CN110943473A - Generator coherence identification method based on wide area measurement system and clustering theory - Google Patents
Generator coherence identification method based on wide area measurement system and clustering theory Download PDFInfo
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Abstract
The invention relates to a generator coherent identification method based on a wide area measurement system and a clustering theory, which comprises the following steps: 8 track similarity indexes representing the generator coherence are provided; determining the weight of each index by an entropy weight analysis method to obtain a comprehensive similarity index; and clustering coherent generators by using the comprehensive similarity index and a coacervation hierarchical clustering method. The method can provide corresponding decision basis for the transient stability judgment and the splitting control strategy of the power system.
Description
Technical Field
The invention relates to the field of power systems, in particular to a generator coherent identification method based on a wide area measurement system and a clustering theory.
Background
The transient stability process after the power system fails is a dynamic process, so that the dynamic characteristics of each generator set can be used as the basis for subsequent decision making. The study of the scholars shows that the power system subjected to disturbance has a coherent phenomenon, namely the tracks of certain generator sets have similarity, and the generator sets can be divided into a group of coherent clusters, so that the dynamic analysis process of the power system is simplified, and important theoretical support is provided for model parameter correction, splitting control and the like of the power system.
The traditional coherent identification methods are various, including a coherent cluster identification method based on electrical distance, an identification method based on rotor angular acceleration, an identification method based on state space, an identification method based on singular perturbation principle, an identification method based on artificial neural network and an identification method based on wavelet transformation. However, the above methods only consider one kind of information in the power angle curve after disturbance, and the indexes on which the algorithm is based are single, and the actual state in the power system cannot be correctly reflected in some cases.
The measured data acquired by the wide area measurement system after the power system is disturbed contains all explicit and implicit information in the actual system. The generator set coherent identification can be better realized by comprehensively utilizing a plurality of types of data in the actual measurement track and reasonably determining the weight among all indexes, but the research is still less in China.
Disclosure of Invention
Based on the above, in order to obtain a better coherent generator clustering effect in an electric power system, the invention provides a generator coherent identification method based on a wide area measurement system and a clustering theory.
A generator coherence identification method based on a wide area measurement system and a clustering theory comprises the following steps:
1) 8 track similarity indexes representing the generator coherence are provided;
2) determining the weight of each index by an entropy weight analysis method to obtain a comprehensive similarity index;
3) clustering coherent generators by using the comprehensive similarity index and the agglomerative hierarchical clustering method in the step 2).
In the above technical solution, 8 trajectory similarity indexes characterizing generator coherence are provided in step 1), specifically as follows:
suppose that in a power system with a total of M generators, a sampling trajectory obtained by vector measurement units (PMUs) is T ═ T { (T)r1,Tr2,Tr3,...,Trm,...,TrM}(1≤m≤M)，TrmRepresenting the power angle or rotating speed track of the mth generator, and setting Trm＝{Pm,1,Pm,2,Pm,3,...,Pm,n,...,Pm,NN is more than or equal to 1 and less than or equal to N), wherein Pm,nIs the data of the nth sampling point of the mth generator measured by the PMUs, and N is the sampling number. Will Pm,nIs represented by (t)n,δm,n) And (t)n,ωm,n)，tnIs the time of the nth sample, δm,nAnd ωm,nRespectively are the power angle and the rotating speed data of the nth sampling of the mth generator measured by the PMUs, and the following indexes are extracted aiming at the M generators: .
a) Power angle offset similarity
In an actual power system, the power angle deviation between two generators and the similarity between the two generators are greatly related, so that the power angle deviation similarity can be used as an index for representing the generator coherence. The power angle deviation similarity is defined as the root mean square of the sum of the distances of each point between two power angle curves, and the mathematical expression is as follows:
in the formula, deltai,nAnd deltaj,nThe sampled data of the ith and jth generators at the nth sampling time are deltai,1And deltaj,1The sampled data of the ith and jth generators at the beginning, I1And (i, j) can well reflect the offset degree of the ith power angle curve and the jth power angle curve.
