the scale of power system measurement data has continued to expand, making causal analysis show great potential in revealing the causal relationship between variables. This analysis method can explore the potential driving factors in time series, reveal the mechanism of event occurrence, and provide guidance for intervention measures. Using causal analysis methods to solve the problem of locating the source of forced power oscillation disturbances will get rid of the dependence on system models and parameters. However, at this stage, there are few studies on the application of causal analysis methods to the location of forced power oscillation disturbance sources.

[0005] Therefore, a new technical solution is urgently needed in the prior art to solve this problem. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a forced power oscillation disturbance source locating method based on KDE transfer entropy causal analysis to solve the technical problem that causal analysis methods are rarely applied to forced power oscillation disturbance source locating research at this stage.

[0007] The method for locating the source of forced power oscillation disturbance based on KDE transfer entropy causal analysis includes the following steps, and the following steps are performed in sequence:

[0008] Step 1: Obtain the generator G based on time domain simulation or vector measurement unit PMU measurement A , G BThe active power response signal preprocesses the active power input signal through low-pass filtering and band-pass filtering, filters out the frequency band ranges that are not of concern, and normalizes the oscillation data to eliminate the influence on the positioning result accuracy caused by the difference in the order of magnitude of the measurement data; the processed data is used to establish the generator G A and G B Active power time series: and where P GAn represents the active power of generator G A at the nth sampling point, and P GBn represents the active power of generator G B at the nth sampling point. The time series P GA satisfies the k-order Markov process, and the time series P GB satisfies the i-order Markov process. Then, the transfer entropy between the active power time series P GA and P GB is defined;

[0009] Step 2: Based on Bayes' theorem, convert the transfer entropy between the active power time series P GA and P GB into a joint probability density;

[0010] Step 3: Establish a multivariate kernel density estimation model, and select a Gaussian function as the multivariate kernel function in this model to improve the accuracy and applicability of the transfer entropy calculation;

[0011] Step 4: Use the multivariate kernel density estimation model established in Step 3 to improve the conditional probability of the joint probability density in Step 2 to obtain the improved conditional probability; according to the transfer entropy between the active power time series P GA and P GB in Step 1, and the improved conditional probability, calculate the kernel probability density KDE transfer entropy of the two active power time series;

[0012] Step 5: To avoid the influence of the contingency of the single causal analysis calculation result on the accuracy of the disturbance source positioning result, adopt a sliding window analysis method, repeat the process of Steps 1 to 4, calculate and obtain multiple groups of transfer entropy data sets between the active powers of generators G A and G B , and calculate the mean result of the transfer entropy data set. According to the magnitude of the mean, accurately quantify the causal relationship between the active powers of generators G A and G B ;

[0013] Step 6: By comparing the magnitudes of the kernel probability density KDE transfer entropies of the active power time series of generators G A and G B ​Identify generator G A , G B The causal relationship between the active powers, so as to judge generator G A , G B The direction of power transfer between the active powers, specifically:

[0014] 1) P GA The transfer entropy of P GB is greater than the transfer entropy of P GB to P GA , that is Then P GA is called the dependent variable, P GB is called the independent variable, indicating that the power transfer direction in this forced oscillation mode is P GA →P GB , then it is determined that the disturbance source of the forced power oscillation is generator G A ;

[0015] 2) P GA The transfer entropy of P GB is less than the transfer entropy of P GB to P GA , that is Then P GB is called the dependent variable, P GA is called the independent variable, indicating that the power transfer direction in this forced oscillation mode is P GB →P GA , then it is determined that the disturbance source of the forced power oscillation is generator G B ;

[0016] 3) The difference between the transfer entropy of P GA to P GB and the transfer entropy of P GB to P GA is within the set approximate relationship threshold range, then it is determined that there is no obvious causal relationship between P GA and P GB .

[0017] The transfer entropy between the active power time series P GA and P GB in the first step is:

[0018]

[0019] In the formula: represents and 's joint probability density;, represents and 's joint probability density; and Represents the conditional probability;

[0020] Among them, represents the active power of the generator G A at the (n + 1)-th sampling point, represents the active power of the generator G B at the (n + 1)-th sampling point, represents the time series P that satisfies the k-th Markov process GA , represents the time series P that satisfies the i-th Markov process GB ; is P GB taking the (n + 1)-th sampling point, while P GA takes the conditional probability of the n-th sampling point; is P GA taking the (n + 1)-th sampling point, while P GB takes the conditional probability of the n-th sampling point.

