CN101408586B - On-line low-frequency oscillation detection and node coherence grouping method based on experience modal decomposition - Google Patents

Abstract

The invention belongs to the technical field of the low-frequency oscillation on-line detection and analysis in an electric power system and provides a low-frequency oscillation modal analysis method, which is based on wide area phasor metrical information and an empirical mode decomposition method and can carry out the on-line detection and node homology grouping toward the complex low-frequency oscillation of the electric power system. The modal analysis method not only has strong adaptability to the complex waveforms of non-linearity, non-stationarity or those containing non-periodic constituents, but also can carry out phase comparison toward nonsine or cosinoidal inherent modal curves which belong to the oscillation mode of the same electric power system but are slightly different in frequency and realize the homology grouping of the nodes participating in each oscillation mode, thus obtaining the power conversion relation among the nodes and the position of an oscillation center or interface.

Description

On-Line Low Frequency Oscillation Detection and Node Coherence Grouping Based on Empirical Mode Decomposition

technical field

The invention belongs to the technical field of on-line detection and analysis of low-frequency oscillations in electric power systems, and more specifically relates to a method for on-line low-frequency oscillation detection of electric power systems and coherent grouping of nodes by using information from a wide-area phasor measurement system.

Background technique

When low-frequency oscillation occurs in the power system, in order to understand and take measures to suppress the oscillation, operators need to know the modal information of the low-frequency oscillation in addition to the frequency, amplitude and damping ratio of the oscillation. The modal information of low-frequency oscillation includes the coherent grouping relationship of the oscillation nodes, that is, the interaction relationship of active oscillation power between nodes, and the position of the oscillation center or interface. For these modal information, the previous methods are obtained by solving the eigenvalues and eigenvectors of the system state matrix through a small disturbance analysis program based on a mathematical model. The correctness of the analysis results of this type of method depends on the accuracy of the mathematical model, component parameters, and state parameters used, and the accuracy of these models and parameters in the actual power system is often not guaranteed, so this type of method based on mathematical model analysis The results are unreliable or not believable. In addition, due to the need to calculate the eigenvalues and eigenphasors of the matrix, such methods also have the problem of slow calculation speed for large-scale systems.

The wide area measurement system (WAMS) based on the phasor measurement unit (PMU) can send the voltage phasor, current phasor, power, frequency and other information of each measuring point of the power grid to the WAMS master at a frequency of tens or hundreds of frames per second. Station transmission, with the help of the Global Positioning System (GPS) to ensure the synchronization of data across the network. Therefore, real-time observation of the dynamic process of each measuring point of the power grid can be realized, which makes it possible to conduct low-frequency oscillation mode analysis directly based on the measurement information. However, in the past, the low-frequency oscillation detection and analysis functions of the wide-area measurement system were limited to performing frequency spectrum analysis on the oscillation curves of each node to obtain oscillation frequency, amplitude, and damping ratio information, and based on this, alarms were issued for dangerous oscillations that occurred, and The modal information of the low-frequency oscillation of the power grid cannot be given, especially the phase information of the oscillation curve cannot be given correctly, and the correct phase information of the oscillation curve is the prerequisite for coherent grouping of nodes, and it is also the prerequisite for operators to understand the oscillation mode and take correct measures . The shortcomings of various low-frequency oscillation analysis methods in the field of wide-area measurement system research are discussed separately below.

(1) Discrete Fourier transform (DFT): Although the discrete Fourier transform method is very fast, it can only obtain the frequency and amplitude of the oscillation mode, but cannot obtain the damping ratio and phase information. Therefore, in most actual WAMS systems, it is only used as Detection tools and rough analysis tools for oscillation occurrence.

(2) Prony analysis method: The Prony-based spectrum analysis method can not only calculate the frequency, amplitude and damping ratio of the oscillation curve, but also obtain the initial phase of the oscillation curve. The frequency of the oscillation curve is different, and even the frequency of the own oscillation curve of the same node is still changing, so the coherent grouping of nodes directly based on the initial phase will often get wrong results. Moreover, because the Prony method cannot correctly deal with nonlinear, non-stationary changes, and complex waveforms containing non-periodic components, the spectrum analysis results obtained by this method are not reliable regardless of frequency or initial phase. Cannot be used in low frequency oscillation analysis. In addition, compared with other spectrum analysis methods, the Prony method has a large amount of calculation and a very slow speed. When the number of measurements to be analyzed is large (this is necessary when performing coherent grouping of nodes with low-frequency oscillations in large-scale power grids), it is difficult to Meet the real-time requirements of online computing. (About the unreliability and slow calculation speed of the Prony method in frequency calculation, an example is given in the "specific implementation" section of this document to illustrate). For the above reasons, although the Prony method has the function of calculating the phase of the oscillation curve, so far no practical wide-area measurement system has used it to realize the coherent grouping of nodes.

(3) Autoregressive moving average method (ARMA) and random subspace method (N4SID): These methods are mainly used for spectrum analysis in the relatively strong white noise environment, the signal does not have obvious oscillation data, the calculation time is long, and cannot give It is not suitable for rapid detection and alarm of large-scale low-frequency oscillations.

(4) Hilbert-Huang transformation method: The Empirical Mode Decomposition (EMD) method proposed by NASA scientist Huang E in 1998 can decompose complex waveforms with nonlinear, non-stationary changes, and non-periodic components into several natural mode oscillations component (that is, a curve that satisfies the difference between the number of poles and the number of zero points is 1 or equal, and the average value of the upper and lower envelopes is 0, it can be seen that the component is not necessarily a sine or cosine curve) and a non-oscillating component, and its speed is much faster than Prony analysis. However, the EMD method itself cannot provide the frequency, amplitude, damping ratio and phase information of each natural mode oscillation component. When performing spectrum analysis, it is necessary to use the Hilbert-Huang transformation based on the EMD method to solve the instantaneous frequency and amplitude of the modal components. However, the Hilbert-Huang transform does not provide the phase information of the intrinsic mode components, and its calculation is large and time-consuming. Therefore, although some scholars have used the Hilbert-Huang transform method to analyze low-frequency oscillations in research, its application is limited to detecting low-frequency oscillations based on the analyzed oscillation frequency and amplitude, and cannot perform phase analysis and grouping of synchronous points. .

From the above overview, it can be seen that none of the existing low-frequency oscillation analysis methods can or are not suitable for the relative phase analysis of the nodes participating in the low-frequency oscillation. Since the degree of participation of each node in the oscillation is not only related to the amplitude of the oscillation, but also related to the relative phase between nodes, these methods cannot quantitatively evaluate the degree of participation of the units associated with each node in the oscillation. Aiming at the above-mentioned problems of the existing low-frequency oscillation analysis methods, the method proposed by the present invention realizes online modal analysis of low-frequency oscillations using wide-area measurement data, correctly calculates the phase relationship between nodes in the same mode of oscillation, and analyzes the relationship between these nodes. Coherence relation and power exchange relation.