b) Similarity of power angle swing
The power angle swing similarity is used for reflecting the overall offset direction of a power angle curve, and describes the size of an offset direction included angle between two curves, and the mathematical expression of the power angle swing similarity is as follows:
in the formula (I), the compound is shown in the specification,
and
the starting point in the ith power angle curve and the jth power angle curve is (t)1,δi,1) And (t)1,δj,1) End point is (t)N,δi,N) And (t)N,δj,N) The vector of (2).
c) Rotational speed offset similarity
When the power system is in failure, besides the fluctuation of the power angle curve, the rotation speed curve of the generator also fluctuates greatly, so that the rotation speed change of the generator is used as an index to beneficially help the homodyne identification. The deviation degree of the generator speed curve is reflected by the speed deviation similarity, and the mathematical expression of the deviation degree is as follows:
in the formula, ωi,nAnd ωj,nThe sampled data of the ith and jth generators at the nth sampling time, omegai,1And ωj,1The data are sampled at the beginning of the ith and jth generators respectively.
d) Power angle direction shift similarity
After a fault occurs, the direction of the power angle curve changes all the time, and the power angle swing similarity only describes the total offset direction included angle of the power angle curve, so the power angle direction offset similarity is defined as an index reflecting the direction of curve offset on each sampling point, and the mathematical expression is as follows:
in the formula (I), the compound is shown in the specification,
and
respectively, the starting point in the ith power angle curve is (t)n-1,δi,n-1) And (t)n,δi,n) End point is (t)n,δi,n) And (t)n+1,δi,n+1) The vector of (2). According to the mathematical definition of the angle between the vectors, if deltai,n+1-δi,n-1≥δi,n-δi,n-1Then, then
And
angle theta therebetweeni,nIs a positive number if deltai,n+1-δi,n-1≤δi,n-δi,n-1Then, then
And
angle theta therebetweeni,nThe value of (d) is negative.
e) Distance similarity of power angle Chebyshev
After a power system is disturbed, the power angle dynamic tracks of a part of units in the system are similar, the invention provides power angle Chebyshev distance similarity, and the mathematical definition expression of the similarity is as follows:
f) rotational speed Chebyshev distance similarity
Converting the power angle of the generator in the index of e) into the rotating speed of the rotor of the generator to obtain the similarity of the rotating speed Chebyshev distance, wherein the mathematical definition expression of the similarity is as follows:
g) similarity of power angle correlation coefficient
Coherence between the generator sets can be evaluated through a correlation coefficient between the generator sets, because the correlation coefficient represents the strength of linear correlation between the generator sets. In statistics, the pearson correlation coefficient is used to characterize the linear correlation strength between two scalars, and the coefficient ρ is equal to the covariance between two statistical objects divided by their standard deviation, so as to define the similarity of the power angle correlation coefficient between the generator groups, and its mathematical expression is:
h) similarity of coefficient of correlation of rotational speed
Similar to g), the similarity of the rotation speed correlation coefficients among the generator groups can be defined, and the mathematical expression of the similarity is as follows:
in the step 2), the weight of each index is determined through an entropy weight analysis method to obtain a comprehensive similarity index, and the method comprises the following steps:
in order to obtain the weight of the similarity index matrix by using an entropy weight method, U is set as an index number, U is 8, Q is the number of schemes to be decided, any two generator pairs form a decision scheme, and Q is M (M-1)/2. After the 8 similarity indexes are normalized, the problem of solving the weight can be described as the following form:
D＝(duq)U×Q
in the formula (d)uqFor the u th normalizationThe q-th element of the upper triangle in the post-similarity index matrix; u-1, 2, …, U; q is 1,2, …, Q.