[0021] The joint probability density in the second step is shown in Formulas (2) and (3):

[0022]

[0023]

[0024] The multivariate kernel density estimation model in the third step is shown in Formulas (4) and (5):

[0025]

[0026] In the formula: H is the coefficient matrix, which is a symmetric positive definite matrix of dimension i×i, and its coefficient selection meets the requirement of maximizing the accuracy of the joint probability density; K(.) is the multivariate kernel function;

[0027] K(.) is represented by the function K(x) and meets the following requirements to minimize its impact on the accuracy of probability density estimation:

[0028]

[0029] Select the Gaussian function as the multivariate kernel function K(x) to further improve the accuracy of transfer entropy calculation:

[0030]

[0031] In Formulas (6) and (7), R i represents the set of real numbers, I i represents the set of imaginary numbers, x i represents the time series, x represents the sampling value of the time series x i and θ represents the time series xi Variance;

[0032] The improved conditional probability in Step 4 is expressed as:

[0033]

[0034] In the formula: H1, H2, and H3 are all symmetric positive definite coefficient matrices; K(.) is a multivariate kernel function, and the Gaussian function is selected here; N is the corresponding discrete number in the univariate kernel probability density estimation model, m represents the active power time series of generator G B The m-th term of the active power time series, d represents the d-th term of the active power time series of generator G A The d-th term of the active power time series.

[0035] Through the above design scheme, the present invention can bring the following beneficial effects:

[0036] By analyzing the causal relationship between the disturbance source and the non-disturbance source unit measurement signals during the forced power oscillation process of the system, the present invention realizes the positioning of the forced power disturbance source. The present invention uses the causal analysis method to solve the problem of positioning the forced power oscillation disturbance source, getting rid of the dependence on the system model and parameters, and can realize the fast online positioning of the forced oscillation disturbance source only based on the measurement data, effectively improving the positioning accuracy and efficiency of the forced oscillation disturbance source. Brief Description of the Drawings

[0037] The following further describes the present invention in conjunction with the drawings and specific embodiments:

[0038] Figure 1 It is a flow chart of the forced power oscillation disturbance source positioning method based on KDE transfer entropy causal analysis of the present invention.

[0039] Figure 2 It is a wiring diagram of the IEEE 4-machine 2-area structure in the embodiment of the forced power oscillation disturbance source positioning method based on KDE transfer entropy causal analysis of the present invention.

[0040] Figure 3 It is a diagram of the directional relationship of the transfer entropy of the active power of the generator in the embodiment of the forced power oscillation disturbance source positioning method based on KDE transfer entropy causal analysis of the present invention.

[0041] Figure 4 It is the calculation result of the change of the transfer entropy difference over time in the embodiment of the forced power oscillation disturbance source positioning method based on KDE transfer entropy causal analysis of the present invention. Detailed Embodiment

[0042] The forced power oscillation disturbance source positioning method based on KDE transfer entropy causal analysis, as Figure 1 shown, includes the following steps, and the following steps are carried out sequentially.

[0043] Step 1: Based on time-domain simulation or measurements from a Phasor Measurement Unit (PMU), obtain the active power response signals of generators G A 、G B ; perform low-pass filtering and band-pass filtering preprocessing on the active power input signals to filter out the frequency bands that are not of concern, and normalize the oscillation data to eliminate the impact of the difference in the order of magnitude of measurement data on the accuracy of the positioning result; establish the active power time series of generators G A 、G B : P GA :{P GA1 , P GA2 , …, P GAn} and P GB :{P GB1 , P GB2 , …, P GBn}, where P GAn represents the active power of P GA at the nth sampling point, and P GBn represents the active power of P GB at the nth sampling point. The time series P GA satisfies a k-order Markov process, and the time series P GB satisfies an i-order Markov process. Then, define the transfer entropy between the active power time series P GA and P GB ;

[0044] Step 2: Based on Bayes' theorem, convert the transfer entropy between the active power time series P GA and P GB into a joint probability density;