Finally, the concept of node homology grouping in the method of this patent application is distinguished and clarified from the existing similar concepts. Although the identification of coherent clusters is often used in the field of stability analysis of power systems, and there are many methods for judging coherence, these methods all judge the coherence of curves based on the similarity of the original measurement (or simulation) curve shape; and this paper The coherence in the patent application method refers to the phase coherence of each oscillation mode curve in the original curve, and the natural mode curve decomposition method based on the empirical mode decomposition method is adopted to avoid nonlinearity, non-stationary changes, and non-linear Periodic components pose problems and difficulties to traditional spectral analysis methods such as Prony and DFT (traditional spectral analysis methods consider that any curve is composed of several sine or cosine curves with different fixed frequencies lasting the entire time period). For example, in a well-known manufacturer’s WAMS-based low-frequency oscillation analysis method, based on the dominant mode theory of the extended equal-area criterion, the coherent grouping is performed based on the original power angle curves measured by each PMU and combined with the generator’s moment of inertia. Then, Prony-based spectrum analysis is carried out. This grouping obtains the coherence of the overall movement trend of each generator node, rather than the phase coherence of the oscillation component superimposed on the trend. And the method of the present invention is to first carry out the rapid spectrum analysis of each PMU original active power or frequency measurement, then carry out the coherent grouping of the node oscillation phase about a certain system oscillation mode according to the natural mode oscillation curve decomposed, and each system oscillation mode The results of homology grouping of nodes do not affect each other.

Contents of the invention

Aiming at the problem that the existing low-frequency oscillation detection based on Wide Area Measurement System (WAMS) cannot realize the coherent grouping of online nodes and the spectrum analysis of non-stationary oscillation may be incorrect. The invention provides a low-frequency oscillation mode analysis method based on the empirical mode decomposition method, which can realize on-line detection and coherent grouping of nodes for the complex low-frequency oscillation of the power system. A typical flow chart for realizing the method is shown in Figure 1 of the specification.

The analytical method specifically adopts the following technical solutions:

A low-frequency oscillation modal analysis method based on wide-area information and empirical mode decomposition method that can realize online detection of complex low-frequency oscillations in power systems and coherent grouping of nodes. The analysis method is not only suitable for nonlinear and non-stationary changes , the actual complex waveform containing non-periodic components, and phase comparison of non-sine or cosine natural mode curves belonging to the same power system oscillation mode but with slightly different frequencies, so as to realize the coherent grouping of nodes participating in each oscillation mode , so as to obtain the power exchange relationship between the nodes and the position of the oscillation center or interface; it is characterized in that the analysis method includes the following steps:

(1) In the current time window, the spectrum analysis method based on empirical mode decomposition is used to decompose the measured oscillation curves of active power injection power or frequency of nodes collected by the phasor measurement unit PMU and sent to the wide-area measurement master station into natural mode curves ;

(2) Calculate the oscillation parameters of each natural mode curve according to the defined natural mode curve parameter calculation method;

(3) According to the calculated oscillation parameters of each natural mode curve, the dangerous oscillation mode of the power system is identified, and the natural mode curves are grouped according to the found dangerous oscillation mode of the power system, that is, the frequency of the natural mode curve and the frequency of the dangerous mode of the system Similar natural mode curves belong to the same oscillation mode;

(4) Coherently group the nodes participating in the dangerous oscillation mode of the power system according to the phase difference of the corresponding natural mode curve;

(5) Determine the line set where the oscillation center or interface of each dangerous oscillation mode of the power system is located according to the lines passed by the cut planes between coherence groups;

(6) Divide the nodes that are not directly connected electrically in the same homology group into different homology subgroups according to geographical location or topological relationship.

In step (1), when there is no electromagnetic ring network in the power grid or the range of the electromagnetic ring network is very small, and the active power injected by almost all nodes is measured by the PMU or can be estimated by other PMU measurements, the active power injected by the node is used for the calculation. Spectrum analysis and low-frequency oscillation detection and modal analysis; when the electromagnetic ring network is serious or most nodes inject active power without PMU measurement, use the node frequency for spectrum analysis and perform low-frequency oscillation detection and modal analysis.

In step (2), the oscillation parameters of each natural mode curve are calculated according to the defined natural mode curve parameter calculation method; the defined natural mode curve parameters are as follows:

(a) The phase of the data points of the natural mode curve: the phase of each data point is obtained by the zero-crossing method, that is, the positive zero-crossing point of the curve is 0°, the negative zero-crossing point is ±180°, and the maximum point is 90°, the minimum value point is -90°, and the phase of the data points between adjacent zero and pole points is obtained by equally dividing 90 parts;

(b) The phase difference of the natural mode curves and the relative phase of the natural mode curves: In order to compare the phases of the two natural mode curves in the case of a slight difference in frequency, the phase difference of the natural mode curves Φ is defined as Corresponding to the arithmetic mean of the phase difference φ _i of the data points, the φ _i satisfies -180°<φ _i ≤180°. In low-frequency oscillation modal analysis, for a group of natural mode curves belonging to the same oscillation mode frequency, the curve with the largest amplitude is used as the reference curve, that is, the relative phase of the natural mode curve is 0, and the other natural mode curves are relative to the The phase difference of the reference natural mode curve is the relative phase of the other natural mode curves;

(c) The data point frequency of the natural mode curve and the natural mode curve frequency: the frequency of each data point of the natural mode curve is obtained by converting the angular frequency obtained by the phase-to-time difference between the phase of the data point and the previous data point , in order to compare the frequency of two modal curves in the case of non-stationary frequency, the frequency of the natural mode curve is defined as the average frequency of each data point of the curve; in order to improve the calculation speed, the simplified method expressed by the following formula is used to approximate the natural mode Modal curve frequency f _curve :

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; curve</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; extrm</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; last</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; first</span>}}}$

Among them, n _extrm is the number of extreme points of the natural mode curve, and the extreme points include maximum points and minimum points, t _last is the moment of the last extreme point of the natural mode curve, and t _first is the time of the natural mode curve. The moment of the first extreme point of the modal curve;

(d) The amplitude of the natural mode curve: defined as the average value of the amplitudes of the maximum and minimum points of the natural mode curve;

(e) The damping ratio of the data point of the natural mode curve and the damping ratio of the natural mode curve: Let the amplitude of the data point i of the natural mode curve be A _i , and the amplitude of the data point corresponding to the phase in the adjacent previous cycle is A _iT , due to the reason of fixed-interval sampling, the data point corresponding to the phase of the current data point in the previous cycle often does not have a sampling point. At this time, it is necessary to use the interpolation method to use the current data point in the previous cycle. The amplitude and phase of the actual sampling points before and after the point can be obtained to obtain the amplitude A _iT , and the damping ratio of the data point i on the natural mode curve can be approximated according to the following formula:

${\mathrm{<span\; class="notranslate">\; \&zeta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}$

The damping ratio of the natural mode curve is defined as the average value of the damping ratio of each data point of the natural mode curve; in order to reduce the amount of calculation, it can also be approximated by the average value of the damping ratio of each extreme point.

