CN111695580B - Characteristic pattern matching method and system during continuous change of state matrix parameters - Google Patents
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Abstract
The invention discloses a characteristic pattern matching method when state matrix parameters continuously change, which comprises the following steps: acquiring a state matrix sequence to be matched and respectively calculating characteristic roots of each state matrix; calculating standard characteristic root vector lambda one by oneSWith the current section feature root vector lambdakA step-by-step matrix D; according to lambdaSElement classification at λkMedium iterative search and lambdaSEach element has a continuous characteristic root, and lambda is adjusted according to the resultkSorting the medium characteristic roots; according to λSAnd λkDegree of difference ε ofkJudging the matching completion of the section or the overlarge marking error by combining the iteration times, and outputting the section matching result lambdak' and proceeds with the matching of the next cross-sectional feature root. The method realizes the automatic matching of the corresponding characteristic patterns when the state matrix continuously changes based on the continuous characteristic of the characteristic root to the matrix parameter change, and greatly improves the efficiency and the accuracy of the characteristic pattern matching in the oscillation analysis process of the power system compared with the prior method.
Description
Technical Field
The invention relates to a characteristic pattern matching method and a characteristic pattern matching system when state matrix parameters continuously change, and belongs to the technical field of power systems.
Background
When the oscillation characteristics of the power system are analyzed, the track section characteristic root method is linearized along a disturbed track in a segmented mode, and the instantaneous characteristics of the oscillation of the original system are extracted from a series of linear time-varying differential equations; in the analysis process, corresponding characteristic roots need to be solved for continuous change of the state matrix within a period of time. However, in actual solution, the problem that the ordering and correlation of the feature roots are not matched occurs in adjacent sections, which is specifically shown that the trajectory of the feature roots corresponding to the state matrix continuously changing along with time loses continuity, which brings great inconvenience to identification of the critical time section and the dangerous feature pattern, and causes difficulty in further analysis of the instantaneous oscillation characteristic of the power system.
On the other hand, in order to study the sensitivity of the parameters to the dangerous feature mode damping in the conventional origin feature root method, the element values of the state matrix need to be continuously changed and the variation of the corresponding origin feature root needs to be analyzed. The conventional method does not track the evolution of the characteristic root ordering along with the state matrix parameters, so that the traditional method has the same problem as the characteristic root of the track section when calculating the sensitivity of the original point characteristic root parameters, and the specific expression is that the state matrix continuously changing along with the parameters loses continuity corresponding to the characteristic root track.
This phenomenon is called "drunkenness" in some studies on flutter in the field of aeroelastic stability, and is generally used for matching a characteristic pattern of a continuously changing state matrix in a manual adjustment mode according to analysis experience so as to obtain a continuous characteristic root track for subsequent analysis. During the analysis of an actual power system, the trace section features often and thousands of sections bring huge workload for manually matching the feature patterns, the existing method cannot meet the requirements of high efficiency and accuracy during engineering application, and the partial research in the technical field of the power system is still blank at present.
Disclosure of Invention
The invention aims to solve the difficulty brought by matching the characteristic mode of a continuously changed state matrix by using a manual adjustment mode during data analysis in engineering, provides a characteristic mode matching method and a system during continuous change of state matrix parameters, and can accurately realize automatic matching of the corresponding characteristic mode during continuous change of the state matrix parameters in the oscillation analysis process of a power system.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method of feature pattern matching when state matrix parameters are continuously varied, the method comprising the steps of:
acquiring a state matrix sequence to be matched and respectively calculating characteristic root vectors of each state matrix to be used as the characteristic root vectors to be matched of each section;
matching the standard characteristic root vector of the current section with the characteristic root vector to be matched of the current section one by one from a second section, wherein the standard characteristic root vector of the second section is the characteristic root of the first section state matrix; taking the matching result of the current section as the standard characteristic root vector of the next section; and repeating the steps until the state matrix sequences to be matched of all the sections are completely matched.
Further, the method for matching the standard characteristic root vector of the current section with the characteristic root vector to be matched is as follows:
1) calculating the standard characteristic root vector lambda of the current sectionSCharacteristic root vector lambda to be matched with current sectionkA step-by-step matrix D; preferably, the calculation method of the difference-by-difference matrix D includes:
let dijIs the element of the ith row and the jth column of the n × n step difference matrix D, Dij＝(λS.i-λk.j)2，λS,iAs a standard feature root vector lambda of the current sectionSThe ith element of (a)k,jFor the root vector lambda of the feature to be matched of the current sectionkWherein i is 1 ton, j is a natural number between 1 and n.
