LTP system characteristic value sensitivity analysis method considering parameter time-varying characteristic and used for power system stability analysis

Abstract

The invention discloses a parameter time-varying characteristic considered LTP system characteristic value sensitivity analysis method for power system stability analysis, and belongs to the field of linear period time-varying system analysis control. According to the method, the influence relation of the change of a time-varying parameter alpha (t) on a dominant characteristic value lambda i is analyzed by utilizing the partial derivative of the dominant characteristic value lambda i of the power system to the time-varying parameter alpha (t), and the size and direction of the influence of the change of the time-varying parameter alpha (t) on the dominant characteristic value lambda i are quantified according to the actual time-varying parameter change. Analyzing and depicting the influence degree of changes of time-varying operation parameters, time-varying control parameters and the like on characteristic values in the power system, so as to realize stable analysis and control of planning, scheduling optimization, parameter optimization, controller design and the like of the power system; wherein the functional relationship between the LTP system matrix and the time-varying parameter is considered, and the functional derivative of the system matrix to the time-varying parameter is adopted to represent the partial derivative of the system matrix to the time-varying parameter.

Description

Technical Field

[0001] The present invention belongs to the field of linear periodic time-varying system analysis and control, and more specifically, relates to an LTP system eigenvalue sensitivity analysis method for power system stability analysis taking into account parameter time-varying characteristics. Background Art

[0002] The safe and stable operation of power systems is the cornerstone of modern social and economic development. With the large-scale integration of renewable energy and the widespread application of direct current (DC) transmission technology, modern power systems are undergoing a profound transformation towards power electronics. While this transformation improves system flexibility, efficiency, and cleanliness, it also introduces new dynamic characteristics and stability challenges, making small-signal stability analysis more critical and complex than ever before.

[0003] In power system stability analysis, sensitivity analysis within modal analysis quantitatively studies the sensitivity of power system small-signal stability to various parameter changes. Embedding sensitivity analysis into the optimization process provides effective support for power system operation planning. It extends and deepens eigenvalue analysis and serves as a core tool for understanding system stability mechanisms, optimizing control parameters, identifying key influencing factors, and evaluating system robustness.

[0004] Sensitivity analysis for linear time-invariant (LTI) systems is currently relatively mature. Therefore, sensitivity analysis for power systems with general periodic time-varying characteristics often simplifies the problem to LTI sensitivity analysis using traditional time-invariant modeling methods, resulting in inaccurate results. While the harmonic state-space (HSS) modeling method can accurately characterize the dynamic characteristics of power systems with general periodic time-varying characteristics, the traditional sensitivity calculation process uses the system matrix derived from the linearization of a nonlinear time-invariant system, while the HSS model's system matrix Ahss is derived from the linearization of a nonlinear periodic time-varying system followed by series approximation and harmonic balance. These two processes are fundamentally different and require different time-invariant mathematical processing. This makes the first step of the traditional sensitivity solution inapplicable to the analytical expression of the parameter partial derivatives of the system matrix Ahss. Therefore, current HSS sensitivity research remains unapplicable to sensitivity studies of generalized periodic time-varying power electronic systems.

[0005] The linear time-periodic (LTP) system analysis method can accurately characterize the dynamic characteristics of the system. Although the existing sensitivity analysis method of the LTP system realizes the analytical characterization of the sensitivity of the LTP system's eigenvalues ​​to the time-invariant parameters, the time-varying parameters are the key system variables in the LTP system and are also an indispensable part of the dynamic system analysis. The existing technology is unable to analyze and calculate the sensitivity of the LTP system's eigenvalues ​​to the time-varying parameters. Therefore, it is very important to analytically characterize the sensitivity of the LTP system's eigenvalues ​​to the time-varying parameters. Summary of the Invention

[0006] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides an LTP system eigenvalue sensitivity analysis method for power system stability analysis taking into account the time-varying characteristics of parameters. Its purpose is to accurately analyze and characterize the sensitivity of the eigenvalues ​​of the power system to changes in time-varying parameters, and use this as a basis to achieve stability tuning and controller design of the power system.

[0007] To achieve the above objectives, according to a first aspect of the present invention, a method for analyzing the eigenvalue sensitivity of an LTP system considering the time-varying characteristics of parameters for power system stability analysis is provided, comprising:

[0008] The dynamic equation of the power system f in y ss (t) as the system matrix A(t) of the LTP system, and the implicit expression part A of the time-varying parameter α(t) of the power system in the system matrix A(t) is used. I and display expression part A E and calculate the partial derivative of the system matrix A(t) with respect to the time-varying parameter α(t)

[0009] in, They are The abbreviation of is the variation of α(t), y is the time domain trajectory of the power system, y ss (t) is the steady-state periodic trajectory of the power system;

[0010] Calculate the dominant eigenvalue λ of the system matrix A(t) of the LTP system i The corresponding left and right eigenvectors r i (t), l i (t);

[0011] Calculate the dominant eigenvalue λ i Partial derivative with respect to the time-varying parameter α(t) Take it as the dominant eigenvalue λ iThe sensitivity of the time-varying parameter α(t) to the dominant eigenvalue λ is determined by determining the effect of the change of the time-varying parameter α(t) on the dominant eigenvalue λ. i The magnitude and direction of the impact are determined to perform stability analysis on the power system.

