CN111695580B - A method and system for eigenmode matching when state matrix parameters change continuously - Google Patents

Abstract

The invention discloses a characteristic pattern matching method when state matrix parameters change continuously. The method includes: acquiring a sequence of state matrices to be matched and calculating the characteristic roots of each state matrix respectively; calculating a standard characteristic root vector λ _S and a current cross section one by one The difference-by-difference matrix D of the eigenroot _vector λk; according to the classification of _λS elements, iteratively searches _λk for the eigenvalues that have continuity with each element of _λS , and adjusts the order of the eigenvalues in _λk according to the results; according to _λS and λ The difference degree ε _k of _k is combined with the number of iterations to judge whether the section matching is completed or the marking error is too large, output the section matching result λ _k ' and continue to match the characteristic root of the next section. The invention realizes the automatic matching of the corresponding characteristic patterns when the state matrix changes continuously based on the continuous characteristic of the characteristic root to the change of the matrix parameters, and greatly improves the efficiency and accuracy of the characteristic pattern matching in the process of power system oscillation analysis compared with the existing method. .

Description

A method and system for eigenmode matching when state matrix parameters change continuously

technical field

The invention relates to a characteristic pattern matching method and system when state matrix parameters change continuously, belonging to the technical field of electric power systems.

Background technique

When analyzing the oscillation characteristics of the power system, the characteristic root method of the trajectory section is piecewise linearized along the disturbed trajectory, and the instantaneous characteristics of the original system oscillation are extracted from a series of linear time-varying differential equations; The continuous variation of , solves the corresponding eigenroot. However, in the actual solution, the eigenroot will have a problem of mismatching in the ordering and correlation of adjacent sections, which is manifested in the loss of continuity of the trajectories of the eigenvalues corresponding to the state matrix that changes continuously with time. It brings great inconvenience and makes it difficult to further analyze the transient characteristics of power system oscillation.

On the other hand, in order to study the sensitivity of parameters to the damping of dangerous eigenmodes, the traditional eigenroot method needs to continuously change the value of the elements of the state matrix and analyze the variation of the corresponding origin eigenroot. The conventional method does not track the evolution of the eigenroot ordering with the parameters of the state matrix. Therefore, the traditional method will encounter the same problem as the eigenroot of the trajectory section when calculating the sensitivity of the eigenroot parameter at the origin, which is manifested in the state matrix corresponding to the continuous change with the parameters. The characteristic root locus loses continuity.

This phenomenon is called "channeling branch" in some studies on flutter in the field of aeroelastic stability. Generally, manual adjustment is used to match the eigenmode of the continuously changing state matrix according to the analysis experience, so as to obtain a continuous characteristic root locus for subsequent follow-up. analyze. In the actual power system analysis, the number of cross-sections of the trajectory cross-sections is often over a thousand, which brings a huge workload for manual feature pattern matching. The existing methods cannot meet the requirements of high efficiency and accuracy in engineering applications. At present, the field of power system technology This part of the research is still blank.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the difficulty caused by using manual adjustment to match the characteristic pattern of the continuously changing state matrix during data analysis in engineering, and to provide a characteristic pattern matching method and system when the parameters of the state matrix change continuously, which can accurately realize Automatic matching of corresponding eigenmodes when state matrix parameters continuously change during power system oscillation analysis.

To achieve the above object, the present invention adopts the following technical solutions to realize:

A characteristic pattern matching method when a state matrix parameter changes continuously, the method comprises the following steps:

Obtain the sequence of state matrices to be matched and calculate the eigenvectors of each state matrix as the eigenvectors of each section to be matched;

Starting from the second section, match the standard eigenvectors of the current section with the eigenvectors to be matched one by one, where the standard eigenvectors of the second section are the eigenvalues of the state matrix of the first section; The matching result is used as the standard feature root vector of the next section; this step is repeated until all the matching state matrix sequences of all sections are completed.

Further, the method for matching the standard eigenvectors of the current section with the eigenvectors to be matched is as follows:

1) calculate the standard eigenvector λ _S of the current section and the difference-by-difference matrix D of the eigenvector λ _k of the current section to be matched; Preferably, the calculation method of the difference-by-difference matrix D includes:

Let d _ij be the element of the i-th row and the j-th column of the n×n-order difference-by-difference matrix D, d _ij =(λ _Si -λ _kj ) ² , λ _S,i be the i-th element of the standard eigenvector λ _S of the current section λ _k,j is the jth element of the feature root vector λ _k of the current section to be matched, where i is a natural number between 1 and n, and j is a natural number between 1 and n.