2) λ is the absolute value of the real and imaginary partsSClassification of elements; preferably, the classification method is to classify the feature root whose imaginary absolute value is greater than omicron as a complex root; classifying the characteristic root of which the absolute value of the real part and the absolute value of the imaginary part are less than omicron as a zero root; classifying the characteristic root with the absolute value of the imaginary part less than omicron and the real part less than-into a negative root; and classifying the characteristic root with the absolute value of the imaginary part smaller than the real part larger than the real part into a real root, wherein the real root is a preset minimum value.
3) According to the classification result at lambdakMedium iterative search and lambdaSThe elements have continuous characteristic roots and adjust lambdakThe matching result lambda of the current section is obtained by sequencing the medium characteristic rootsk'。
Further, the method of step 3) is as follows, in the first step, making l equal to 1;
second step, if λS.lZero or negative root, lambdaS.lRepresents lambdaSThe first element of the difference matrix D is selected, the first row in the difference matrix D is selected, the serial number of the row corresponding to the minimum value of the row is calculated to be m, the first row and the mth row are exchanged in the difference matrix D, and the characteristic root vector lambda to be matched of the current section is exchanged at the same timekMiddle lambdak.lAnd λk.mPosition of (A), λk.lRepresents lambdakThe first element of (a) < lambda >k.mRepresents lambdakThe mth element of (1); let l equal l +1, if l<n, re-executing the second step, otherwise, continuing the third step;
thirdly, the iteration times N are calculatedkSetting the value as 1;
fourthly, making p equal to 1;
fifth step, λS.pIs a true root or a plurality of roots, lambdaS.pRepresenting a row vector lambdaSThe p-th element of the difference-by-difference matrix D is selected, the serial number of the row corresponding to the minimum value of the row is calculated to be q, if lambda isk.pIs a real root and λk.qIs a plurality of roots, whereink.pRepresenting a row vector lambdakP-th element of (a)k.qRepresenting a row vector lambdakThe qth element of (a), the p-th column and the qth column are swapped in the difference-by-difference matrix D, and simultaneously the vector λ is swappedkMiddle lambdak.pAnd λk.qOtherwise, performing the following steps;
if λS.pFor real root, exchanging the p-th column and q-th column in the difference-by-difference matrix D, and simultaneously exchanging the exchange vector lambdakMiddle lambdak.pAnd λk.qThe position of (a); if λS.pCalculating relative error before and after switching for the plural roots
Wherein c issetIs a preset constant;
xi is af>ξbExchanging the p-th column and the q-th column in the difference-by-difference matrix D and simultaneously exchanging the vector lambdakMiddle lambdak.pAnd λk.qIn the position of (a) in the first,
xi is af≤ξbThen the vector λ is not adjustedkThe ordering of the middle elements; let p be p +1, if p<n, re-executing the fifth step, otherwise, continuing the sixth step;
sixthly, recording the matching result as lambda after finishing single iterationk', calculating the vector lambdaSAnd the matching result vector lambdakDegree of difference of `
If epsilonk≥εsetAnd N isk<NsetIn which epsilonsetIs a predetermined error threshold, NsetExecuting N at the preset upper limit of the iteration timesk＝Nk+1 and repeating the second to sixth steps; otherwise, outputting the section matching result lambdak'。
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Fig. 1 is a characteristic pattern matching method when the state matrix parameters continuously change according to an embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
And step S1, acquiring the state matrix sequence to be matched and respectively calculating the characteristic root vector lambda of each state matrix as the vector to be matched of each section.
Assuming a total of N sections, each section can compute a feature root vector. In a specific embodiment, the method for acquiring the state matrix sequence to be matched for each section includes: for the track section characteristic root method, when the oscillation instantaneous characteristics of the power system are extracted, the disturbed tracks of the power system are subjected to time section-by-time section piecewise linearization to obtain a state matrix sequence; for the origin feature root method, when the relation between the parameters and the feature root is researched, a state matrix sequence is generated according to the parameter change. The two methods obtain an arbitrary section state matrix which is an n-order square matrix, and calculate the characteristic root vector of the matrix to be a 1 Xn row vector which is marked as lambdak＝[λk.1,λk.2,…,λk.n]。
Step S2, starting from a second section, matching the standard characteristic root vector of the current section with the characteristic root vector to be matched one by one, wherein the standard characteristic root vector of the second section is the characteristic root of the first section state matrix; taking the matching result of the current section as a standard characteristic root vector of the next section; repeating the step until the state matrix sequences to be matched of all the sections are completely matched, namely N sections are matched in total, the 1 st section lambda is not matched and is directly used as a standard vector to match the 2 nd section lambda, then the 2 nd section matching result is used as the standard vector to match the 3 rd section lambda, and the like until the last section matching is finished.
