CN-115579866-B - EIGD time-lapse power system stability analysis method and device

CN115579866BCN 115579866 BCN115579866 BCN 115579866BCN-115579866-B

Abstract

The application belongs to the technical field of power systems and discloses a method and a device for analyzing the stability of an EIGD time-lapse power system, wherein the method comprises the steps of establishing a linearization model of the time-lapse power system, and converting a differential equation in the model into an abstract Cauchy problem by utilizing an infinitesimal generator; selecting a group of discrete points for each time-lag interval of the time-lag power system, establishing a discrete function space according to the discrete points, discretizing the time-lag variable to generate a low-order partial infinitesimal generation element discretization matrix, carrying out displacement and inverse transformation on the discretization matrix to obtain an inverse matrix, obtaining a characteristic value of the system according to the inverse matrix, checking the characteristic value through Newton method to obtain an accurate characteristic value and a characteristic vector, and analyzing and judging the stability of the time-lag power system. The method solves the problem that the matrix LU decomposition calculated amount is large in the existing EIGD time-lapse power system characteristic value sparse calculation method based on DDAE models.

Inventors

WU CHENG
HAO XUDONG
LI XIN
QIAO LITONG
ZHOU NING
ZHANG HUI
YE HUA
MOU QIANYING
LIU YUTIAN
ZHANG BING
WANG XIAOBO
XING FACAI
MA HUAN
CHENG DINGYI
LIU WENXUE
ZHAO KANG
JIANG ZHE
TIAN HAO
MA LINLIN
ZHANG ZHIXUAN
LI SHAN
FANG QIAO
WANG TING

Assignees

国网山东省电力公司电力科学研究院
国家电网有限公司
山东大学

Dates

Publication Date: 20260508
Application Date: 20220930

Claims (16)

