CN105023090A - Power generator unit coherence grouping scheme based on wide area information - Google Patents

Abstract

The invention provides a power generator unit coherence grouping scheme based on wide area information. The scheme is characterized by performing feature extraction on a power angle locus and the rotor angular speed of a power generating set by using a phasor measurement unit; computing four feature difference value matrixes among power generators by using the extracted feature; computing weighted values WD, WA, WL, and WS by using DirDiv, AngleDiv, LocDiv, and SpeedDiv, so as to compute a structural difference degree matrix SDIV; clustering all power generators according to the SDIV by using a hierarchical cluster procedure; and dividing a clustered result by using an appropriate threshold [epsilon] to obtain a final grouped result. The power generator unit coherence grouping scheme may accurately identify the coherence of a complex power system.

Description

Coherent Grouping Scheme of Generating Sets Based on Wide Area Information

technical field

The invention relates to the field of control of electric power systems, in particular to a scheme for identifying coherence of generating sets based on wide-area information.

Background technique

With the increasing scale and complex structure of power system, the computational complexity of power system security analysis is greatly increased. In order to simplify the calculation, it is often necessary to divide the units in the system into several coherence groups through the coherence analysis of the generating units, and then use the dynamic equivalent to simplify the system ^[1] . In addition, when the power system is severely disturbed and the generating units undergo out-of-step oscillations, emergency decommissioning measures are required to prevent the accident from further expanding and causing the entire network to collapse. Accurate identification of the coherent generator group is a prerequisite for rapid decoupling ^[2] .

Coherence refers to the similarity or consistency of the dynamic response behavior of generators in the system after being disturbed. Grouping into different groups is called homology grouping. There are many methods of coherence grouping, and traditional methods based on model parameters can be divided into: electrical distance grouping method ^[3] , state space grouping method ^[4] , slow coherence method ^[5] and so on. Most of these methods rely too much on the accuracy of system model parameters, and use linearization analysis to approximate the nonlinear model of the system, and the calculation process is relatively complicated, which is difficult to meet the real-time, fast and accurate clustering requirements of large-scale power systems. The development and application of the Wide Area Measurement System (Wide Area Measurement System-WAMS) provides a new way for the identification of the power system coherent fleet. Through the phasor measurement unit (Phasor Measurement Unit-PMU) configured in the power grid, real-time information including power generation can be obtained. Various electrical quantities in the system, including mechanical power angle and rotor angular velocity, perform digital signal feature extraction on the real-time response electrical quantity information, and obtain coherence identification information from it. This kind of data mining method based on real-time electrical quantities is not affected by model parameters, not only fully considers the information of system faults, but also can well avoid problems such as strong nonlinearity of the system ^[6] . Literature [7] uses the generator power angle information obtained by WAMS to perform trigonometric function fitting to obtain preliminary grouping results, and then uses discrete Fréchet distance calculation to complete the final grouping. On the basis of system cluster analysis, literature [8] carried out cluster analysis on the power angle curves based on the minimum distance between the power angle trajectories measured by WAMS, and realized the reasonable grouping of multi-machine system coherent units.

references

[1] An Jun, Mu Gang, Xu Weibin. Recognition of power system coherent clusters based on principal component analysis [J]. Power Grid Technology, 2009,33(3):25-28.

[2] Gao Peng, Wang Jianquan, Gan Deqiang, et al. A review of power system out-of-step separation [J]. Electric Power System Automation, 2005,29(19):90-97.

[3]Pai M A; Adgaonkar R P.Electromechanical distance measure for decomposition of power systems[J].Electrical Power&Energy Systems,1984,6(4):249-254. 

[4] Yin Jian, Xue Fei, Chen Yunping. Application of Grouping Theory in Power System Transient Stability Prediction and Control [J]. Electric Power Information, 2002, (1): 1-4.