Thus, the information entropy H of the u-th normalized similarity index matrixuIs defined as
In the formula (I), the compound is shown in the specification,
k is 1/lnQ; if f isuqWhen f is equal to 0, let fuqlnfuq＝0。
Finally, the weights of the normalized similarity index matrices can be obtained:
and weighting the 8 similarity index matrixes according to the weight to obtain a comprehensive similarity index matrix.
Clustering coherent generators by using the comprehensive similarity index and the agglomeration hierarchical clustering method in the step 3), which specifically comprises the following steps:
agglomerative Hierarchical Clustering (AHC) is a bottom-up strategy that first treats each object as a class, and then merges the classes into larger and larger classes step by step until the end of merging into a given number of classes. The method comprises the following steps:
a) dividing M generators into M groups, wherein only one generator is arranged in each group, and taking the comprehensive similarity index as the distance between each generator pair;
b) combining the groups of the two generators with the nearest distance into a new group;
c) judging whether the current generator group number reaches a given group number, if so, terminating iteration and outputting a generator coherent grouping result; otherwise, entering step d);
d) and c), setting the distance between the newly merged cluster and the original cluster as the shortest distance between the generators respectively contained in the two clusters, and returning to the step b).
The invention has the beneficial effects that:
according to the method, 8 similarity indexes are extracted, the weight of each index is determined based on an entropy weight analysis method, comprehensive similarity indexes are obtained, coherent generator clustering is carried out by combining a coacervation hierarchical clustering method, and corresponding decision basis can be provided for transient stability judgment and a splitting control strategy of a power system.
Drawings
FIG. 1 is a flow chart of an embodiment of a generator coherence identification method based on a wide area measurement system and a clustering theory;
FIG. 2 is a schematic diagram of a 16 machine 68 node of an embodiment;
FIG. 3 is a power angle trajectory diagram of the generator after a system failure of the 16-machine 68 node according to an embodiment;
FIG. 4 is a generator rotor speed trajectory graph after an embodiment of a 16 machine 68 node system failure.
Detailed Description
For better understanding of the objects, technical solutions and effects of the present invention, the present invention will be further explained with reference to the accompanying drawings.
Referring to fig. 1, fig. 1 shows a generator coherence identification method based on a wide area measurement system and a clustering theory according to an embodiment, which includes the following steps:
s10, providing 8 track similarity indexes representing the generator coherence; in one embodiment:
suppose that in a power system with a total of M generators, a sampling trajectory obtained by vector measurement units (PMUs) is T ═ T { (T)r1,Tr2,Tr3,...,Trm,...,TrM}(1≤m≤M)，TrmRepresenting the power angle or rotating speed track of the mth generator, and setting Trm＝{Pm,1,Pm,2,Pm,3,...,Pm,n,...,Pm,NN is more than or equal to 1 and less than or equal to N), wherein Pm,nIs the data of the nth sampling point of the mth generator measured by the PMUs, and N is the sampling number. Will be provided withPm,nIs represented by (t)n,δm,n) And (t)n,ωm,n)，tnIs the time of the nth sample, δm,nAnd ωm,nRespectively are the power angle and the rotating speed data of the nth sampling of the mth generator measured by the PMUs, and the following indexes are extracted aiming at the M generators: .
a) Power angle offset similarity
In an actual power system, the power angle deviation between two generators and the similarity between the two generators are greatly related, so that the power angle deviation similarity can be used as an index for representing the generator coherence. The power angle deviation similarity is defined as the root mean square of the sum of the distances of each point between two power angle curves, and the mathematical expression is as follows:
in the formula, deltai,nAnd deltaj,nThe sampled data of the ith and jth generators at the nth sampling time are deltai,1And deltaj,1The sampled data of the ith and jth generators at the beginning, I1And (i, j) can well reflect the offset degree of the ith power angle curve and the jth power angle curve.