2) the classification of λ _S elements according to the size of the absolute value of the real part and the imaginary part; preferably, the classification method is to classify the characteristic root whose absolute value of the imaginary part is greater than o as a complex root; the absolute value of the real part and the imaginary part are all less than o The eigenroot of σ is classified as zero root; the eigenroot whose absolute value of imaginary part is less than ο and whose real part is less than -ο is classified as negative real root; the eigenroot whose absolute value of imaginary part is less than ο and whose real part is greater than ο is classified as positive real root, where ο is a preset minimum value.

3) According to the classification result, iteratively search λ _k for the eigenvalues that have continuity with λ _S elements and adjust the order of eigenroots in λ _k to obtain the matching result λ _k ' of the current section.

Further, the method of step 3) is as follows: the first step, make l=1;

In the second step, if λ _Sl is a zero root or a negative real root, and λ _Sl represents the l-th element of λ _S , select the l-th row in the difference-by-difference matrix D, calculate the minimum value of this row and the corresponding column number is m. Swap the lth column and the mth column in the difference matrix D, and at the same time exchange the positions of λ _kl and λ _km in the eigenvector λ _k of the current section to be matched, where λ _kl represents the lth element of λ _k , and λ _km represents The mth element of λ _k ; let l=l+1, if l<n, re-execute the second step, otherwise continue to the third step;

The third step is to set the number of iterations N _k to 1;

The fourth step, let p=1;

The fifth step, λ _Sp is a positive real root or a complex root, λ _Sp represents the p-th element of the row vector λ _S , select the p-th row in the difference-by-difference matrix D and calculate the minimum value of this row. The corresponding column number is q, if λ _kp is a real root and λ _kq is a complex root, where λ _kp represents the p-th element of the row vector λ _k , and λ _kq represents the q-th element of the row vector λ _k , then in the difference-by-difference matrix D, exchange the p-th column with Column q, and exchange the positions of λ _kp and λ _kq in the vector λ _k at the same time, otherwise perform the following steps;

其中c_set是预先设定的常数；If λ _Sp is a real root, exchange the p- _th column and the q-th column in the difference-by-difference matrix D, and exchange the positions of λ _kp and λ _kq in the exchange vector λ _k at the same time; error

where c _set is a preset constant;

If ξ _f >ξ _b , exchange the p-th column and the q-th column in the difference-by-difference matrix D, and exchange the positions of λ _kp and λ _kq in the vector λ _k at the same time,

If ξ _f ≤ξ _b , do not adjust the order of elements in the vector λ _k ; let p=p+1, if p<n, re-execute the fifth step, otherwise continue to the sixth step;

The sixth step, after completing a single iteration, record the matching result as λ _k ', and calculate the degree of difference between the vector λ _S and the matching result vector λ _k '

If ε _{k ≥} ε _set and N _k <N _set , where ε _set is the preset error threshold and N _set is the preset upper limit of the number of iterations, execute N _k =N _k +1 and repeat steps 2 to 6 step; otherwise, output the section matching result λ _k '.

Description of drawings

FIG. 1 is a feature pattern matching method provided by an embodiment of the present invention when a state matrix parameter changes continuously.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings. The following examples are only used to illustrate the technical solutions of the present invention more clearly, and cannot be used to limit the protection scope of the present invention.

In step S1, a sequence of state matrices to be matched is obtained, and the eigenvectors λ of each state matrix are calculated respectively as the vectors to be matched for each section.

Assuming a total of N sections, each section can calculate a eigenvector. In a specific embodiment, the method for obtaining the state matrix sequence to be matched for each section is: for the characteristic root method of the trajectory section, when extracting the instantaneous characteristics of oscillation of the power system, the disturbed trajectory of the power system is segmented and linearized for each time section to obtain the state. Matrix sequence; for the origin eigenroot method, when studying the relationship between parameters and eigenroots, a state matrix sequence is generated according to parameter changes. The above two methods can obtain the state matrix of any section as an n-order square matrix, and its characteristic root vector is calculated as a 1×n row vector, denoted as λ _k =[λ _k.1 ,λ _k.2 ,...,λ _kn ].