[0045] Step 3: Establish a multivariate kernel density estimation model, and select a Gaussian function as the multivariate kernel function in this model to improve the accuracy and applicability of the transfer entropy calculation;

[0046] Step 4: Use the multivariate kernel density estimation model established in Step 3 to improve the conditional probability of the joint probability density in Step 2 to obtain the improved conditional probability; according to the transfer entropy between the active power time series P GA and P GB in Step 1, and the improved conditional probability, calculate the KDE (kernel probability density) transfer entropy of the two active power time series;

[0047] Step 5: To avoid the influence of the contingency of the single causal analysis calculation result on the accuracy of the disturbance source positioning result, the present invention adopts a sliding window analysis method, repeats the process of Steps 1 to 4, and calculates multiple groups of generators G A 、G BThe transfer entropy data group between active powers is further calculated to obtain the mean result of the transfer entropy data group. Thus, according to the magnitude of the mean, the causal relationship between the active powers of generators G A and G B is accurately quantified.

[0048] Step 6: By comparing the magnitudes of the KDE transfer entropies of the active power time series of generators G A and G B to identify the causal relationship between the active powers of generators G and G A and G B and thus determine the direction of power transfer between the active powers of generators G A and G B . Specifically, it is embodied as follows:

[0049] 1) If the transfer entropy of P GA with respect to P GB is greater than the transfer entropy of P GB with respect to P GA , that is , then P GA is called the "cause" variable and P GB is called the "effect" variable, indicating that the power transfer direction in this forced oscillation mode is P GA (cause) → P GB (effect), and it is determined that the forced power oscillation disturbance source is generator G A .

[0050] 2) If the transfer entropy of P GA with respect to P GB is less than the transfer entropy of P GB with respect to P GA , that is , then P GB is called the "cause" variable and P GA is called the "effect" variable; indicating that the power transfer direction in this forced oscillation mode is P GB (cause) → P GA (effect), and it is determined that the forced power oscillation disturbance source is generator G B .

[0051] 3) If the difference between the transfer entropy of P GA with respect to P GB and the transfer entropy of P GB with respect to P GA is within the set approximate relationship threshold range, then it is determined that there is no obvious causal relationship between P GA and P GB .

[0052] In step 1, the active power time series P GAWith P GB The transmitted entropy between them is:

[0053]

[0054] In the formula: represents and the joint probability density of; represents and the joint probability density of; and represent conditional probabilities;

[0055] Among them, represents the active power of generator G A at the (n + 1)-th sampling point, represents the active power of generator G B at the (n + 1)-th sampling point, represents the time series P that satisfies the k-th order Markov process GA , represents the time series P that satisfies the i-th order Markov process GB ; is the conditional probability that P GB takes the (n + 1)-th sampling point, while P GA takes the n-th sampling point; is the conditional probability that P GA takes the (n + 1)-th sampling point, while P GB takes the n-th sampling point.

[0056] The joint probability density in the second step is shown in formulas (2) and (3):

[0057]

[0058] The multi-variable kernel density estimation model in the third step is shown in formulas (4) and (5):

[0059]

[0060] In the formula: H is a coefficient matrix, which is an i×i-dimensional symmetric positive definite matrix, and its coefficient selection meets the requirement of maximizing the accuracy of the joint probability density; K(.) is a multi-variable kernel function;

[0061] K(.) is represented by the function K(x) and meets the following requirements to minimize its impact on the accuracy of the probability density estimation:

[0062]

[0063] Select the Gaussian function as the multi-variable kernel function K(x) to further improve the accuracy of transfer entropy calculation:

[0064]

[0065] In equations (6) and (7), R i represents the set of real numbers, I i represents the set of imaginary numbers, x i represents the time series, and x represents the sampling value of the time series x i and θ represents the variance of the time series x i ;

[0066] The improved conditional probability in step four is expressed as:

[0067]

[0068] where: H1, H2, and H3 are all symmetric positive definite coefficient matrices; K(.) is the multi-variable kernel function, and the Gaussian function is selected here; N is the corresponding discrete number in the single-variable kernel probability density estimation model, m represents the m-th term of the active power time series of generator G B and d represents the d-th term of the active power time series of generator G A ;

[0069] The present invention will be further described in detail below with reference to embodiments:

[0070] Such as Figure 2 the typical IEEE 4-machine 2-area system shown. Under the basic operating condition, the small-signal stability analysis results show that there are 3 electromechanical oscillation modes in the system, and the damping characteristics of each oscillation mode are good. The present invention takes the inter-area oscillation mode as an example to verify the accuracy and effectiveness of the proposed forced power oscillation disturbance source location method.