1. An EIGD time-lapse power system stability analysis method, comprising: Establishing a linearization model of a time-lag power system, converting differential equations in the linearization model into abstract cauchy problems by utilizing an infinitesimal generator, describing a small interference stability analysis model of the time-lag power system by a time-lag differential equation set in an augmented form, dividing a state variable and an algebraic variable of the time-lag power system into time-lag related terms and time-lag unrelated terms respectively, so as to rewrite the differential equations according to the division of the state variable and the algebraic variable, wherein the method comprises the steps of dividing the state variable Deltax into non-time-lag state variables Sum time lag state variable I.e. ,n 1 +n 2 =n; Dividing the algebraic variable deltay into non-time-lapse algebraic variables Sum time-lag algebraic variable I.e. ,l 1 +l 2 =l; The linearization model of the time-lapse power system is in the form of: ; in the formula, , And D=n+l, d is the dimension of Δz, n is the dimension of Δz, l is the dimension of Δy, Δz r(p)= e r(p) Δz represents the r (p) th element of Δz, For the (p) th unit vector, As a time lag variable Is set for the vector of coefficients, p=1, 2..q; τ p >0 and are different time-lag constants; wherein E, J are d-dimensional square matrices ; Wherein, E 11 is the same as the main component, ,E 12 , ; ; Selecting a group of discrete points for each time lag section of the time lag power system, establishing a discrete function space according to the discrete points, discretizing time lag variables in the discrete function space to generate a partial infinitesimal generation element discretization matrix of the low-order time lag power system, wherein the method comprises the following steps of: For each time lag interval (p=1, 2, ..., q) Selecting a group of discrete points ; Wherein, the Alpha k is the zero point of the Nth order second class Chebyshev polynomial U N (), namely K=1, 2, & gt, n+1, wherein the generated partial infinitesimal generator discrete matrix of the time-lapse power system is in a double Schur complement form; Performing displacement and inverse transformation on the infinitesimal generation element discretization matrix to obtain an inverse matrix, and acquiring a characteristic value of the time-lag power system according to the inverse matrix; And verifying the characteristic value through Newton's method to obtain an accurate characteristic value and a characteristic vector of the time-lapse power system, and analyzing and judging the stability of the time-lapse power system according to the accurate characteristic value and the characteristic vector.
2. The EIGD time-lapse power system stability analysis method according to claim 1, wherein the steps of shifting and inverse transforming the infinitesimal generator discretization matrix to obtain an inverse matrix, and obtaining the eigenvalue of the time-lapse power system according to the inverse matrix further comprise: And calculating the inverse matrix by using an implicit restarting Arnoldi algorithm, and further obtaining the characteristic value of the time-lag power system.
3. The EIGD time-lapse power system stability analysis method according to claim 2, wherein the steps of shifting and inverse transforming the infinitesimal generator discretization matrix to obtain an inverse matrix, and obtaining the eigenvalue of the time-lapse power system according to the inverse matrix further comprise: And in the process of calculating the inverse matrix, solving the product of the inverse vectors of the inverse matrix by an iterative method to obtain the characteristic value of the time-lag power system.
4. The EIGD time-lapse power system stability analysis method according to claim 3, wherein in calculating the inverse matrix, the step of solving the product of the inverse vectors of the inverse matrix by an iterative method to obtain the eigenvalue of the time-lapse power system further comprises: And calculating the characteristic values of the maximum set number of the partial discretization matrix modulus values of the solution operator by using a subspace method, wherein the characteristic values comprise matrix-vector products in the process of iteratively forming Krylov sub-vectors.
5. The EIGD time-lapse power system stability analysis method according to claim 4, wherein calculating the eigenvalues of the maximum set number of solution operator partial discretization matrix modulus values by subspace method comprises iteratively forming matrix-vector products in Krylov sub-vector process further comprising: the matrix-vector product is calculated using a power method.
6. The EIGD time-lapse power system stability analysis method according to claim 5, wherein calculating the eigenvalues of the maximum set number of solution operator partial discretization matrix modulus values using a subspace method, comprises iteratively forming matrix-vector products in Krylov sub-vectors, further comprising: the matrix inverse-vector product is expressed in the form of an augmented matrix and is calculated using an inverse power method.
7. The EIGD time-lapse power system stability analysis method according to claim 1, wherein the step of verifying the eigenvalues by newton method to obtain accurate eigenvalues and eigenvectors of the time-lapse power system, and analyzing and judging the stability of the time-lapse power system according to the accurate eigenvalues and eigenvectors further comprises: And after the characteristic value of the time-lapse power system is obtained, the accurate characteristic value is obtained after spectrum mapping, inverse displacement-inverse transformation and Newton verification.
8. The EIGD time-lapse power system stability analysis device is characterized by comprising a linear model building module, a discrete matrix generating module, a characteristic value obtaining module and a stability analysis module, A linear model building module for building a linearization model of a time-lapse power system, converting differential equations in the linearization model into abstract cauchy problems by using infinitesimal generator, wherein a small disturbance stability analysis model of the time-lapse power system is described by an augmented form of time-lapse differential equation set, dividing state variables and algebraic variables of the time-lapse power system into time-lapse related terms and time-lapse independent terms, respectively, so as to rewrite differential equations according to the division of the state variables and algebraic variables, comprising dividing the state variables Deltax into non-time-lapse state variables Sum time lag state variable I.e. ,n 1 +n 2 =n; Dividing the algebraic variable deltay into non-time-lapse algebraic variables Sum time-lag algebraic variable I.e. ,l 1 +l 2 =l; The linearization model of the time-lapse power system is in the form of: ; in the formula, D=n+l, d is the dimension of Δz, n is the dimension of Δz, l is the dimension of Δy, Δz r(p)= e r(p) Δz represents the r (p) th element of Δz, For the (p) th unit vector, As a time lag variable Is set for the vector of coefficients, p=1, 2..q; τ p >0 and are different time-lag constants; wherein E, J are d-dimensional square matrices ; Wherein, the ; The discrete matrix generation module is used for selecting a group of discrete points for each time lag section of the time lag power system, establishing a discrete function space according to the discrete points, discretizing time lag variables in the discrete function space to generate a part of infinitesimal generator discretization matrix of the low-order time lag power system, and comprises the following steps: For each time lag interval ; Selecting a group of discrete points ; Wherein, the Alpha k is the zero point of the Nth order second class Chebyshev polynomial U N (), namely K=1, 2, & gt, n+1, wherein the generated partial infinitesimal generator discrete matrix of the time-lapse power system is in a double Schur complement form; The characteristic value acquisition module is used for carrying out displacement and inverse transformation on the infinitesimal generation element discretization matrix to obtain an inverse matrix, and acquiring the characteristic value of the time-lag power system according to the inverse matrix; And the stability analysis module is used for verifying the characteristic value through a Newton method so as to obtain an accurate characteristic value and a characteristic vector of the time-lapse power system, and analyzing and judging the stability of the time-lapse power system according to the accurate characteristic value and the characteristic vector.
9. The EIGD time-lapse power system stability analysis device according to claim 8, wherein the discrete matrix of the infinitesimal generator is shifted and inverse transformed to obtain an inverse matrix, and the characteristic value of the time-lapse power system is obtained from the inverse matrix, further comprising: And calculating the inverse matrix by using an implicit restarting Arnoldi algorithm, and further obtaining the characteristic value of the time-lag power system.
10. The EIGD time-lapse power system stability analysis device according to claim 9, wherein the discrete matrix of the infinitesimal generator is shifted and inverse transformed to obtain an inverse matrix, and the eigenvalue of the time-lapse power system is obtained from the inverse matrix, further comprising: And in the process of calculating the inverse matrix, solving the product of the inverse vectors of the inverse matrix by an iterative method to obtain the characteristic value of the time-lag power system.
11. The EIGD time-lapse power system stability analysis device according to claim 10, wherein in calculating the inverse matrix, solving the product of the inverse vectors of the inverse matrix by an iterative method to obtain the eigenvalue of the time-lapse power system, further comprises: And calculating the characteristic values of the maximum set number of the partial discretization matrix modulus values of the solution operator by using a subspace method, wherein the characteristic values comprise matrix-vector products in the process of iteratively forming Krylov sub-vectors.
12. The EIGD time-lapse power system stability analysis device according to claim 11, wherein calculating the eigenvalues of the maximum set number of solution operator partial discretization matrix modulus values using a subspace method comprises iteratively forming matrix-vector products in Krylov sub-vectors, further comprising: the matrix-vector product is calculated using a power method.
13. The EIGD time-lapse power system stability analysis device according to claim 12, wherein calculating the eigenvalues of the maximum set number of solution operator partial discretization matrix modulus values using a subspace method comprises iteratively forming matrix-vector products in Krylov sub-vectors, further comprising: the matrix inverse-vector product is expressed in the form of an augmented matrix and is calculated using an inverse power method.
14. The EIGD time-lapse power system stability analysis device according to claim 8, wherein the characteristic values are verified by newton's method to obtain accurate characteristic values and characteristic vectors of the time-lapse power system, and the stability of the time-lapse power system is analyzed and judged according to the accurate characteristic values and the characteristic vectors, further comprising: And after the characteristic value of the time-lapse power system is obtained, the accurate characteristic value is obtained after spectrum mapping, inverse displacement-inverse transformation and Newton verification.
15. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the steps of the method of any of claims 1-7 when the computer program is executed.
16. A computer readable storage medium, having stored thereon a computer program, the computer program being executed by a processor to implement the method of any of claims 1-7.