Step S2, starting from the second section, matching the standard eigenvectors of the current section with the eigenvectors to be matched section by section, wherein the standard eigenvectors of the second section are the eigenvalues of the first section state matrix; Use the matching result of the current section as the standard eigenvector of the next section; repeat this step until the matching state matrix sequence of all sections is completed, that is, there are a total of N sections to be matched, and the first section λ does not match directly. Match the second section λ as a standard vector, and then use the matching result of the second section as a standard vector to match the third section λ, and so on until the end of the last section matching.

In this embodiment, the method for matching the standard characteristic root vector of the current section with the characteristic root vector to be matched in the current section is as follows:

Calculate the difference-by-difference _matrix D of the standard eigenvector _λS and the eigenvector λk of the current section to be matched one by one.

The first section is not matched, and λ ₁ (the eigenvalue of the state matrix of the first section, a 1×n row vector) is set as the standard eigenvector λ _S of the second section. For section k, set the matching result of the previous section λ _k-1 ' (the eigenvector of the k-1th section after matching, 1×n row vector) as the standard eigenvalue phasor λ _S of the current section;

Let d _ij be the element of the i-th row and the j-th column of the difference-by-difference matrix D (n-order square matrix), d _ij =(λ _Si -λ _kj ) ² , where i is a natural number between 1 and n, and j is 1 to A natural number between n, λ _{S, i} is the ith element of the standard eigenvector λ _S , λ _{k, j} is the j th element of the eigenroot vector λ _k to be matched.

Step S3, according to the classification of λ _S elements, iteratively searches λ _k for characteristic roots that are continuous with each element of λ _S , and adjusts the order of the characteristic roots in λ _k according to the results.

For a given minimum value ο, the eigenroot whose absolute value of the imaginary part is greater than ο is classified as a complex root; the eigenroot whose absolute value of the real part and the imaginary part are both less than ο is classified as a zero root; the absolute value of the imaginary part is less than ο. The eigenroot whose real part is less than -ο is classified as negative real root; the eigenroot whose absolute value of imaginary part is less than ο real part is greater than ο is classified as positive real root.

Iteratively searches for the eigenvalues that are continuous with each element of _λS in λk and adjusts the order of _eigenroots in _λk according to the results. In this embodiment, the following steps are included:

The first step, let l=1;

In the second step, if λ _Sl is a zero root or a negative real root (λ _Sl represents the ith element of λ _S ), select the ith row in the difference-by-difference matrix D, and calculate the minimum value of this row. The corresponding column number is m. The lth column and the mth column in the difference-by-difference matrix D, and at the same time exchange the positions of λ _kl and λ _km in the row vector λ _k (λ _kl represents the l-th element of the row vector λ _k ), let l=l+1 , if l<n, re-execute the second step, otherwise continue to the third step;

The third step is to set the number of iterations N _k to 1;

The fourth step, let p=1;

The fifth step, λ _Sp is a positive real root or a complex root (λ _Sp represents the p-th element of the row vector λ _S ), select the p-th row in the difference-by-difference matrix D and calculate the minimum value of this row. The corresponding column number is q, if λ _kp is a real root and λ _kq is a complex root (λ _kp represents the p-th element of the row vector λ _k , λ _kq represents the q-th element of the row vector λ _k ), then exchange the p-th column in the difference-by-difference matrix D and the qth column, and exchange the positions of λ _kp and λ _kq in the vector λ _k at the same time, otherwise continue to further judge according to the properties of λ _Sp .

其中c_set是为了防止λ_S.p或λ_S.q数值过小引入数值误差而人为设定的常数，数值一般设定为行向量λ_S全部元素绝对值(复数为模值)的平均值

若ξ_f>ξ_b，则在逐差矩阵D中交换第p列与第q列，并同时交换向量λ_k中λ_k.p与λ_k.q的位置，若ξ_f≤ξ_b，则不调整行向量λ_k中元素的排序。令p＝p+1，若p<n则重新执行第五步，否则继续第六步。If λ _Sp is a real number root, exchange the p-th column and the q-th column in the difference-by-difference matrix D, and exchange the positions of λ _kp and λ _kq in the vector λ _k at the same time; if λ _Sp is a complex number root, calculate the relative error before and after the exchange

Among them, c _set is a constant set artificially to prevent the value of λ _Sp or _{λ Sq} from being too small to introduce numerical errors.