b) Similarity of power angle swing
The power angle swing similarity is used for reflecting the overall offset direction of a power angle curve, and describes the size of an offset direction included angle between two curves, and the mathematical expression of the power angle swing similarity is as follows:
in the formula (I), the compound is shown in the specification,
and
the starting point in the ith power angle curve and the jth power angle curve is (t)1,δi,1) And (t)1,δj,1) End point is (t)N,δi,N) And (t)N,δj,N) The vector of (2).
c) Rotational speed offset similarity
When the power system is in failure, besides the fluctuation of the power angle curve, the rotation speed curve of the generator also fluctuates greatly, so that the rotation speed change of the generator is used as an index to beneficially help the homodyne identification. The deviation degree of the generator speed curve is reflected by the speed deviation similarity, and the mathematical expression of the deviation degree is as follows:
in the formula, ωi,nAnd ωj,nThe sampled data of the ith and jth generators at the nth sampling time, omegai,1And ωj,1The data are sampled at the beginning of the ith and jth generators respectively.
d) Power angle direction shift similarity
After a fault occurs, the direction of the power angle curve changes all the time, and the power angle swing similarity only describes the total offset direction included angle of the power angle curve, so the power angle direction offset similarity is defined as an index reflecting the direction of curve offset on each sampling point, and the mathematical expression is as follows:
in the formula (I), the compound is shown in the specification,
and
respectively, the starting point in the ith power angle curve is (t)n-1,δi,n-1) And (t)n,δi,n) End point is (t)n,δi,n) And (t)n+1,δi,n+1) The vector of (2). According to the mathematical definition of the angle between the vectors, if deltai,n+1-δi,n-1≥δi,n-δi,n-1Then, then
And
angle theta therebetweeni,nIs a positive number if deltai,n+1-δi,n-1≤δi,n-δi,n-1Then, then
And
angle theta therebetweeni,nThe value of (d) is negative.
e) Distance similarity of power angle Chebyshev
After a power system is disturbed, the power angle dynamic tracks of a part of units in the system are similar, the invention provides power angle Chebyshev distance similarity, and the mathematical definition expression of the similarity is as follows:
f) rotational speed Chebyshev distance similarity
Converting the power angle of the generator in the index of e) into the rotating speed of the rotor of the generator to obtain the similarity of the rotating speed Chebyshev distance, wherein the mathematical definition expression of the similarity is as follows:
g) similarity of power angle correlation coefficient
Coherence between the generator sets can be evaluated through a correlation coefficient between the generator sets, because the correlation coefficient represents the strength of linear correlation between the generator sets. In statistics, the pearson correlation coefficient is used to characterize the linear correlation strength between two scalars, and the coefficient ρ is equal to the covariance between two statistical objects divided by their standard deviation, so as to define the similarity of the power angle correlation coefficient between the generator groups, and its mathematical expression is:
h) similarity of coefficient of correlation of rotational speed
Similar to g), the similarity of the rotation speed correlation coefficients among the generator groups can be defined, and the mathematical expression of the similarity is as follows:
s20, determining the weight of each index through an entropy weight analysis method to obtain a comprehensive similarity index; in one embodiment:
in order to obtain the weight of the similarity index matrix by using an entropy weight method, U is set as an index number, U is 8, Q is the number of schemes to be decided, any two generator pairs form a decision scheme, and Q is M (M-1)/2. After the 8 similarity indexes are normalized, the problem of solving the weight can be described as the following form:
D＝(duq)U×Q
in the formula (d)uqThe q element of the upper triangle in the u normalized similarity index matrix; u-1, 2, …, U; q is 1,2, …, Q.