In step (3), according to the calculated oscillation parameters of each natural mode curve, the dangerous oscillation mode of the power system is identified, and the natural mode curves are grouped according to the found dangerous oscillation mode of the power system, that is, the natural mode curve frequency and The natural mode curves with similar frequencies in the dangerous mode of the system belong to the same oscillation mode, and the specific method is as follows:

From the decomposed natural mode curves measured at each node, select the natural mode of a node with the largest amplitude and greater than the specified threshold A _threshold , and at the same time the damping ratio is small enough that is less than the set damping ratio threshold D _threshold State curve frequency, as the oscillation mode frequency 1 of the current system, if any of the natural mode curve frequencies of all nodes is similar to it, that is, the ratio of the absolute value of the frequency difference between the two to the system oscillation mode frequency 1 is less than the set percentage threshold FD _threshold , it is considered that the node participates in the oscillation of oscillation mode 1. For each node, at most one natural mode curve can be classified into the oscillation mode 1 of the system.

Exclude the natural mode curves of all nodes classified into oscillation mode 1, and select the one with the largest amplitude and greater than the specified threshold A _threshold and the damping ratio less than the set damping ratio threshold D _threshold among the remaining natural mode curves. The natural mode curve frequency measured at a node is used as the oscillation mode frequency 2 of the current system, and all natural mode curves and their corresponding nodes participating in the oscillation mode 2 in the system are found according to the aforementioned method.

By analogy, find out all the oscillation modes in which the amplitude of the entire power system is large enough in the current period and the maximum amplitude is greater than the specified threshold A _threshold , and the damping ratio is small enough, that is, less than the set damping ratio threshold D _threshold , that is, the dangerous oscillation mode, and Find the nodes involved in the corresponding dangerous oscillation modes and the corresponding natural mode curves.

For the specified threshold A _threshold of the above amplitude, if active power is injected into the node for low-frequency oscillation detection and analysis, A _threshold is usually taken as 30MW, and if node frequency is used for low-frequency oscillation detection and analysis, A _threshold is usually taken as 0.02Hz; The damping ratio threshold D _threshold is usually taken as 0.05; the absolute value of the frequency difference and the system oscillation mode frequency percentage threshold FD _threshold is usually taken as 10%.

In step (4), the nodes participating in the dangerous oscillation mode of the power system are coherently grouped according to the phase difference of the corresponding natural mode curve, and the specific method is as follows:

For each dangerous system oscillation mode found in the previous steps, compare the phases of the natural mode curves corresponding to all the nodes participating in the oscillation mode, and use the natural mode curve with the largest amplitude as the reference curve to calculate the relationship between the remaining natural mode curves and the The relative phase Φ of the reference natural mode curve, where -180°<Φ≤180°; if the absolute value of the relative phase of the natural mode curve measured at a certain node is less than 90°, then the node corresponding to the reference curve belongs to the same homology group; on the contrary, if the absolute value of the relative phase of the natural mode curve measured by a node is greater than 90°, then the node belongs to the homology group opposite to the reference node; accordingly, all nodes participating in a certain mode oscillation Divided into two groups, the oscillation power is mainly exchanged back and forth between the two groups.

When visually expressing the group, the coherent grouping of different system oscillation modes is drawn on different plant geographic maps, and the colored vector arrows are used at each plant bus node to describe the oscillation of the natural mode curve corresponding to the corresponding node , the different colors of the vector arrows represent different homology groups, the length of the arrow represents the magnitude of the natural mode curve, and the direction of the arrow is determined by the relative phase of the natural mode curve.

In step (5), when the phasor measurement unit PMU is densely distributed, that is, when there is no other ungrouped substation bus between the substation bus coherent groups, the oscillation center or interface can be accurately determined by the line through which the cut planes between coherent groups pass It is composed of which lines, that is, the set of lines where the oscillation center or interface of the oscillation mode of the system is determined. On the visual representation of the group, the lines on the oscillation interface are marked with short dashed lines perpendicular to the lines.

In step (6), nodes that are not directly connected electrically in the same coherence group are further divided into different coherence subgroups according to geographic location or topological relationship. The nodal vector arrows of different coherent subgroups are colored in different shades of the same color.

The concept and calculation method of the phase difference of the natural mode curve (not necessarily a sine or cosine curve) and the relative phase of the natural mode curve proposed by the present invention are the key to grouping online low-frequency oscillation nodes by using the empirical mode decomposition method. There is no similar definition and method in the Hilbert-Huang transform spectrum analysis method based on empirical mode decomposition. This method can be used to achieve a reasonable phase comparison of the oscillation curves in the case of slightly different frequencies, so that this method is suitable for reasonable phase comparison of the oscillation components in complex waveforms that are nonlinear, non-stationary, and contain non-periodic components. comparison and analysis. It overcomes the shortcomings of FFT, Prony and other spectrum analysis methods in the case of nonlinear, non-stationary, and complex waveforms with non-periodic components, which cannot calculate the phase of the oscillation component or can not reasonably perform phase comparison. On the basis of using the method proposed by the present invention to compare the phases of the natural mode curves of the PMU measured oscillation curves, the present invention realizes for the first time the grouping of online low-frequency oscillations and adjustment points based on the PMU measured data and the determination of the line where the oscillation center or interface is located set. Compared with the results obtained by the traditional small disturbance analysis program based on mathematical models, the above-mentioned low-frequency oscillation modal analysis results obtained by this method have the advantage of not being limited by the accuracy of mathematical models, component parameters, and state parameters, so its The reliability, reliability and accuracy of the low-frequency oscillatory modal analysis results are high.

Description of drawings

Figure 1 is a block diagram of online low-frequency oscillation detection and node coherence grouping algorithm based on empirical mode decomposition;

Figure 2 is a block diagram of the sub-band online low-frequency oscillation detection and modal analysis algorithm in the actual system;

Fig. 3 is the spectrum analysis result based on empirical mode decomposition of active power injected into the external network of power grid A;

Figure 4 shows the natural mode curves of the four main stations in the 0.7Hz system oscillation mode and their grouping by relative phase;

Fig. 5 is a visual geographical map of the node coherence grouping and amplitude and phase of the oscillation mode of the 0.7Hz system.

Detailed ways

The technical solution of the present invention will be further described in detail below in accordance with the drawings in the description and in conjunction with specific embodiments.