[5] Song Honglei, Wu Junyong, Ji Luyu. On-line coherence recognition of generators based on slow coherence theory and Hilbert-Huang transform [J]. Electric Power Automation Equipment, 2013, 33(8): 70-77.

[6] Ni Jingmin, Shen Shen, Tan Wei, etc. A method of coherence recognition based on linearization at non-equilibrium points [J]. Electric Power System Automation, 2010,34(20):7～12.

[7] Feng Kangheng, Zhang Yanxia, Liu Zhixiong, et al. Online identification method of coherent cluster based on wide area information [J]. Power Grid Technology, 2014,38(8):2082-2086

[8] Shi Kunpeng, Mu Gang, Li Ting, etc. Clustering tree method based on empirical mode decomposition and its application in coherent unit grouping [J]. Power Grid Technology, 2007, 31(22):21-25.

Contents of the invention

Based on the wide-area information measurement system, the present invention proposes a new coherent grouping scheme of generator sets with certain self-adaptiveness. The scheme starts from the perspective of hierarchical clustering analysis method, calculates the difference indexes among the electrical quantities of generator sets, and weights Finally, the structural difference degree of the unit is obtained, which is used as the standard for grouping. Technical scheme of the present invention is as follows:

A coherent grouping scheme for generator sets based on wide-area information. This method uses phasor measurement units to extract features from the power angle trajectory and rotor angular velocity of generator sets to obtain information that can reflect coherence. The extracted features include four indicators Comparison: direction comparison DirDiv (δ _i , δ _j ), angle comparison AngleDiv (δ _i , δ _j ), position comparison LocDiv (δ _i , δ _j ) and rotor angular velocity, that is, speed comparison SpeedDiv (δ _i , δ _j ) , where δ _i , δ _j are the power angle trajectories of different generator sets, 1≤i≠j≤m, m is the total number of trajectories, and the trajectory δ _i is composed of δ _i1 , δ _i2 ,...,δ _in , and the trajectory δ _j consists of δ _j1 , δ _j2 ,..., δ _jn , n is the number of sampling points, where,

(1) Direction comparison DirDiv(δ _i , δ _j ) represents the difference in deflection degree of power angle trajectories δ _i , δ _j in the overall change trend, δ _is , δ _js are the starting points of sampling of trajectories δ _i , δ _j respectively, δ _ie , δ _je are the termination points of the trajectory δ _i , δ _j sampling respectively, and the vector and angle of To represent the direction difference DirDiv(δ _i ,δ _j ) between trajectories;

(2) Angle comparison AngleDiv(δ _i , δ _j ) reflects the directional change characteristics inside the trajectory. _Let the angle between the trajectory at the sampling point δ _p be denoted as β, and the rotational angle be denoted as θ. The distance between a sampling point δ _p-1 , and b is the distance between this sampling point and the next sampling point δ _p+1 , and c is the distance between sampling points δ _p-1 and δ _p+1 , and the included angle β is:

β = arccos((a ² +b ² -c ² )/2ab)

According to the right-hand rule of the angle β and vector cross product direction, the rotation angle θ is obtained, and the calculation formula of the rotation angle θ is:

It can be obtained from the above formula that the outwardly changing rotation angle θ is a positive value, and the inwardly changing rotation angle θ is a negative value. The angle comparison AngleDiv(δ _i ,δ _j ) is an accumulative quantity that changes with the sampling time, and the calculation formula is:

$\mathrm{<span\; class="notranslate">\; A</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; |</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}$

In the case of an ideal coherent fleet, the angle difference of each sampling point of δ _i and δ _j is 0, and AngleDiv is also 0. In the case of the most mismatched power angle curve, the rotation angle of each sampling point is equal to In the opposite direction, that is to say, the two trajectories are oppositely sawtoothed during the sampling time, and AngleDiv is 1 at this time;

(3) Position comparison LocDiv(δ _i ,δ _j ) reflects the relative distance between generator power angle trajectories, the calculation formula is as follows:

$\begin{array}{cc}\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\end{array}$

Where dist(u, v) represents the Euclidean distance between two points u and v, u and v are any sampling points on the trajectory of δ _i and δ _j respectively; h(δ _i , δ _j ) is δ _i , The direct Hausdorff distance of δ _j is the maximum distance from each point in δ _i to the minimum distance set of all points in δ _j . If h(δ _i , δ _j )=d, then each sample in δ _i The distance from the point to the nearest sampling point in δ _j does not exceed d, and the distance difference between d response curves, H(δ _i ,δ _j ) is h(δ _i ,δ _j ) and h(δ _j ,δ _i ) The maximum value of , if H(δ _i , δ _j )=d, it shows the distance from each sampling point in δ _i to the nearest sampling point in δ _j and the distance from each sampling point in δ _j to the nearest sampling point in δ _i The distance between the points does not exceed d;

(4) Speed comparison SpeedDiv(δ _i , δ _j ) represents the difference in angular velocity of the rotor of the generator set, as follows

$\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

The difference between the angular velocity changes of the rotors of the two generators is measured by the Euclidean distance between the angular velocity sampling values, and ω _i (t) and ω _j (t) represent the sampling values of the i and j generator sets at the sampling time t, respectively;

The generator set coherent grouping scheme includes the following steps:

Step 1: Calculate the above four indicators between two generators in the power system, and store the values in the four matrices of DirDiv, AngleDiv, LocDiv and SpeedDiv respectively. If there are m generators in the system, the matrix is A symmetrical square matrix of order m, the diagonal elements of each matrix are all zero;

Step 2: Define W={W _D , W _A , W _L , W _S } as the feature weight, corresponding to the above four features respectively; each weight satisfies: (1) all weight values are greater than or equal to zero; (2) W _D +W _A +W _L +W _S ＝1, since the value range of each feature is different, it is necessary to normalize the difference value of each feature. The normalization process is to divide the obtained four matrices Divide each element by the maximum value of the elements in each matrix; then use the idea of variation coefficient method to calculate the weight, and use the obtained weight to weight and sum the above four indicators to form the trajectory structure difference:

SDIV＝W _D ×DirDiv+W _A ×AngleDiv+W _L ×LocDiv+W _S ×SpeedDiv

The third step: Calculate the difference degree matrix SDIV of the generator set, and then use the hierarchical clustering analysis method to cluster;

Step 4: After the clustering is over, select an appropriate threshold ε to divide the clustering tree solution to obtain the final clustering result;

As a preferred embodiment, wherein, the steps of calculating the weight using the idea of the coefficient of variation method are:

1) Obtain all the elements above the main diagonal of the DirDiv, AngleDiv, LocDiv and SpeedDiv matrices respectively, and store them in the 4 columns of the matrix X in turn, then the 4 columns in the matrix store the distance between the generators under 4 different indicators Difference value vector; if there are m generator sets, then the number of rows p=m(m-1)/2 of the matrix X, and the number of columns q=4;

2) Calculate the mean value and standard deviation of each feature index, that is, find the mean value and standard deviation of each column vector of X;

3) Calculate the coefficient of variation of each index;

4) Normalize the coefficient of variation of each index to obtain the weight of each index;

Let S={s ₁ ,s ₂ ,...,s _m } respectively represent m generating units in the system, and the steps of clustering by hierarchical clustering analysis are as follows:

1) Set each s _i as a class, forming m classes in total: s ₁ , s ₂ ,..., s _m ;

2) From the existing m classes, find out the two classes s _r and s _k with the smallest trajectory structure difference degree SDIV;

3) Merge classes s _r and s _k into a new class s _rk , and the number m of existing classes will be reduced by 1;

4) Detect all samples, if all samples belong to the same class, then terminate the algorithm; otherwise, return to 2).