Thus, the information entropy H of the u-th normalized similarity index matrixuIs defined as
In the formula (I), the compound is shown in the specification,
k is 1/lnQ; if f isuqWhen f is equal to 0, let fuqlnfuq＝0。
Finally, the weights of the normalized similarity index matrices can be obtained:
s30, performing coherent generator clustering analysis by using the comprehensive similarity index and a coacervation hierarchical clustering method; in one embodiment:
agglomerative Hierarchical Clustering (AHC) is a bottom-up strategy that first treats each object as a class, and then merges the classes into larger and larger classes step by step until the end of merging into a given number of classes. The method comprises the following steps:
a) dividing M generators into M groups, wherein only one generator is arranged in each group, and taking the comprehensive similarity index as the distance between each generator pair;
b) combining two generators with the nearest distance into a new cluster;
c) judging whether the current generator group number reaches a given group number, if so, terminating iteration and outputting a generator coherent grouping result; otherwise, go to step d)
d) Setting the distance between the newly merged cluster and the original cluster as the shortest distance between the generators in the two clusters, and returning to the step b)
In order to explain the effect of the present invention, a 16-machine 68-node system will be explained below. The 16-machine 68 node system is a simplified network of interconnected New England System (NETS) and New York Power System (NYPS), a single line diagram of which can be seen in FIG. 2
Assuming that a transient three-phase ground short circuit fault occurs at the node 16, and the fault disappears after 0.16s, a power angle curve of the generator and a rotating speed curve of the rotor of the generator are drawn by a time domain analysis method as shown in fig. 3 and 4, and data collected by a wide area measurement system is simulated for subsequent analysis.
It can be found from the figure that the coherent unit is difficult to identify through subjective judgment of people, and after the entropy weight method is applied to coherent identification, the information entropy and the entropy weight of 8 similarity index matrixes of the generator track can be obtained, and specific numerical values are shown in table 1. As can be seen from the table, the smaller the information entropy, the larger the entropy weight, that is, the more useful information contained in the index is, the larger the weight should be in the subsequent clustering analysis, and the important consideration is needed. Given a cluster number of 2, 16 generators can be divided into 2 coherent clusters, with group 1 being { G1, G2, G3, G4, G5, G6, G7, G8, G9, G10, G11, G12, G13} and group 2 being { G14, G15, G16 }.
TABLE 1 entropy and entropy weight table after 68 node system failure of NETS-NYPS 16 machine
Claims (4)
1. A generator coherence identification method based on a wide area measurement system and a clustering theory is characterized by comprising the following steps:
1) 8 track similarity indexes representing the generator coherence are provided;
2) determining the weight of each index by an entropy weight analysis method to obtain a comprehensive similarity index;
3) clustering coherent generators by using the comprehensive similarity index and the agglomerative hierarchical clustering method in the step 2).
2. The wide area measurement system and clustering theory-based generator coherence identification method according to claim 1, wherein 8 track similarity indexes representing generator coherence are provided, specifically as follows:
suppose that in a power system with a total of M generators, a sampling trajectory obtained by vector measurement units (PMUs) is T ═ T { (T)r1,Tr2,Tr3,...,Trm,...,TrM}(1≤m≤M)，TrmRepresenting the power angle or rotating speed track of the mth generator, and setting Trm＝{Pm,1,Pm,2,Pm,3,...,Pm,n,...,Pm,N}(N is not less than 1 and not more than N), wherein Pm,nIs the data of the nth sampling point of the mth generator measured by the PMUs, N is the sampling number, and P ism,nIs represented by (t)n,δm,n) And (t)n,ωm,n)，tnIs the time of the nth sample, δm,nAnd ωm,nRespectively are the power angle and the rotating speed data of the nth sampling of the mth generator measured by the PMUs, and the following indexes are extracted aiming at the M generators:
a) power angle offset similarity
The power angle deviation similarity is defined as the root mean square of the sum of the distances of each point between two power angle curves, and the mathematical expression is as follows:
in the formula, deltai,nAnd deltaj,nThe sampled data of the ith and jth generators at the nth sampling time are deltai,1And deltaj,1Respectively sampling data of the ith generator and the jth generator at the beginning;