The present invention proposes a low-frequency oscillation modal analysis method based on wide-area measurement information and empirical mode decomposition method, which can realize on-line rapid detection of complex low-frequency oscillations in non-stationary power systems and coherent grouping of nodes. The typical implementation of this method The flow chart is shown in Figure 1 of the instruction manual, and the detailed steps are as follows:

(1) In the current time window, the spectrum analysis method based on empirical mode decomposition is used to decompose the measured oscillation curve of active power injection power or frequency of the node collected by PMU and sent to the wide-area measurement master station into natural mode curve; When there is no electromagnetic ring network or the range of the electromagnetic ring network is small, and almost all the active power injected by the nodes is measured by PMU or can be calculated by other PMU measurements, the active power injected by the nodes is used for spectrum analysis and low-frequency oscillation detection and modal Analysis; when the electromagnetic ring network is serious or most nodes inject active power without PMU measurement, use the node frequency for spectrum analysis and perform low-frequency oscillation detection and modal analysis.

(2) Calculate the oscillation parameters of each natural mode curve according to the defined natural mode curve parameter calculation method. The present invention proposes and defines concepts such as the data point phase of the intrinsic mode curve (not necessarily a sine or cosine curve) obtained by the empirical mode decomposition method, the phase difference of the intrinsic mode curve and the relative phase of the intrinsic mode curve, for use in Phase comparison of the oscillatory modal curves at slightly different frequencies. These definitions are the key to the clustering of oscillatory nodes using the empirical mode decomposition method, and there is no similar definition in the EMD-based Hilbert-Huang transform method. In addition, the natural mode curve data point damping ratio and data point frequency, natural mode curve damping ratio, natural mode curve frequency, and natural mode curve amplitude are defined. These definitions are different from the calculation method of instantaneous frequency and instantaneous amplitude based on Hilbert transform for the natural mode curve decomposed by EMD in Hilbert-Huang transform, but they are simple, fast, and the accuracy meets the requirements of power system low-frequency oscillation analysis. The natural mode curve parameter and calculation method thereof defined by the present invention are as follows:

(a) The phase of the data points of the natural mode curve: the phase of each data point is obtained by the zero-crossing method, that is, the positive zero-crossing point of the curve is 0°, the negative zero-crossing point is ±180°, and the maximum point is 90°, the minimum value point is -90°, and the phase of the data points between adjacent zero and pole points is obtained by dividing 90 equal intervals.

(b) The phase difference of the natural mode curves and the relative phase of the natural mode curves: In order to compare the phases of the two natural mode curves in the case of a slight difference in frequency, the phase difference of the natural mode curves Φ is defined as Corresponding to the arithmetic mean of the phase difference φ _i of the data points, the φ _i satisfies -180°<φ _i ≤180°. In low-frequency oscillation modal analysis, for a group of natural mode curves belonging to the same oscillation mode frequency, the curve with the largest amplitude is used as the reference curve, that is, the relative phase of the natural mode curve is 0, and the other natural mode curves are relative to the The phase difference of the reference natural mode curve is the relative phase of the remaining natural mode curves.

(c) The data point frequency of the natural mode curve and the natural mode curve frequency: the frequency of each data point of the natural mode curve is obtained by converting the angular frequency obtained by the phase-to-time difference between the phase of the data point and the previous data point , in order to compare the frequency of two natural mode curves in the case of non-stationary frequency, the natural mode curve frequency is defined as the average frequency of each data point of the curve; in order to improve the calculation speed, the simplified method expressed by the following formula is used to approximate Natural mode curve frequency f _curve :

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; curve</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; extrm</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; last</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; first</span>}}}$

Among them, n _extrm is the number of extreme points of the natural mode curve, and the extreme points include maximum points and minimum points, t _last is the moment of the last extreme point of the natural mode curve, and t _first is the time of the natural mode curve. The moment of the first extreme point of the modal curve.

(d) The amplitude of the natural mode curve: defined as the average value of the maximum and minimum point amplitudes of the natural mode curve.

(e) The damping ratio of the data point of the natural mode curve and the damping ratio of the natural mode curve: Let the amplitude of the data point i of the natural mode curve be A _i , and the amplitude of the data point corresponding to the phase in the adjacent previous cycle is A _iT , due to the reason of fixed-interval sampling, the data point corresponding to the phase of the current data point in the previous cycle often does not have a sampling point. At this time, it is necessary to use the interpolation (such as linear interpolation) The amplitude and phase of the actual sampling points before and after the corresponding phase data points in the cycle can be used to obtain the amplitude A _iT , and the damping ratio of the data point i on the natural mode curve can be approximated according to the following formula:

${\mathrm{<span\; class="notranslate">\; \&zeta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}$

The damping ratio of the natural mode curve is defined as the average value of the damping ratio of each data point of the natural mode curve; in order to reduce the amount of calculation, it can also be approximated by the average value of the damping ratio of each extreme point.

(3) According to the calculated oscillation parameters of each natural mode curve, the dangerous oscillation mode of the power system is identified, and the natural mode curves are grouped according to the found dangerous oscillation mode of the power system, that is, the frequency of the natural mode curve and the frequency of the dangerous mode of the system Similar natural mode curves belong to the same oscillation mode, and the specific method is as follows:

From the decomposed natural mode curves measured at each node, select the natural mode of a node with the largest amplitude and greater than the specified threshold A _threshold , and at the same time the damping ratio is small enough that is less than the set damping ratio threshold D _threshold State curve frequency, as the oscillation mode frequency 1 of the current system, if any of the natural mode curve frequencies of all nodes is similar to it, that is, the ratio of the absolute value of the frequency difference between the two to the system oscillation mode frequency 1 is less than the set percentage threshold FD _threshold , it is considered that the node participates in the oscillation of oscillation mode 1. For each node, at most one natural mode curve can be classified into the oscillation mode 1 of the system.

Exclude the natural mode curves of all nodes classified into oscillation mode 1, and select the one with the largest amplitude and greater than the specified threshold A _threshold and the damping ratio less than the set damping ratio threshold D _threshold among the remaining natural mode curves. The natural mode curve frequency measured at a node is used as the oscillation mode frequency 2 of the current system, and all natural mode curves and their corresponding nodes participating in the oscillation mode 2 in the system are found according to the aforementioned method.

By analogy, find out all the oscillation modes in which the amplitude of the entire power system is large enough in the current period and the maximum amplitude is greater than the specified threshold A _threshold , and the damping ratio is small enough, that is, less than the set damping ratio threshold D _threshold , that is, the dangerous oscillation mode, and Find the nodes involved in the corresponding dangerous oscillation modes and the corresponding natural mode curves.

For the specified threshold A _threshold of the above amplitude, if active power is injected into the node for low-frequency oscillation detection and analysis, A _threshold is usually taken as 30MW, and if node frequency is used for low-frequency oscillation detection and analysis, A _threshold is usually taken as 0.02Hz; The damping ratio threshold D _threshold is usually taken as 0.05; the absolute value of the frequency difference and the system oscillation mode frequency percentage threshold FD _threshold is usually taken as 10%.