The beneficial effects of the present invention are as follows:

1. Using the generator power angle trajectory and rotor angular velocity measured by the PMU in the wide-area measurement system can realize the division of the coherent machine group, avoiding the influence of the system model parameters on the grouping;

2. It can flexibly and objectively determine the feature weight value according to the different operating conditions of the multi-machine system, and has certain adaptability;

3. It fully considers the multi-aspect characteristic information of the power angle trajectory of the generator, and can accurately identify the coherence of the complex power system, which has practical value.

Description of drawings

The degree of direction difference of the trajectory in Figure 1

Figure 2 Schematic diagram of the corner of the trajectory

Figure 3 Clustering tree and clustering using threshold ε

Detailed ways

The present invention will be described below in conjunction with the accompanying drawings and embodiments.

The invention obtains the information that can reflect the coherence by extracting the features of the generating set power angle track and the rotor angular velocity obtained by the wide-area measuring system. The extracted features include the comparison of four indicators: the direction comparison DirDiv(δ _i ,δ _j ), the rotation angle comparison AngleDiv(δ _i ,δ _j ), the position comparison LocDiv(δ _i ,δ _j ) and the rotor angular velocity, that is, the rotation speed SpeedDiv(δ _i ,δ _j ). Where δ _i , δ _j are the power angle trajectories of different generator sets, 1≤i≠j≤m (m is the total number of trajectories), and the trajectory δ _i is composed of δ _i1 , δ _i2 ,...,δ _in (n is Sampling points).

(4) Direction comparison. DirDiv(δ _i , δ _j ) represents the difference in the degree of deflection of the power angle trajectory δ _i , δ _j in the overall trend. Figure 1 shows the direction comparison between the unstabilized generator i and the unstable generator j, where δ _is and δ _js are the starting points of trajectory sampling respectively, and δ _ie and δ _je are the ending points of trajectory sampling respectively. Use the angle between two vectors L _i and L _j To represent the direction difference DirDiv(δ _i ,δ _j ) between trajectories.

(5) Corner comparison. AngleDiv(δ _i ,δ _j ) reflects the directional change characteristics inside the trajectory, and reflects the difference in the degree of fluctuation within the power angle trajectory. As shown in Figure 2, the included angle of the trajectory at the sampling point is represented by β, and the rotation angles of the trajectory are represented by θ ₁ and θ ₂ . It can be seen from the figure that a, b, and c are the adjacent and opposite sides of the included angle β respectively, and the calculation formula of the included angle β is as follows.

β = arccos((a ² +b ² -c ² )/2ab) (1)

According to the above formula and the right-hand rule of vector cross product direction discrimination, the calculation formula of the rotation angle θ is:

According to formula (2), the angle θ ₁ of outward change is positive, and the angle θ ₂ of inward change is negative. Therefore, the difference between the angle changes of the power angle trajectories of two generators is an accumulative quantity, as shown in formula (3).

$\mathrm{<span\; class="notranslate">\; A</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; |</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}\mathrm{<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

The above formula shows that AngleDiv(δ _i , δ _j ) accumulates the difference between the power angle change trends of two generators at each sampling time, and quantifies the difference in dynamic characteristics of generators at each time from the microcosm. In the case of an ideal coherent fleet, the angle difference of each sampling point of δ _i and δ _j is 0, and AngleDiv is also 0. In the case where the power angle curves do not match the most, the rotation angles of each sampling point are opposite to each other, that is to say, the two trajectories are opposite to each other in the sampling time, and AngleDiv is 1 at this time.

(6) Position comparison LocDiv(δ _i ,δ _j ). An important criterion for distinguishing coherent units is the relative distance between generator power angle trajectories. Among the present invention, the calculation of LocDiv (δ _i , δ _j ) adopts the Hausdorff distance formula, which is a measure of similarity between two groups of point sets, and it is a defined form of distance between two point sets. It is used to reflect the proximity of the trajectory in space.