In this embodiment, the method for matching the standard feature root vector of the current section with the feature root vector to be matched of the current section is as follows:
calculating standard characteristic root vector lambda one by oneSCharacteristic root vector lambda to be matched with current sectionkThe difference-by-difference matrix D.
The 1 st section is not matched, and the section is divided into1(1 st sectional momentCharacteristic root of array, 1 xn row vector) as standard characteristic root vector lambda of 2 nd sectionSFor any section k after the second section, the last section is matched with the result lambdak-1' (feature root vector after matching of k-1 th section, 1 Xn row vector) is set as standard feature root phasor lambda of current sectionS；
Let dijIs the element of the ith row and the jth column of the difference matrix D (n-order square matrix), Dij＝(λS.i-λk.j)2Where i is a natural number between 1 and n, j is a natural number between 1 and n, λS,iAs a standard feature root vector lambdaSThe ith element of (a)k,jFor the root vector lambda of the features to be matchedkThe jth element of (1).
Step S3, according to lambdaSClassification of elements at λkMedium iterative search and lambdaSEach element has a continuous characteristic root, and lambda is adjusted according to the resultkAnd (4) sorting the middle characteristic root.
For an artificially given minimum value omicron, classifying a characteristic root with an absolute value of the imaginary part greater than omicron as a complex root; classifying the characteristic root of which the absolute value of the real part and the absolute value of the imaginary part are less than omicron as a zero root; classifying the characteristic root with the absolute value of the imaginary part less than omicron and the real part less than-into a negative root; and classifying the characteristic root with the absolute value of the imaginary part smaller than the real part larger than the real part into a real root.
At λkMedium iterative search and lambdaSEach element has a continuous characteristic root and lambda is adjusted according to the resultkAnd (5) sorting the medium characteristic roots. In this embodiment, the method comprises the following steps:
step one, making l equal to 1;
second step, if λS.lIs zero root or negative root (lambda)S.lRepresents lambdaSThe ith element) of the difference matrix D, the ith row in the difference matrix D is selected, the serial number of the row corresponding to the minimum value of the row is calculated to be m, the ith column and the mth column in the difference matrix D are exchanged, and the row vector lambda is exchanged simultaneouslykMiddle lambdak.lAnd λk.mPosition (λ) ofk.lRepresenting a row vector lambdakThe first element of (1), let l be l +1, if l<n, re-executing the second step, otherwise, continuing the third step;
thirdly, the iteration number N is calculatedkSetting as 1;
fourthly, making p equal to 1;
fifth step, λS.pIs a true root or a plurality of roots (lambda)S.pRepresenting a row vector lambdaSP-th element of) in the difference-by-difference matrix D, and calculating the sequence number of the row corresponding to the minimum value of the row as q, if λk.pIs a real root and λk.qIs a plurality of roots (lambda)k.pRepresenting a row vector lambdakP-th element of (a)k.qRepresentative of a row vector λkQ-th element of) then the p-th and q-th columns are swapped in the difference-by-difference matrix D, and simultaneously the vector λ is swappedkMiddle lambdak.pAnd λk.qOtherwise, according to λS.pThe properties are further distinguished.
If λS.pFor real root, exchanging the p-th column and q-th column in the difference-by-difference matrix D, and simultaneously exchanging the vector lambdakMiddle lambdak.pAnd λk.qThe position of (a); if λS.pCalculating relative error before and after switching for the plural roots
Wherein c issetIs to prevent lambdaS.pOr λS.qAn excessively small value, which is generally set as a row vector lambda, introduces a numerical error and is artificially set as a constantSAverage of absolute values (complex number is modulus) of all elements
If xif>ξbExchanging the p-th column and the q-th column in the difference-by-difference matrix D and simultaneously exchanging the vector lambdakMiddle lambdak.pAnd λk.qPosition of (c), if xif≤ξbThen the row vector λ is not adjustedkThe ordering of the elements in (c). Let p be p +1, if p<And n, re-executing the fifth step, otherwise, continuing the sixth step.