(4) Coherently group the nodes participating in the dangerous oscillation mode of the power system according to the phase difference of the corresponding natural mode curve, and the specific method is as follows:

For each dangerous system oscillation mode found in the previous steps, compare the phases of the natural mode curves corresponding to all the nodes participating in the oscillation mode, and use the natural mode curve with the largest amplitude as the reference curve to calculate the relationship between the remaining natural mode curves and the The relative phase Φ of the reference natural mode curve, where -180°<Φ≤180°; if the absolute value of the relative phase of the natural mode curve measured at a certain node is less than 90°, then the node corresponding to the reference curve belongs to the same homology group; on the contrary, if the absolute value of the relative phase of the natural mode curve measured by a node is greater than 90°, then the node belongs to the homology group opposite to the reference node; accordingly, all nodes participating in a certain mode oscillation Divided into two groups, the oscillation power is mainly exchanged back and forth between the two groups.

When expressing the group visually, the coherent grouping of different system oscillation modes is plotted on different plant geographic maps. Use colored vector arrows to describe the oscillation of the natural mode curves corresponding to the corresponding nodes at the bus nodes of each plant station. Different colors of the vector arrows represent different homology groups (for example, red and blue are used to distinguish two homology groups), The length of the arrow indicates the magnitude of the natural mode curve, and the direction of the arrow is determined by the relative phase of the natural mode curve.

(5) Determine the line set where the oscillation center or interface of the system oscillation mode is located. Since the oscillation center or interface of the power system oscillation mode is located on the line between two opposite coherent groups, when the phasor measurement unit PMU is densely distributed, that is, when there is no other ungrouped substation bus between the coherent groups of the substation bus, it can be determined by The lines through which the cut planes between coherence groups pass determine exactly which lines the center of oscillation or the interface consists of. On the visual representation of the group, the lines on the oscillation interface are marked with short dashed lines perpendicular to the lines.

(6) The nodes that are not directly connected electrically in the same coherence group are further divided into different coherence subgroups according to geographical location or topological relationship. When visualized, the nodal vector arrows of different homology subgroups are colored in different shades of the same color. For example, Northeast Power Grid and Shandong Power Grid oscillate relative to North China Power Grid (excluding Shandong). Although the nodes of Northeast Power Grid and Shandong Power Grid belong to the same coherent group from the natural mode curve, they are not directly connected electrically, so they can be reconnected It is subdivided into two coherent subgroups, whose coherence is represented by blue and light blue respectively, while the coherence of nodes in the North China Power Grid is uniformly represented by red.

The specific implementation of the present invention will be described here in combination with an application example in an actual 500kV regional power grid (hereinafter referred to as A power grid).

The low-frequency oscillation detection and analysis software developed based on the principle of the invention runs online on the advanced application server of the main station of the wide-area measurement system in the power grid dispatching center. The phasor measurement unit PMU distributed in each substation or power plant in the power grid real-time information of voltage phasor, current phasor, power, frequency and other information with accurate GPS time scale at the rate of dozens or hundreds of frames per second ( For example, 100 frames per second or 50 frames per second) are sent to the wide-area measurement master station of the power grid dispatching center, processed by the front-end communication unit and stored in the real-time data server. The online low-frequency oscillation detection and analysis software running on the advanced application server obtains the real-time measurement results of each PMU substation in the whole network from the real-time data server, and after online detection and analysis, gives an alarm or analysis result, and stores the analysis results in the main The historical data server of the station. At present, PMU substations are mainly installed in 500kV substations and main 220kV power plants of various provincial or regional power grids. With the help of these data, low-frequency oscillation detection on the 500kV backbone grid can be realized, and the main power plants and the associated power plants under each 500kV substation can be analyzed contribution to oscillations.

Based on the above hardware and software environment, the low-frequency oscillation analysis program proposed by the present invention running on the advanced application server performs online low-frequency oscillation detection, analysis and alarm. Since most of the 500kV substations of power grid A have PMU measurement or can calculate the injection active power of the transformer high voltage side and external network measurement, that is, each injection active power has PMU measurement or can be calculated by other PMU measurement, and A Although there is an electromagnetic ring network in the local area of the power grid, for various oscillation modes on the 500kV grid frame, the ring network part can usually be equivalent to a node, so the electromagnetic ring network has little influence on the analysis of the oscillation mode. Therefore, the method of injecting active power into the analysis node can be used to detect and analyze the low frequency oscillation. (If the electromagnetic ring network is serious or most nodes inject active power without PMU measurement, the method of analyzing frequency can be used for low-frequency oscillation detection and analysis, but due to the limited variation range of power frequency frequency, the numerical resolution is relatively low compared to power , which is not conducive to the detection and analysis of small-amplitude low-frequency oscillations). In addition, in the actual system, in order to realize timely alarms for low-frequency oscillations in various frequency bands with different alarm time requirements and improve the analysis speed of low-frequency oscillations, it is recommended to use frequency division, variable time window, variable sampling rate, variable moving step spectrum Analytical method. Under the above premise, the steps of the online fast low-frequency oscillation detection and node coherence grouping modal analysis based on the frequency division of the present invention are as follows, and the overall algorithm block diagram is shown in Figure 2:

(1) Empirical mode decomposition is performed on the PMU measured curve: the injected active power of the high-voltage side of all substation transformers is obtained from the real-time database of the WAMS master station, and the rate is 100 frames per second. The low-frequency oscillation detection and analysis program divides the entire low-frequency oscillation frequency range into three frequency bands, namely 0.1-0.5Hz, 0.5-1.0Hz and 1.0-2.5Hz, and uses three empirical mode decomposition EMD threads to perform low-frequency analysis on these three frequency bands respectively. Oscillation detection and analysis. For the above three frequency bands, the data sampling rates of 2Hz, 5Hz and 10Hz are used to sample all the PMU measurements of active power injection. When the accumulated data lengths in the active power measurement data windows of each PMU reach 30 seconds, 10 seconds and 5 seconds respectively, the empirical mode decomposition method EMD is used to perform empirical mode decomposition on the data point curves in each data window to obtain the natural modes curve, when the frequency of the decomposed natural mode curve is less than 0.1Hz, 0.5Hz, 1.0Hz respectively, the empirical mode decomposition of the current curve in the corresponding window is terminated, and then the oscillation mode and Oscillatory modal analysis. The data windows of each frequency band move forward with a step size of 2 seconds, 1 second and 0.4 seconds respectively, and then start new PMU data accumulation, empirical mode decomposition, and oscillation mode and modal analysis. For a very large-scale system, if the spectrum analysis time of the whole network exceeds the window moving step, the data in the time window with the current moment as the end point is taken to continue spectrum analysis and modal analysis.