LocDiv(δ _i ,δ _j )=H(δ _i ,δ _j )=max(h(δ _i ,δ _j ),h(δ _j ,δ _i )) (4)

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Where dist(a,b) represents the Euclidean distance between a and b, h(δ _i , δ _j ) is the direct Hausdorff distance of δ _i , δ _j , that is, each point in δ _i to δ _j The maximum distance in the set of minimum distances for all points. If h(δ _i , δ _j )=d, then the distance from each sampling point in δ _i to the nearest sampling point in δ _j does not exceed d, and d just reflects the distance difference between the curves. H(δ _i ,δ _j ) is the maximum value of h(δ _i ,δ _j ) and h(δ _j ,δ _i ), if H(δ _i ,δ _j )=d, it means that each of δ _i The distance from a sampling point to the nearest sampling point in δ _j and the distance from each sampling point in δ _j to the nearest sampling point in δ _i do not exceed d, H(δ _i , δ _j ) represents the distance between power angle trajectories relative distance.

(4) Speed comparison. After the power system is greatly disturbed, the sudden change in the power flow distribution of the system will cause the output power of each generator to change, resulting in the destruction of the power balance between the prime mover and the generator, and the acceleration or deceleration torque will be generated on the shaft of the unit. The power angle of the engine changes relative to the speed difference. Therefore, when analyzing the factors that affect the change of power angle, the deviation between the rotational speed of each generator and the synchronous rotational speed is also an important indicator that changes significantly. Considering the influence of speed deviation will also help to group correctly and quickly. Here, SpeedDiv(δ _i , δ _j ) is used to represent the difference in the angular velocity of the generator rotor, and formula (6) gives the comparison formula of the speed information.

$\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

The difference between the rotor angular velocity changes of the two generators is measured by the Euclidean distance, and ω _i (t) and ω _j (t) represent the sampling values of the i and j generators at the sampling time t, respectively.

Calculate the four difference values between two generators in the power system, and store the values in the four matrices of DirDiv, AngleDiv, LocDiv and SpeedDiv respectively. If there are m generators in the system, the matrix is a symmetrical square matrix of order m, and the diagonal elements of each matrix (the diagonal elements of the generator compared with itself) are all zero.

The weighted sum of the above four indicators constitutes the calculated value of the trajectory structure difference:

SDIV＝W _D ×DirDiv+W _A ×AngleDiv+W _L ×LocDiv+W _S ×SpeedDiv (7)

Define W={W _D , W _A , W _L, W _S } as the feature weight, corresponding to the above four features respectively. Each weight satisfies: (1) all weight values are greater than or equal to zero; (2) W _D +W _A +W _L +W _S =1. Since the value range of each feature is different, it is necessary to normalize the difference value of each feature. The normalization processing method adopted in the present invention is to divide each element in the obtained four matrices by the maximum value of the elements in each matrix.

This program uses the idea of variation coefficient method to calculate the weight, and the specific calculation steps are as follows:

1) Obtain all the elements above the main diagonal of the DirDiv, AngleDiv, LocDiv and SpeedDiv matrices respectively, and store them in the 4 columns of the matrix X in turn, then the 4 columns in the matrix store the distance between the generators under 4 different indicators A vector of difference values. If there are m generators, the number of rows of the matrix X is p=m(m-1)/2, and the number of columns is q=4.

2) Calculate the average value and standard deviation of each feature index, that is, calculate the average value and standard deviation of each column vector of X. where i=1,2,...,p; j=1,2,3,4.

$\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

3) Calculate the coefficient of variation of each index, j=1,2,3,4.

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

4) Normalize the coefficient of variation of each index to obtain the weight of each index.

${\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 4</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

Among them, j=1,2,3,4. Therefore, the respective weights are W _D =W ₁ , W _A =W ₂ , W _L =W ₃ , and W _S =W ₄ .

Using the obtained weight values W _D , _{WA , W L , WS} and formula (7), the structural difference degree matrix SDIV between generators can be calculated.