Sixthly, after finishing single iteration, exchanging corresponding elementsIs noted as λk' and as a result of the matching, a row vector λ is calculatedSAnd the matching result row vector lambdakDegree of difference of `
If epsilonk≥εsetAnd N isk<Nset(εsetIs a predetermined error threshold, NsetA preset upper limit of the number of iterations), N is executedk＝Nk+1 and repeating the second to sixth steps; otherwise, the process continues to step S4.
Step S4, according to lambdaSAnd λkDegree of difference ε ofkJudging the matching completion of the section or the overlarge marking error by combining the iteration times, and outputting the section matching result lambdak'。
If epsilonk<εsetThe adjusted sorted row vector lambda is outputk'; if epsilonk≥εsetAnd N isk≥NsetThen the row vector lambda is outputk' and mark that the section matching error is too large to be corrected manually.
Step S5, converting the lambdak' as the standard feature root phasor of the next section, repeating the steps S2 to S4 until the state matrix sequences to be matched of all the sections are completely matched.
According to the method, based on the continuous characteristic of the matrix characteristic root to the matrix parameter change, the automatic matching of the adjacent section characteristic modes when the state matrix continuously changes is achieved, and compared with the existing method, the efficiency and the accuracy of characteristic root sequencing in the oscillation analysis process of the power system are greatly improved.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, it is possible to make various improvements and modifications without departing from the technical principle of the present invention, and those improvements and modifications should be considered as the protection scope of the present invention.
Claims (8)
1. A method for matching a feature pattern when parameters of a state matrix are continuously changed, the method comprising the steps of:
acquiring a state matrix sequence to be matched and respectively calculating characteristic root vectors of each state matrix to be used as the characteristic root vectors to be matched of each section;
matching the standard characteristic root vector of the current section with the characteristic root vector to be matched of the current section one by one from a second section, wherein the standard characteristic root vector of the second section is the characteristic root of the first section state matrix; taking the matching result of the current section as a standard characteristic root vector of the next section; repeating the step until all the state matrix sequences to be matched of all the sections are completely matched;
the method for matching the standard characteristic root vector of the current section with the characteristic root vector to be matched of the current section comprises the following steps:
calculating the standard characteristic root vector lambda of the current sectionSCharacteristic root vector lambda to be matched with current sectionkA step-by-step matrix D;
λ is the absolute value of the real and imaginary partsSClassification of elements;
according to the classification result at lambdakMedium iterative search and lambdaSThe elements have continuous characteristic roots and adjust lambdakThe matching result lambda of the current section is obtained by sequencing the medium characteristic rootsk'；
According to the classification result at lambdakMedium iterative search and lambdaSThe elements have continuous characteristic roots and adjust lambdakThe matching result lambda of the current section is obtained by sequencing the medium characteristic rootskThe specific method of' is as follows:
firstly, making l equal to 1;
second step, if λS.lZero or negative root, lambdaS.lRepresents lambdaSThe first element of the difference matrix D is selected, the first row in the difference matrix D is selected, the serial number of the row corresponding to the minimum value of the row is calculated to be m, the first row and the mth row are exchanged in the difference matrix D, and the characteristic root vector lambda to be matched of the current section is exchanged at the same timekMiddle lambdak.lAnd λk.mPosition of (A), λk.lRepresents lambdakThe first element of (b), λk.mRepresents lambdakThe mth element of (1); let l equal l +1, if l<n is thenRe-executing the second step, otherwise, continuing the third step;
thirdly, the iteration number N is calculatedkSetting as 1;
fourthly, making p equal to 1;
fifth step, λS.pIs a true root or a plurality of roots, λS.pRepresenting a row vector lambdaSThe p-th element of the difference-by-difference matrix D is selected, the serial number of the row corresponding to the minimum value of the row is calculated to be q, if lambda isk.pIs a real root and λk.qIs a plurality of roots, wherein λk.pRepresentative of a row vector λkP-th element of (a)k.qRepresenting a row vector lambdakThe qth element of (a), the p-th column and the qth column are swapped in the difference-by-difference matrix D, while the vector λ is swappedkMiddle lambdak.pAnd λk.qOtherwise, the following steps are executed;