(2) Calculate the oscillation parameters of each natural mode curve: calculate the frequency of the natural mode curve, the amplitude of the natural mode curve, the phase of each data point of the natural mode curve, and the natural mode curve for each decomposed natural mode curve The damping ratio of each extreme point, the damping ratio of the natural mode curve and other information, and according to the general definition of the energy and power of the oscillation curve, the signal energy and signal power of the corresponding natural mode curve can be calculated. The calculation method of the main oscillation description parameters is as follows:

a) The phase of the data points of the natural mode curve: the phase of each data point is obtained by the zero-crossing method, that is, the positive zero-crossing point of the curve is 0°, the negative zero-crossing point is ±180°, and the maximum point is 90 °, the minimum value point is -90°, and the phase of the data points between adjacent zero and pole points is obtained by dividing 90 equal intervals.

b) Natural mode curve frequency: use the simplified method represented by the following formula to find the natural mode curve frequency f _curve :

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; curve</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; extrm</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; last</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; first</span>}}}$

Among them, n _extrm is the number of extreme points of the natural mode curve (including maximum and minimum points), t _last is the moment of the last extreme point of the natural mode curve, and t _first is the first time of the natural mode curve. A moment of extreme point.

c) Amplitude of the natural mode curve: defined as the average value of the amplitudes of the maximum and minimum points of the natural mode curve.

d) The damping ratio of the extreme point of the natural mode curve and the damping ratio of the natural mode curve: let the amplitude of the maximum (minimum) value point i of the natural mode curve be A _i , and the maximum ( The amplitude of the small) point is A _iT . The damping ratio of the maximum (small) value point i on the natural mode curve can be approximated according to the following formula:

${\mathrm{<span\; class="notranslate">\; \&zeta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; .</span>$

Further use the average value of the damping ratio of each extreme point to obtain the damping ratio of the natural mode curve.

e) The energy of the discrete signal oscillation curve is the sum of the squares of the amplitudes of each data point, and the power of the discrete signal oscillation curve is the ratio of the energy of the oscillation curve to the number of sampling points.

For the example of power grid A, the active power injection of the external power grid to the power grid is represented by _Psys , and the above-mentioned analysis based on empirical mode decomposition is performed on a section of PMU measurement curve of _Psys . The main results are shown in Figure 3 (the comparison of phase As shown in Figure 4), three natural oscillation modes are obtained, namely 0.70Hz, 0.32Hz and 0.18Hz. In the interval oscillation mode, 0.32Hz is the oscillation mode between the A grid and the external grid, and 0.18Hz is a larger range of interval oscillation mode between the two external grids with the participation of the A grid.

For the spectrum analysis of the original curve shown in Figure 3, under the same computing environment, when using 75 sampling points, the calculation time of the EMD method is 2.8ms, and the above-mentioned correct results are obtained; while the calculation time of the Prony method is 37.8ms, and The above correct results cannot be obtained, and the first three oscillation modes with the largest residues obtained are 0.64Hz, 1.37Hz and 1.38Hz respectively, which are quite different from the analysis results of the grid oscillation mode by the operation mode department. When the number of sampling points increases to 150, although the Prony method can find approximately correct results (the first three modes with the largest residues are 0.32Hz, 0.70Hz, and 0.19Hz), the calculation time reaches 115ms. It can be seen that the spectrum analysis based on the EMD method is superior to the spectrum analysis based on the Prony method in terms of calculation speed and accuracy.

(3) Identification of dangerous oscillation modes and grouping of natural mode curves by oscillation mode: In the current time window, among the natural mode curves of each node decomposed by the previous steps, select the one with the largest amplitude and greater than the specified threshold A _threshold (for example, 30MW), and the natural mode curve frequency of a node whose damping ratio is small enough to be less than the set damping ratio threshold D _threshold (for example, 0.05) at the same time, is used as the oscillation mode frequency 1 of the frequency band of the current system; all nodes If there is a natural mode curve frequency close to it, that is, the ratio of the absolute value of the frequency difference between the two to the system oscillation mode frequency 1 is less than the set percentage threshold FD _threshold (for example, 10%), then the node is considered to participate in the oscillation For the oscillation of mode 1, there can only be at most one natural mode curve for each node that can be classified into the oscillation mode 1 of the frequency band of the system. In this way, all nodes participating in the oscillation mode 1 of the frequency band of the system can be found out. Exclude all the natural mode curves that fall into the frequency band oscillation mode 1 in all nodes, and select the natural mode measured at a node with the largest amplitude and greater than the specified threshold, and the damping ratio is small enough from the remaining natural mode curves. The frequency of the state curve is used as the oscillation mode frequency 2 of the frequency band of the current system, and all the natural mode curves and their corresponding nodes participating in the oscillation mode 2 of the frequency band in the system are found according to the aforementioned method. And so on to find out that the amplitude of this frequency band is large enough (in this example, the amplitude of the curve with the largest amplitude in the relevant natural mode curves is greater than 30MW) and the damping ratio is small enough (in this example, the amplitude of the largest amplitude in the relevant natural mode curves Curves with damping ratios less than 0.05) for all oscillation modes, as well as the participating nodes and corresponding natural mode curves. In the actual power system, at most 2-3 such oscillation modes can be found in each frequency band. Each frequency band is processed according to this method, so as to find out the dangerous oscillation modes of all frequency bands of the system, as well as the nodes participating in the corresponding dangerous oscillation modes and the corresponding natural mode curves.

From the above method, it is found that the oscillation mode of the entire A grid in the current period with sufficiently large amplitude and sufficiently small damping ratio is 0.7 Hz. In addition, two oscillation modes of 0.32Hz and 0.18Hz can be found, but the amplitude of the curve with the largest amplitude in the natural mode curves related to them does not exceed the threshold value of 30MW, so it is not regarded as the dangerous oscillation mode of the current system, and will not be carried out. Further analysis and alarms such as coherence grouping. Figure 4 shows the 0.7Hz system oscillation mode in the active power injection measurement of the bus nodes of the four main stations participating in the 0.7Hz system oscillation mode (take the two stations with the largest amplitude from the two opposite groups). Natural mode curves and natural mode curve parameters. In the actual system, the program also records the frequency, amplitude, damping ratio, start-stop time and other information of the natural mode curve related to the non-dangerous oscillation mode to the database, so as to prepare for the statistical analysis of the operating state of the system. use.