Clustering is then performed using hierarchical clustering analysis. Hierarchical clustering method, also known as tree clustering algorithm, uses a layered architecture system and uses data association rules to repeatedly divide or merge sample data to form a bottom-up clustering tree solution. Assuming that S={s ₁ ,s ₂ ,...,s _m } respectively represent m generators in the system, the specific steps are as follows:

Step 1: Set each s _i as a class, forming m classes in total: s ₁ , s ₂ ,...,s _m .

The second step: from the existing m classes, find out the two classes s _r and s _k with the smallest trajectory structure difference degree SDIV.

Step 3: Combine classes s _r and s _k into a new class s _rk , and the number m of existing classes will be reduced by 1.

Step 4: Detect all samples, if all samples belong to the same class, then terminate the algorithm; otherwise, return to the second step.

After the clustering is over, select the appropriate threshold ε to divide the clustering results to obtain the final clustering results, as shown in Figure 3, the figure shows the situation of 8 generators, which are divided into two groups according to the given ε.

Claims (3)

1. A coherent grouping scheme for generator sets based on wide-area information. This method uses phasor measurement units to extract features from the power angle trajectory and rotor angular velocity of generator sets to obtain information that can reflect coherence. The extracted features include four Comparison of two indicators: direction comparison DirDiv (δ _i , δ _j ), rotation angle comparison AngleDiv (δ _i , δ _j ), position comparison LocDiv (δ _i , δ _j ) and rotor angular velocity, that is, speed comparison SpeedDiv (δ _i , δ j ) _j ), where δ _i , δ _j are power angle trajectories of different generator sets, 1≤i≠j≤m, m is the total number of trajectories, and δ _i is composed of δ _i1 , δ _i2 ,...,δ _in , The trajectory δ _j consists of δ _j1 , δ _j2 ,..., δ _jn , where n is the number of sampling points, where, (1) Direction comparison DirDiv(δ _i , δ _j ) represents the difference in deflection degree of power angle trajectories δ _i , δ _j in the overall change trend, δ _is , δ _js are the starting points of sampling of trajectories δ _i , δ _j respectively, δ _ie , δ _je are the termination points of the trajectory δ _i , δ _j sampling respectively, and the vector and angle of To represent the direction difference DirDiv(δ _i ,δ _j ) between trajectories; (2) Angle comparison AngleDiv(δ _i , δ _j ) reflects the directional change characteristics inside the trajectory. _Let the angle between the trajectory at the sampling point δ _p be denoted as β, and the rotational angle be denoted as θ. The distance between a sampling point δ _p-1 , and b is the distance between this sampling point and the next sampling point δ _p+1 , and c is the distance between sampling points δ _p-1 and δ _p+1 , and the included angle β is: β = arccos((a ² +b ² -c ² )/2ab) According to the right-hand rule of the angle β and vector cross product direction, the rotation angle θ is obtained, and the calculation formula of the rotation angle θ is: It can be obtained from the above formula that the outwardly changing rotation angle θ is a positive value, and the inwardly changing rotation angle θ is a negative value. The angle comparison AngleDiv(δ _i ,δ _j ) is an accumulative quantity that changes with the sampling time, and the calculation formula is: $\mathrm{<span\; class="notranslate">\; AngleDiv</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}$ In the case of an ideal coherent fleet, the angle difference of each sampling point of δ _i and δ _j is 0, and AngleDiv is also 0. In the case of the most mismatched power angle curve, the rotation angle of each sampling point is equal to In the opposite direction, that is to say, the two trajectories are oppositely sawtoothed during the sampling time, and AngleDiv is 1 at this time; (3) Position comparison LocDiv(δ _i ,δ _j ) reflects the relative distance between generator power angle trajectories, the calculation formula is as follows: LocDiv(δ _i ,δ _j )=H(δ _i ,δ _j )=max(h(δ _i ,δ _j ),h(δ _j ,δ _i )), Where dist(u, v) represents the Euclidean distance between two points u and v, u and v are any sampling points on the trajectory of δ _i and δ _j respectively; h(δ _i , δ _j ) is δ _i , The direct Hausdorff distance of δ _j is the maximum distance from each point in δ _i to the minimum distance set of all points in δ _j . If h(δ _i , δ _j )=d, then each sample in δ _i The distance from the point to the nearest sampling point in δ _j does not exceed d, and the distance difference between d response curves, H(δ _i ,δ _j ) is h(δ _i ,δ _j ) and h(δ _j ,δ _i ) The maximum value of , if H(δ _i , δ _j )=d, it shows the distance from each sampling point in δ _i to the nearest sampling point in δ _j and the distance from each sampling point in δ _j to the nearest sampling point in δ _i The distance between the points does not exceed d; (4) Speed comparison SpeedDiv(δ _i , δ _j ) represents the difference in angular velocity of the rotor of the generator set, as follows $\mathrm{<span\; class="notranslate">\; SpeedDiv</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\sqrt{\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$ The difference between the angular velocity changes of the rotors of the two generators is measured by the Euclidean distance between the angular velocity sampling values, and ω _i (t) and ω _j (t) represent the sampling values of the i and j generator sets at the sampling time t, respectively; The generator set coherent grouping scheme includes the following steps: Step 1: Calculate the above four indicators between two generators in the power system, and store the values in the four matrices of DirDiv, AngleDiv, LocDiv and SpeedDiv respectively. If there are m generators in the system, the matrix is A symmetrical square matrix of order m, the diagonal elements of each matrix are all zero; Step 2: Define W={W _D , W _A , W _L , W _S } as the feature weight, corresponding to the above four features respectively; each weight satisfies: (1) all weight values are greater than or equal to zero; (2) W _D +W _A +W _L +W _S ＝1, since the value range of each feature is different, it is necessary to normalize the difference value of each feature. The normalization process is to divide the obtained four matrices Divide each element by the maximum value of the elements in each matrix; then use the idea of variation coefficient method to calculate the weight, and use the obtained weight to weight and sum the above four indicators to form the trajectory structure difference: SDIV＝W _D ×DirDiv+W _A ×AngleDiv+W _L ×LocDiv+W _S ×SpeedDiv The third step: Calculate the difference degree matrix SDIV of the generator set, and then use the hierarchical clustering analysis method to cluster; Step 4: After the clustering is over, select an appropriate threshold ε to divide the clustering tree solution to obtain the final clustering result; 2. the generator set coherent grouping scheme based on wide-area information according to claim 1, is characterized in that, utilizes the step of the thinking calculation weight of coefficient of variation method to be: 1) Obtain all the elements above the main diagonal of the DirDiv, AngleDiv, LocDiv and SpeedDiv matrices respectively, and store them in the 4 columns of the matrix X in turn, then the 4 columns in the matrix store the distance between the generators under 4 different indicators Difference value vector; If there are m generator sets, then the row number p=m(m-1)/2 of matrix X, column number q=4; 2) Calculate the mean value and standard deviation of each feature index, that is, find the mean value and standard deviation of each column vector of X; 3) Calculate the coefficient of variation of each index; 4) Normalize the coefficient of variation of each index to obtain the weight of each index; 3. The coherent grouping scheme of generating sets based on wide-area information according to claim 1, wherein S={s ₁ , s ₂ ,...,s _m } respectively represent m generating sets in the system , the specific steps of clustering with hierarchical clustering analysis are as follows: 1) Set each s _i as a class, forming m classes in total: s ₁ , s ₂ ,..., s _m ; 2) From the existing m classes, find out the two classes s _r and s _k with the smallest trajectory structure difference degree SDIV; 3) Merge classes s _r and s _k into a new class s _rk , and the number m of existing classes will be reduced by 1; 4) Detect all samples, if all samples belong to the same class, then terminate the algorithm; otherwise, return to 2).