if λS.pFor real root, exchanging the p and q columns in the difference matrix D and exchanging the vector lambdakMiddle lambdak.pAnd λk.qThe position of (a); if λS.pCalculating relative error before and after switching for the plural roots
Wherein c issetIs a preset constant;
xi is af>ξbThen, the p-th column and the q-th column are swapped in the difference-by-difference matrix D, and the row vector λ is swapped at the same timekMiddle lambdak.pAnd λk.qIn the position of (a) in the first,
xi is af≤ξbThen the vector λ is not adjustedkThe ordering of the middle elements; let p be p +1, if p<n, re-executing the fifth step, otherwise, continuing the sixth step;
sixthly, recording the matching result as lambda after finishing single iterationk', calculating the vector lambdaSAnd the matching result vector lambdakDegree of difference of `
If epsilonk≥εsetAnd N isk<NsetWherein epsilonsetIs a predetermined error threshold, NsetExecuting N at the preset upper limit of the iteration timesk＝Nk+1 and repeating the second to sixth steps; otherwise, outputting the section matching result lambdak'。
2. The method for matching the feature pattern when the state matrix parameters continuously change according to claim 1, wherein the method for obtaining the state matrix sequence to be matched comprises:
for the track section characteristic root method, when the oscillation instantaneous characteristics of the power system are extracted, the disturbed tracks of the power system are subjected to time section-by-time section piecewise linearization to obtain a state matrix sequence;
for the origin feature root method, when the relation between the parameters and the feature root is researched, a state matrix sequence is generated according to the parameter change.
3. The method for matching the signature pattern when the parameters of the state matrix change continuously according to claim 1, wherein the method for calculating the difference matrix D comprises:
let dijIs the element of the ith row and the jth column of the n × n step difference matrix D, Dij＝(λS.i-λk.j)2，λS,iAs a standard feature root vector lambda of the current sectionSThe ith element of (a)k,jFor the root vector lambda of the feature to be matched of the current sectionkWherein i is a natural number between 1 and n, and j is a natural number between 1 and n.
4. The method for matching a characteristic pattern when parameters of a state matrix are continuously changed as claimed in claim 1, wherein λ is a pair of absolute values of real and imaginary partsSThe method for classifying the elements comprises the following steps:
classifying the characteristic root with the absolute value of the imaginary part greater than DEG into a complex root; classifying the characteristic root of which the absolute value of the real part and the absolute value of the imaginary part are less than omicron as a zero root; classifying the characteristic root with the absolute value of the imaginary part less than omicron and the real part less than-into a negative root; and classifying the characteristic root with the absolute value of the imaginary part smaller than the real part larger than the real part into a real root, wherein the real root is a preset minimum value.
5. The method of claim 1, wherein the constant c is a constant of the pattern matching method when the state matrix parameters are continuously changedsetIs set as a row vector lambdaSThe average of the absolute values of all elements is expressed as follows:
wherein λS,iAs a standard feature root vector lambda of the current sectionSI is a natural number between 1 and n.
6. The method of claim 1, wherein the profile matching result λ is outputtedkThe method of' comprising:
if epsilonk<εsetThe adjusted sorted row vector lambda is outputk'; if epsilonk≥εsetAnd N isk≥NsetThen the column vector λ is outputk' and the cross section matching error is marked to be too large and needs to be corrected manually.
7. A system for applying the method for matching feature patterns when the state matrix parameters are continuously changed according to any one of claims 1 to 6, comprising:
the characteristic root vector calculation module is used for acquiring a state matrix sequence to be matched and calculating characteristic root vectors of each state matrix respectively as characteristic root vectors to be matched of each section;
the characteristic root vector matching module is used for matching the standard characteristic root vector of the current section with the characteristic root vector to be matched one by one from the second section, wherein the standard characteristic root vector of the second section is the characteristic root of the first section state matrix; taking the matching result of the current section as a standard characteristic root vector of the next section; and repeating the steps until all the state matrix sequences to be matched are completely matched.
8. The system of feature pattern matching method when the state matrix parameters continuously change according to claim 7, wherein the feature root vector matching module comprises:
a difference matrix D calculation module for calculating the standard characteristic root vector lambda of the current sectionSCharacteristic root vector lambda to be matched with current sectionkThe difference-by-difference matrix D.
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