(4) Coherent grouping of nodes for each dangerous oscillation mode of the power system: For each dangerous system oscillation mode found in the previous steps, phase comparison is performed on the natural mode curves corresponding to all nodes participating in the oscillation mode. Taking the natural mode curve with the largest amplitude as the reference curve, calculate the relative phase Φ (-180°<Φ≤180°) between the remaining natural mode curves and the reference natural mode curve, and the relative phase Φ is defined as two natural modes The arithmetic mean of the phase difference φ _i of each corresponding data point on the curve (so that φ _i satisfies -180°<φ _i ≤180°). If the absolute value of the relative phase of the natural mode curve measured by a certain node is less than 90°, then the node corresponding to the reference curve belongs to the same homology group; otherwise, if the relative phase of the natural mode curve measured by a certain node The absolute value of is greater than 90°, then the node belongs to the homology group opposite to the reference node. Accordingly, all nodes participating in a certain oscillation mode of the system are divided into two groups, and the oscillation power is mainly exchanged back and forth between the two groups. The above method is used to carry out node coherence grouping for each dangerous system oscillation mode separately, and visualize them on different geographic maps.

Figure 4 shows the corresponding natural mode curves of the four main stations in the 0.7Hz system oscillation mode and their grouping by relative phase. In Figure 4, the 0.7Hz natural mode curve of ZX plant active power injection has the largest amplitude, so it is selected as the reference curve; the relative phase of the 0.7Hz natural mode curve of WS station relative to the reference curve is 4.7°, which is less than 90°, so The WS station and the ZX plant belong to the same coherence group G1 in the 0.7Hz system oscillation mode; while the relative phases of the 0.7Hz natural mode curves of the active power injection of the LY station and the external network are 133.0° and 121.3° respectively, so they belong to the ZX The homology group G2 opposite to the group where the factory is located. Fig. 5 shows the 0.7Hz system oscillation mode node coherence grouping and the visualized geographical map of amplitude and phase. The length of the vector arrows of each station in the figure indicates the amplitude of the corresponding natural mode curve, the direction of the arrow is determined by the relative phase of the natural mode curve, and the different colors of the vector arrows (red and blue in Figure 5) represent different For the homology group, the specific values of the amplitude and phase of the natural mode curve represented by the arrow are also marked next to the corresponding plant. The larger the magnitude of the vector arrows in the two coherence groups, the closer the angle is to 0° or ±180°, and the greater the degree of participation of the generator set associated with the corresponding node in the oscillation, the more likely it is the key unit of the oscillation in this mode. In the actual system, when a dangerous low frequency oscillation is detected, this screen will pop up, thus helping the dispatcher to recognize and deal with the low frequency oscillation problem.

(5) Determine the line set where the oscillation center or interface of the system oscillation mode is located: the oscillation center or interface of the system oscillation mode is located on the line between two opposite coherence groups. When the phasor measurement unit PMU is densely distributed, that is, when there is no other non-grouped substation bus between the substation bus coherent groups, it is possible to accurately determine which lines the oscillation center or interface is composed of by the lines through which the cut planes between the coherent groups pass. It can be seen from Figure 5 that the line set where the interface of the 0.7Hz oscillation mode of power grid A is located is composed of several lines marked with vertical short dashed lines located between two opposite coherence groups.

(6) Coherence group subdivision: according to geographic location or topological relationship, nodes that are not directly connected electrically in the same coherence group can be divided into different coherence subgroups. When visualized, the nodal vector arrows of different homology subgroups are colored in different shades of the same color. For example, Northeast Power Grid and Shandong Power Grid oscillate relative to North China Power Grid (excluding Shandong). Although the nodes of Northeast Power Grid and Shandong Power Grid belong to the same coherent group from the natural mode curve, they are not directly connected electrically. Therefore, they can be subdivided It is divided into two coherent subgroups, whose coherence is represented by blue and light blue respectively, while the coherence of the North China power grid nodes is uniformly represented by red.

Claims (7)

1. one kind based on Wide-area Measurement Information and Empirical mode decomposition, can realize low-frequency oscillation modal analysis method to electric system complicated low-frequency oscillation carrying out online detection and node coherence grouping, described analytical approach is not only applicable to non-linear, non-stationary changes, the actual complex waveform that contains composition non-periodic, also can be to belonging to same power system oscillation pattern, but the natural mode of vibration curve of non-sinusoidal that frequency is slightly variant or cosine carries out the phase bit comparison, realization is to the coherence grouping of the node that participates in each mode of oscillation, thereby obtains internodal Power Exchange relation and oscillation center or interfacial position; It is characterized in that described analytical approach may further comprise the steps:

(1) at the current time window, the meritorious injecting power of node or the frequency actual measurement oscillating curve that adopt the frequency spectrum analysis method that decomposes based on empirical modal will deliver to the wide area measurement main website in the phasor measurement unit PMU collection are decomposed into the natural mode of vibration curve;

(2) calculate the parameter of oscillation of each natural mode of vibration curve according to natural mode of vibration parameter of curve computing method;

(3) parameter of oscillation according to each the natural mode of vibration curve that is calculated carries out the dangerous mode of oscillation identification of electric system, and by the dangerous mode of oscillation of the electric system found to the grouping of natural mode of vibration curve, be about to the natural mode of vibration curve frequency natural mode of vibration curve close and belong to same mode of oscillation with system's limit risk frequency;

(4) node that participates in the dangerous mode of oscillation of electric system is carried out coherence grouping according to the phase place difference of corresponding natural mode of vibration curve;

(5) circuit that passes through according to the cutting plane between homology group is determined the oscillation center of each dangerous mode of oscillation of electric system or the sets of lines at interphase place;

(6) according to geographic position or topological relation the node division that does not directly link to each other on electric in the same homology group is become different people having the same aspiration and interest subgroups.

2. low-frequency oscillation modal analysis method according to claim 1, it is characterized in that: when in step (1), phasor measurement unit PMU actual measurement oscillating curve being carried out spectrum analysis, in electrical network, there are not electromagnetic looped network or electromagnetic looped network scope very little, and nearly all node injects active power to be had PMU to measure or can be measured extrapolate the time by other PMU, adopts node to inject active power and carries out spectrum analysis and carry out low-frequency oscillation detection and model analysis; When the serious or most of node injection of electromagnetic looped network in electrical network active power does not have the PMU measurement, adopt nodal frequency to carry out spectrum analysis and carry out low-frequency oscillation detection and model analysis.