If ξ _f >ξ _b , exchange the p-th column and the q-th column in the difference-by-difference matrix D, and exchange the positions of λ _kp and λ _kq in the vector λ _k at the same time. If ξ _f ≤ξ _b , the row vector is not adjusted The ordering of elements in _λk . Let p=p+1, if p<n, execute the fifth step again, otherwise continue to the sixth step.

若ε_k≥ε_set且N_k<N_set(ε_set为预设的误差阈值，N_set为预设的迭代次数上限)，则执行N_k＝N_k+1并重复第二步至第六步；否则继续执行步骤S4。The sixth step, after completing a single iteration, record the characteristic root vector after exchanging the corresponding elements as λ _k ' and use it as the matching result, and calculate the degree of difference between the row vector λ _S and the matching result row vector λ _k '

If ε _{k ≥} ε _set and N _k <N _set (ε _set is the preset error threshold, N _set is the preset upper limit of the number of iterations), then execute N _k =N _k +1 and repeat the second to sixth steps step; otherwise, continue to step S4.

Step S4, according to the degree of difference ε _k between λ _S and λ _k , in combination with the number of iterations, it is determined that the section matching is complete or the marking error is too large, and the section matching result λ _k ' is output.

If ε _k <ε _set , output the adjusted row vector λ _k '; if ε _{k ≥} ε _set and N _{k ≥} N _set , output the row vector λ _k ' and mark the section matching error is too large and needs manual correction.

In step S5, λ _k ' is used as the standard characteristic root phasor of the next section, and steps S2 to S4 are repeated until all the to-be-matched state matrix sequences of all sections are matched.

Based on the continuous characteristic of the matrix characteristic root for the change of the matrix parameters, the invention realizes the automatic matching of the characteristic pattern of the adjacent section when the state matrix changes continuously, and greatly improves the efficiency of the characteristic root sorting in the power system oscillation analysis process compared with the existing method. with accuracy.

The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the technical principles of the present invention, several improvements and modifications can also be made. These improvements and Deformation should also be regarded as the protection scope of the present invention.

Claims (8)

1. a characteristic pattern matching method when a state matrix parameter changes continuously, it is characterised in that the method comprises the steps: Obtain the sequence of state matrices to be matched and calculate the eigenvectors of each state matrix as the eigenvectors of each section to be matched; Starting from the second section, match the standard eigenvectors of the current section with the eigenvectors to be matched one by one, where the standard eigenvectors of the second section are the eigenvalues of the state matrix of the first section; The matching result is used as the standard feature root vector of the next section; this step is repeated until all the matching state matrix sequences of all sections are completed; The method of matching the standard eigenvector of the current section with the eigenvector of the current section to be matched is as follows: Calculate the difference-by-difference _matrix D of the standard eigenvector _λS of the current section and the eigenvector λk of the current section to be matched; Classification of λ _S elements according to the absolute value of real and imaginary parts; According to the classification result, iteratively search λk for the _eigenroot that has continuity with the _λS element, and adjust the order of _eigenroots in λk to obtain the matching result _λk ' of the current section; According to the classification result, iteratively search λ _k for the characteristic roots that have continuity with the λ _S element and adjust the order of the characteristic roots in λ _k to obtain the matching result λ _k ' of the current section. The specific method is as follows: The first step, let l=1; In the second step, if λ _Sl is a zero root or a negative real root, and λ _Sl represents the l-th element of λ _S , select the l-th row in the difference-by-difference matrix D, calculate the minimum value of this row and the corresponding column number is m. Swap the lth column and the mth column in the difference matrix D, and at the same time exchange the positions of λ _kl and λ _km in the eigenvector λ _k of the current section to be matched, where λ _kl represents the lth element of λ _k , and λ _km represents The mth element of λ _k ; let l=l+1, if l<n, re-execute the second step, otherwise continue to the third step; The third step is to set the number of iterations N _k to 1; The fourth step, let p=1; The fifth step, λ _Sp is a positive real root or a complex root, λ _Sp represents the p-th element of the row vector λ _S , select the p-th row in the difference-by-difference matrix D and calculate the minimum value of this row. The corresponding column number is q, if λ _kp is a real root and λ _kq is a complex root, where λ _kp represents the p-th element of the row vector λ _k , and λ _kq represents the q-th element of the row vector λ _k , then in the difference-by-difference matrix D, exchange the p-th column with In the qth column, exchange the positions of λ _kp and λ _kq in the vector λ _k at the same time, otherwise perform the following steps; If λ _Sp is a real root, exchange the p-th column and the q-th column in the difference-by-difference matrix D, and at the same time exchange the positions of λ _kp and λ _kq in the vector λ _k ; if λ _Sp is a complex number root, calculate the relative error before and after the exchange