b) similarity of power angle swing
The power angle swing similarity is used for reflecting the overall offset direction of a power angle curve, and describes the size of an offset direction included angle between two curves, and the mathematical expression of the power angle swing similarity is as follows:
in the formula (I), the compound is shown in the specification,
and
the starting point in the ith power angle curve and the jth power angle curve is (t)1,δi,1) And (t)1,δj,1) End point is (t)N,δi,N) And (t)N,δj,N) The vector of (a);
c) rotational speed offset similarity
Reflecting the deviation degree of the generator speed curve by using the speed deviation similarity, wherein the mathematical expression is as follows:
in the formula, ωi,nAnd ωj,nThe sampled data of the ith and jth generators at the nth sampling time, omegai,1And ωj,1Respectively sampling data of the ith generator and the jth generator at the beginning;
d) power angle direction shift similarity
The power angle direction deviation similarity is used as an index for reflecting the direction of curve deviation on each sampling point, and the mathematical expression is as follows:
in the formula (I), the compound is shown in the specification,
and
respectively, the starting point in the ith power angle curve is (t)n-1,δi,n-1) And (t)n,δi,n) End point is (t)n,δi,n) And (t)n+1,δi,n+1) According to the mathematical definition of the angle between the vectors, if deltai,n+1-δi,n-1≥δi,n-δi,n-1Then, then
And
angle theta therebetweeni,nIs a positive number if deltai,n+1-δi,n-1≤δi,n-δi,n-1Then, then
And
angle theta therebetweeni,nIs negative;
e) distance similarity of power angle Chebyshev
The similarity of the power angle Chebyshev distance is mathematically defined as follows:
f) rotational speed Chebyshev distance similarity
Converting the power angle of the generator in the index of e) into the rotating speed of the rotor of the generator to obtain the similarity of the rotating speed Chebyshev distance, wherein the mathematical definition expression of the similarity is as follows:
g) similarity of power angle correlation coefficient
The method comprises the following steps of defining power angle correlation coefficient similarity among generator groups, wherein the mathematical expression of the similarity is as follows:
h) similarity of coefficient of correlation of rotational speed
Similar to the step g), the similarity of the rotation speed correlation coefficients among the generator groups is defined, and the mathematical expression of the similarity is as follows:
3. the wide area measurement system and clustering theory-based generator coherence identification method according to claim 1, wherein the weights of the indexes are determined by an entropy weight analysis method to obtain a comprehensive similarity index, which is as follows:
in order to obtain the weight of the similarity index matrix by using an entropy weight method, U is taken as an index number, 8 is taken, Q is a number of schemes to be decided, any two generator pairs form a decision scheme, Q is M (M-1)/2, and after the similarity index is subjected to standardization processing, the problem of obtaining the weight is described as the following form:
D＝(duq)U×Q
in the formula (d)uqThe q element of the upper triangle in the u normalized similarity index matrix; u-1, 2, …, U; q ═ 1,2, …, Q;
information entropy H of the u-th normalized similarity index matrixuIs defined as
In the formula (I), the compound is shown in the specification,
k is 1/lnQ; if f isuqWhen f is equal to 0, let fuqlnfuq＝0；
Finally, the weights of the normalized similarity index matrices can be obtained:
and weighting the 8 similarity index matrixes according to the weight to obtain a comprehensive similarity index matrix.
4. The wide-area measurement system and clustering theory-based generator coherent identification method according to claim 1, wherein coherent generator clustering is performed by using a comprehensive similarity index and a cohesive hierarchical clustering method, and specifically, the following steps are performed:
a) dividing M generators into M groups, wherein only one generator is arranged in each group, and taking the obtained comprehensive similarity index as the distance between each generator pair;
b) combining the groups of the two generators with the nearest distance into a new group;
c) judging whether the current generator group number reaches a given group number, if so, terminating iteration and outputting a generator coherent grouping result; otherwise, entering step d);
d) and c), setting the distance between the newly merged cluster and the original cluster as the shortest distance between the generators respectively contained in the two clusters, and returning to the step b).
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Application publication date: 20200331 |