3. low-frequency oscillation modal analysis method according to claim 1 is characterized in that: comprise in natural mode of vibration parameter of curve described in the step (2): the amplitude of the relative phase of natural mode of vibration curve data point phase place, natural mode of vibration curve phase differential and natural mode of vibration curve, natural mode of vibration curve data dot frequency and natural mode of vibration curve frequency, natural mode of vibration curve, the damping ratio of natural mode of vibration curve data point and natural mode of vibration curve damping ratio; These parameters are provided as giving a definition and computing method:

(a) the data point phase place of natural mode of vibration curve: the phase place of each data point adopts zero-crossing method to obtain, be that curve positive going zeror crossing point place is 0 °, negative sense zero crossing place is ± 180 °, maximum point is 90 °, minimum point is-90 °, and the phase place of the data point between the adjacent zeros limit is tried to achieve according to uniformly-spaced dividing 90 parts equally;

(b) relative phase of natural mode of vibration curve phase differential and natural mode of vibration curve: in the frequency phase place of two natural mode of vibration curves relatively under the difference condition slightly, definition natural mode of vibration curve phase differential Φ is the difference φ of each corresponding data point phase place on two curves _iArithmetic mean, described φ _iSatisfy-180 °＜φ _i≤ 180 °, in the low-frequency oscillation model analysis, for one group of natural mode of vibration curve that belongs to same mode frequencey, with the curve of amplitude maximum wherein is reference curve, even its natural mode of vibration curve relative phase is 0, all the other natural mode of vibration curves should be the relative phase of all the other natural mode of vibration curves with reference to the phase differential of natural mode of vibration curve relatively;

(c) the data point frequency of natural mode of vibration curve and natural mode of vibration curve frequency: the frequency of each data point of natural mode of vibration curve is tried to achieve through conversion the angular frequency that time difference obtains by the phase place and the last data point phase place of this data point, in order to compare the frequency of two natural mode of vibration curves under the situation of non-stationary frequency, definition natural mode of vibration curve frequency is the mean value of each data point frequency of this curve; In order to improve computing velocity, the approximate natural mode of vibration curve frequency f of representing with following formula of asking of short-cut method _Curve:

N wherein _ExtrmCount for this natural mode of vibration curve extreme value, described extreme point contains maximum point and minimum point, t _LastBe the moment of this last extreme point of natural mode of vibration curve, t _FirstBe the moment of this first extreme point of natural mode of vibration curve;

(d) amplitude of natural mode of vibration curve: be defined as each maximum point of natural mode of vibration curve and the mean value of minimum point amplitude;

(e) damping ratio of natural mode of vibration curve data point and natural mode of vibration curve damping ratio: the amplitude that makes natural mode of vibration curve data point i is A _i, the amplitude of the data point of corresponding phase is A in the adjacent last cycle _I-TReason owing to fixed sampling interval technique, often there is not sampled point in the data point of current data point corresponding phase in last cycle, at this moment, need utilize the amplitude and the phase place of current data point actual samples point before and after the corresponding phase data point in last cycle to obtain amplitude A with the method for interpolation _I-T, can be similar to the damping ratio of obtaining the data point i on the natural mode of vibration curve according to following formula:

Natural mode of vibration curve damping ratio is defined as the mean value of this each data point damping ratio of natural mode of vibration curve; In order to reduce calculated amount, the mean value of also available each extreme point damping ratio is similar to.

4. low-frequency oscillation modal analysis method according to claim 1, it is characterized in that: the parameter of oscillation according to each the natural mode of vibration curve that is calculated in step (3) carries out the dangerous mode of oscillation identification of electric system, and by the dangerous mode of oscillation of the electric system found to the grouping of natural mode of vibration curve, its concrete grammar is as follows:

In the natural mode of vibration curve that each node that decomposites measures, select amplitude maximum and amplitude greater than regulation amplitude threshold A _Threshold, damping ratio is enough little promptly less than the damping ratio threshold value D that sets simultaneously _ThresholdThe natural mode of vibration curve frequency of a certain node, mode frequencey 1 as current system, close with it as if having in the natural mode of vibration curve frequency of all nodes, promptly the ratio of absolute value of both frequency differences and system oscillation mode frequency 1 is less than the percentage threshold FD that sets _Threshold, think that then this node participates in the vibration of mode of oscillation 1, can only have a natural mode of vibration curve to be included into the mode of oscillation 1 of system at most for each node;

The natural mode of vibration curve that is included into mode of oscillation 1 of getting rid of all nodes is selected amplitude maximum and amplitude greater than regulation amplitude threshold A in remaining natural mode of vibration curve _Threshold, damping ratio is less than the damping ratio threshold value D that sets simultaneously _ThresholdThe natural mode of vibration curve frequency that measures of a certain node, as the mode frequencey 2 of current system, find out all natural mode of vibration curves and the corresponding node thereof that participates in mode of oscillation 2 in the system according to aforesaid method;

The rest may be inferred find out whole electric system at current period amplitude enough big and maximum amplitude greater than regulation amplitude threshold A _Threshold, damping ratio is enough little promptly less than the damping ratio threshold value D that sets simultaneously _ThresholdAll mode of oscillation, promptly dangerous mode of oscillation, and find out node and the corresponding natural mode of vibration curve that participates in corresponding dangerous mode of oscillation.

5. low-frequency oscillation modal analysis method according to claim 1 is characterized in that: in step (4) node that participates in the dangerous mode of oscillation of electric system is carried out coherence grouping according to the phase place difference of corresponding natural mode of vibration curve, its concrete grammar is as follows:

On the basis of claim 1 step (3) for each the dangerous system oscillation pattern that finds, all natural mode of vibration curves that participate in the node correspondence of this mode of oscillation are carried out the phase bit comparison, natural mode of vibration curve with the amplitude maximum is a reference curve, calculate all the other natural mode of vibration curves and this relative phase Φ with reference to the natural mode of vibration curve, wherein-180 °＜Φ≤180 °; If the absolute value of the relative phase of the natural mode of vibration curve that certain node measures is less than 90 °, then the node that this node and reference curve are corresponding belongs to identical homology group; Otherwise if the absolute value of the relative phase of the natural mode of vibration curve that certain node measures is greater than 90 °, then this node belongs to the homology group opposite with reference mode; In view of the above, all nodes that participate in certain mode oscillation are divided into two groups, hunting power mainly back and forth exchanges between these two groups.

6. low-frequency oscillation modal analysis method according to claim 4 is characterized in that: for the regulation amplitude threshold A of described amplitude _Threshold, carry out low-frequency oscillation detection and analysis, then amplitude threshold A if adopt node to inject active power _ThresholdUsually be taken as 30MW, detect and analyze if adopt nodal frequency to carry out low-frequency oscillation, then amplitude threshold A _ThresholdUsually be taken as 0.02Hz; For described damping ratio threshold value D _ThresholdUsually be taken as 0.05; For the absolute value of described frequency difference and the percentage threshold FD of system oscillation mode frequency _ThresholdUsually be taken as 10%.

7. low-frequency oscillation modal analysis method according to claim 1, it is characterized in that: when the grouping result of will vibrating is carried out visual expression, the coherence grouping situation of different system mode of oscillation is plotted on different factory's station geographic maps, the vibration of the natural mode of vibration curve of respective nodes correspondence is described with colored vector arrow in each factory's station bus nodes, the different homology group of different colours representative of vector arrow, the length of arrow is represented the amplitude of natural mode of vibration curve, and the direction of arrow is determined by the relative phase of natural mode of vibration curve; Indicate the circuit of vibration on the interphase with short dash line with the circuit square crossing; The knot vector arrow of different people having the same aspiration and interest subgroup adopts the same color of different depth degrees to carry out painted.

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