where c _set is a preset constant; If ξ _f >ξ _b , exchange the p-th column and the q-th column in the difference-by-difference matrix D, and at the same time exchange the positions of λ _kp and λ _kq in the row vector λ _k , If ξ _f ≤ξ _b , do not adjust the order of elements in the vector λ _k ; let p=p+1, if p<n, re-execute the fifth step, otherwise continue to the sixth step; The sixth step, after completing a single iteration, record the matching result as λ _k ', and calculate the degree of difference between the vector λ _S and the matching result vector λ _k '

If ε _{k ≥} ε _set and N _k <N _set , where ε _set is the preset error threshold and N _set is the preset upper limit of the number of iterations, execute N _k =N _k +1 and repeat steps 2 to 6 step; otherwise, output the section matching result λ _k '. 2. the characteristic pattern matching method when the state matrix parameter according to claim 1 changes continuously, it is characterized in that, the method that obtains the state matrix sequence to be matched comprises: For the trajectory section characteristic root method, when extracting the instantaneous characteristics of the power system oscillation, the state matrix sequence is obtained by piecewise linearization of the disturbed trajectory of the power system for each time section; For the origin eigenroot method, when studying the relationship between parameters and eigenroots, the state matrix sequence is generated according to the parameter changes. 3. according to the characteristic pattern matching method when the state matrix parameter continuously changes according to claim 1, it is characterized in that, the calculation method of the difference-by-difference matrix D comprises: Let d _ij be the element of the i-th row and the j-th column of the n×n-order difference-by-difference matrix D, d _ij =(λ _Si -λ _kj ) ² , λ _S,i be the i-th element of the standard eigenvector λ _S of the current section λ _k,j is the jth element of the feature root vector λ _k of the current section to be matched, where i is a natural number between 1 and n, and j is a natural number between 1 and n. 4. according to the characteristic pattern matching method when the state matrix parameter continuously changes according to claim 1, it is characterized in that, according to real part and imaginary part absolute value size, the method that λ _S element is classified comprises: The eigenroot whose absolute value of the imaginary part is greater than ο is classified as a complex root; the eigenroot whose absolute value of the real part and the imaginary part are both less than ο is classified as a zero root; the eigenroot whose absolute value of the imaginary part is less than ο and the real part is less than -ο is classified is a negative real root; the characteristic root whose absolute value of the imaginary part is less than ο and the real part is greater than ο is classified as a positive real root, where ο is a preset minimum value. 5. according to the characteristic pattern matching method when the state matrix parameter continuously changes according to claim 1, it is characterized in that, constant c _set is set as the mean value of the absolute value of all elements of row vector λ _S , and the expression is as follows:

Where λ _S,i is the i-th element of the standard eigenvector λ _S of the current section, and i is a natural number between 1 and n. 6. according to the characteristic pattern matching method when the state matrix parameter continuously changes according to claim 1, it is characterized in that, the method for outputting this section matching result λ _k ' comprises: If ε _k <ε _set , output the adjusted row vector λ _k '; if ε _{k ≥} ε _set and N _{k ≥} N _set , output the row vector λ _k ' and mark the section matching error is too large and needs manual correction. 7. A system using the characteristic pattern matching method when the state matrix parameter continuously changes according to any one of claims 1 to 6, characterized in that, comprising: The eigenvector calculation module is used to obtain the sequence of state matrices to be matched and calculate the eigenvectors of each state matrix as the eigenvectors of each section to be matched; The eigenvector matching module is used to match the standard eigenvectors of the current section with the eigenvectors to be matched section by section starting from the second section, where the standard eigenvectors of the second section are the state of the first section The characteristic root of the matrix; the matching result of the current section is used as the standard characteristic root vector of the next section; this step is repeated until all the state matrix sequences to be matched are all matched. 8. the system of the characteristic pattern matching method when the state matrix parameter according to claim 7 changes continuously, it is characterized in that, the characteristic root vector matching module comprises: The difference-by-difference matrix D calculation module is used to calculate the difference-by-difference matrix D of the standard eigenvector λ _S of the current section and the eigenroot vector λ _k of the current section to be matched.

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