[0071] In the simulation, a sinusoidal disturbance signal with an amplitude of 0.015 p.u. and a frequency of 0.6 Hz is continuously injected into the excitation system of generator G1 to resonate with the 0.61 Hz inter-area mode of the system. At the same time, in order to simulate environmental excitation, all loads in the system randomly fluctuate by 3% of the base value, and the simulation lasts for 200 seconds.

[0072] Using the KDE transfer entropy method of the present invention, the transfer entropy between the active powers of the 4 generators in the system is calculated. The single-time transfer entropy calculation results (at the time point of the 50th second) are shown in Table 1.

[0073] Table 1 Single-time transfer entropy calculation result table

[0074]

[0075] Here, if X takes G1 and Y takes G2, it represents the transfer entropy T of the active power of generator G1 to the active power of generator G2 G1→G2 ; if X takes G2 and Y takes G1, it is the transfer entropy T of the active power of generator G2 to the active power of generator G1 G2→G1 . The calculation methods of other transfer entropies are similar, and the directional relationship of the active power transfer entropy of 4 generators is as shown in Figure 3 .

[0076] From the analysis of Table 1 and Figure 3 , it can be seen that the KDE transfer entropies (T G1→G2 , T G1→G3 , T G1→G4 ) of the active power of generator G1 to the other 3 generators (G2, G3, G4) are 1.004, 1.131, and 1.333 in sequence, all higher than the KDE transfer entropies (T G2→G1 , T G3→G1 , T G4→G1 ) of the active power of the other 3 generators to generator G1, which are 0.859, 1.010, and 1.037 in sequence. According to the causal analysis perturbation source localization method of KDE transfer entropy, it can be analyzed that the active power oscillation of generator G1 is the main reason for the active power oscillation of generators G2, G3, and G4. This localization result is consistent with the perturbation source setting, further verifying the accuracy of the method proposed by the present invention

[0077] In the actual operation of the system, due to the different noise intensities at each moment, there will be certain differences in the measurement data at different time sections. In order to reduce the influence of the contingency of the single calculation result on the accuracy of the localization result, the present invention adopts the sliding window analysis method to calculate the transfer entropy between the active powers of each generator. Similarly, a 50 - second analysis window is selected, the active power of the input generator is input, and the window slides once every 2 seconds. The transfer entropy between the active powers of each generator is calculated within 200 seconds, and the mean statistical results are listed in Table 2. The difference results of different transfer entropies are as shown in Figure 4 .

[0078] Table 2 Statistical table of the mean value of the system transfer entropy

[0079]

[0080] From Figure 4 , it can be seen that as the calculation window slides, the difference between T G1→G2、G3、G4 and T G2、G3、G4→G1 also shows a certain degree of fluctuation, but the difference of the transfer entropy is always greater than 0. This means that T G1→G2、G3、G4 is always higher than T G2、G3、G4→G1, indicating that the oscillation transfer direction of the generator active power is always from generator G1 to other generators in the system. Therefore, generator G1 is identified as the disturbance source unit, further verifying the accuracy of the disturbance source location method proposed by the present invention.