Description

EIGD time-lapse power system stability analysis method and device Technical Field The application relates to the technical field of power systems, in particular to an EIGD time-lapse power system stability analysis method and device. Background With the continuous expansion of the internet scale, wide-area measurement systems based on phasor measurement units are widely used in electric power systems. However, wide area measurement signals generally have certain communication time lags in the processes of acquisition, routing, transmission, processing and execution. For example, the communication time lag of wide area damping control systems based on synchronous measurements varies from tens to hundreds of milliseconds, with the communication time lag and sample-induced time lag of frequency control systems being up to several seconds. The time lag has a significant impact on the performance of the wide area controller and poses a risk to the stable operation of the power system, so the impact of the wide area communication time lag must be accounted for in the analysis of the stability of the small disturbances of the power system and the controller design that involve the wide area control. At present, the stability research method of the time-lag system mainly comprises a time domain method and a frequency domain method. The time domain analysis mainly utilizes Lyapunov-Krasovskii functional to provide sufficiency conditions for judging progressive stability of the system. The time domain analysis method can effectively process the change time lag, and in recent researches, quadratic integral terms are scaled into integral inequality by utilizing Jensen, wiringer and other inequality in functional derivative estimation, so that decision variables are reduced, and the conservation of criteria is reduced. In the frequency domain, the characteristic equation of the time-lag power system comprises an index term related to time lags, and the system has an infinite number of characteristic values. For analysis, methods such as Pad approximation, rekasius transformation and the like are generally adopted to eliminate the index time lag term. The other frequency domain analysis method is a characteristic value method based on spectrum discretization, and is to directly calculate the characteristic value without any transformation on an overrun characteristic equation of a time-lapse power system. The basic principle of the characteristic value method based on spectrum discretization is that the most right or minimum damping ratio partial characteristic value of a time-lapse power system is converted into partial characteristic values of a high-dimensional discretization matrix of two half-group operators (comprising infinitesimal generator and solution operators). The Chinese patent publication CN108647906A proposes a large-scale time-lag power system characteristic value algorithm based on low-order display infinitesimal generator discretization (Explicit Infinitesimal Generator Discretization, EIGD), wherein only the time-lag state variable is discretized, and the characteristic value of the time-lag power system is calculated, so that the stability of the system is judged. However, the small interference stability analysis of the time-lapse power system is based on a time-lapse differential equation set (DELAYED DIFFERENTIAL Equation, DDE) model, the DDE model needs to cancel a system algebraic equation first, more state variables are easy to introduce, and the improvement of the calculation efficiency is limited. Researchers put forward an EIGD time-lapse power system characteristic value sparse calculation method based on a time-lapse differential algebraic equation set (DELAYED DIFFE RENTIAL-algebraic Equation, DDAE) model, and an algebraic equation is reserved in a DDAE model, so that a time-lapse variable is discretized directly, and key characteristic values of the time-lapse power system are calculated efficiently. The inventor discovers that the existing EIGD characteristic value sparse calculation method based on DDAE models has the problem of large matrix LU decomposition calculation amount in the realization process because singular matrixes exist in the discrete matrix submatrices of infinitesimal generation elements, and limits the further improvement of algorithm calculation efficiency. Disclosure of Invention The embodiment of the application provides an EIGD time-lapse power system stability analysis method and device, which are used for solving the problem that the matrix LU decomposition calculated amount is large in the realization process because singular matrixes exist in discrete matrix submatrices of infinitesimal generation elements in the existing time-lapse power system eigenvalue sparse calculation method based on DDAE model. The following presents a simplified summary in order to provide a basic understanding of some aspects of the disclosed embodiments. This summary is not an exte