Claims

1. A method for locating the disturbance source of forced power oscillation based on KDE transfer entropy causality analysis, characterized in that: Including the following steps, and the following steps are carried out sequentially: Step 1: Based on time-domain simulation or measurements from a Phasor Measurement Unit (PMU), obtain the active power response signals of generators G A , G B . Perform low-pass filtering and band-pass filtering preprocessing on the active power input signals to filter out the frequency bands that are not of concern, and normalize the oscillation data to eliminate the impact of data magnitude differences on the accuracy of the positioning result. Establish the active power time series of generators G A , G B : and where represents the active power of generator G A at the (n + 1)-th sampling point, represents the active power of generator G B at the (n + 1)-th sampling point, and the time series P GA satisfies a k-order Markov process, and the time series P GB satisfies an i-order Markov process. Then, define the transfer entropy between the active power time series P GA and P GB . Step 2: Convert the transfer entropy between the active power time series P GA and P GB into a joint probability density; The joint probability density is as shown in Formulas (2) and (3): In the formula: denotes and the joint probability density of; denotes and the joint probability density of; and represent conditional probabilities; Among them, represents the active power of the generator G A at the (n + 1)-th sampling point, represents the active power of the generator G B at the (n + 1)-th sampling point, represents the time series P that satisfies the k-th Markov process GA , represents the time series P that satisfies the i-th Markov process GB ; is the conditional probability that P GB takes the (n + 1)-th sampling point while P GA takes the n-th sampling point; is the conditional probability that P GA takes the (n + 1)-th sampling point while P GB takes the n-th sampling point; Step 3: Establish a multivariate kernel density estimation model, and select a Gaussian function as the multivariate kernel function in this model to improve the accuracy and applicability of transfer entropy calculation; The multivariate kernel density estimation model is as shown in Formulas (4) and (5): In the formula: H is a coefficient matrix, which is a symmetric positive definite matrix of i×i dimension, and the selection of its coefficients meets the requirement of maximizing the accuracy of the joint probability density; K(.) is a multivariate kernel function; K(.) is represented by the function K(x) and meets the following requirements to minimize its influence on the accuracy of probability density estimation: Select a Gaussian function as the multivariate kernel function K(x) to further improve the accuracy of transfer entropy calculation: In formulas (6) and (7), R i represents the set of real numbers, I i represents the set of imaginary numbers, x i represents a time series, and x represents the sampling value of the time series x i ; θ represents the variance of the time series x i ; Step 4. Use the multi-variable kernel density estimation model established in Step 3 to improve the conditional probability of the joint probability density in Step 2 to obtain the improved conditional probability; according to the active power time series P in Step 1 GA and P GB to calculate the transfer entropy between them, and calculate the kernel probability density KDE transfer entropy of the two active power time series based on the improved conditional probability; The improved conditional probability is expressed as: where: H1, H2, and H3 are all symmetric positive definite coefficient matrices; K(.) is a multivariate kernel function, and the Gaussian function is selected here; n is the corresponding number of discretizations in the univariate kernel probability density estimation model. represents generator G B the m-th term of the active power time series, represents generator G A the d-th term of the active power time series; Step 5: To avoid the influence of the contingency of the single causal analysis calculation results on the accuracy of the disturbance source location results, the sliding window analysis method is adopted to repeat the processes of Steps 1 to 4, calculate and obtain multiple groups of transfer entropy data sets between the active powers of generators G A and G B , and calculate the mean result of the transfer entropy data set. The accurate quantification of the causal relationship between the active powers of generators G A and G B is realized according to the magnitude of the mean value; Step 6: By comparing the A generators G B , identify the causal relationship between the active power of generators G A , G B by comparing the magnitudes of the KDE transfer entropy of their active power time series, and thus determine the transfer direction of the active power between generators G A , G B as follows: 1) P GA The transfer entropy of P GB is greater than that of P GB to P GA , that is then P GA is called the dependent variable, and P GB is called the independent variable, indicating that the power transfer direction under this forced power oscillation mode is from P GA →P GB . Then it is determined that the disturbance source of the forced power oscillation is the generator G A ; 2) P GA The transfer entropy of P GB is less than that of P GB The transfer entropy of P GA , that is then P GB is called the dependent variable, and P GA is called the independent variable, indicating that the power transfer direction under this forced power oscillation mode is from P GB →P GA . Then it is determined that the disturbance source of the forced power oscillation is the generator G B ; 3)P GA The transfer entropy of P GB and the transfer entropy of P GB to P GA If the difference between them is within the set approximate relationship threshold range, then it is determined that P GA and P GB have no obvious causal relationship.

2. The method for locating the forced power oscillation disturbance source based on the KDE transfer entropy causality analysis according to claim 1, wherein: The active power time series P in the first step GA and P GB The transfer entropy between them is as follows:

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