[0012] According to a second aspect of the present invention, there is provided an electronic device comprising: a computer-readable storage medium and a processor;

[0013] The computer-readable storage medium is used to store executable instructions;

[0014] The processor is configured to read the executable instructions stored in the computer-readable storage medium and execute the method according to the first aspect.

[0015] According to a third aspect of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to execute the method according to the first aspect.

[0016] According to a fourth aspect of the present invention, there is provided a computer program product comprising a computer program or instructions, which implement the method according to the first aspect when executed by a processor.

[0017] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0018] The present invention utilizes the dominant characteristic value λ of the power system i The partial derivative of the time-varying parameter α(t) analyzes the effect of the change of the time-varying parameter α(t) on the dominant eigenvalue λ i Influence relationship, according to the actual time-varying parameter change, the change of the time-varying parameter α(t) affects the dominant eigenvalue λ i The magnitude and direction of the influence are determined, and the degree of influence of changes in time-varying operating parameters, time-varying control parameters, etc. in the power system on the eigenvalues ​​is analytically characterized, and then the stability analysis and control of power system planning, scheduling optimization, parameter optimization, controller design, etc. are realized. Among them, considering the functional relationship between the LTP system matrix and the time-varying parameters, the functional derivative of the system matrix with respect to the time-varying parameters is used to characterize the partial derivative of the system matrix with respect to the time-varying parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A flow chart of a method for analyzing the eigenvalue sensitivity of an LTP system considering the time-varying characteristics of parameters for power system stability analysis provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0020] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0021] An embodiment of the present invention provides a method for analyzing the eigenvalue sensitivity of an LTP system for power system stability analysis taking into account the time-varying characteristics of parameters, including:

[0022] The dynamic equation of the power system f in y ss (t) as the system matrix A(t) of the LTP system, and the implicit expression part A of the time-varying parameter α(t) of the power system in the system matrix A(t) is used. I and display expression part A E and calculate the partial derivative of the system matrix A(t) with respect to the time-varying parameter α(t)

[0023] Calculate the dominant eigenvalue λ of the system matrix A(t) of the LTP system i The left and right eigenvectors r corresponding to and i (t), l i (t);

[0024] Calculate the dominant eigenvalue λ i Partial derivative with respect to the time-varying parameter α(t) Take it as the dominant eigenvalue λ i The sensitivity of the time-varying parameter α(t) to the dominant eigenvalue λ is determined by determining the effect of the change of the time-varying parameter α(t) on the dominant eigenvalue λ. i The magnitude and direction of the impact are determined to perform stability analysis on the power system.

[0025] like Figure 1 As shown, the LTP system eigenvalue sensitivity analysis method considering the time-varying characteristics of parameters for power system stability analysis provided by the present invention includes the following steps:

[0026] First, analyze the influence of the time-varying parameter α(t) on the system matrix A(t): According to steps S1 to S2, determine the partial derivative of the LTP system matrix A(t) with respect to the power system time-varying parameter α(t):

[0027] S1, calculate the steady-state trajectory y of the power system ss The partial derivative of (t) with respect to the time-varying parameter α(t).

[0028] First, a time domain simulation is performed based on the power system model to obtain the steady-state periodic trajectory y of the power system.ss (t).

[0029] The general expression of the power system is:

[0030]

[0031] in, represents the state variables of the power system; f represents the dynamic equation of the power system. The steady-state solution of the power system presents a periodic time-varying characteristic, so y ss (t) = y ss (t+T), y ss Substituting (t) into formula (1), the steady-state solution of the power system can be obtained as:

[0032]

[0033] γ(t) is used to simplify the partial derivative of the steady-state trajectory with respect to the time-varying parameters. That is in, The form of the change of the time-varying parameter, such as sinusoidal change sin(ωt), is then obtained by taking the partial derivatives of α(t) on both sides of the steady-state solution of the power system to obtain the differential equations governing the dynamics of γ(t):

[0034]

[0035] in, Indicates that f is on the steady-state trajectory y ss The Jacobi matrix on , and can be represented by the system matrix A(t), that is, therefore:

[0036]

[0037] This shows that the dynamics of γ(t) is determined by the input The general solution of the linear differential equations can be expressed as:

[0038]

[0039] Among them, Φ(t,0) is the state transition matrix of the LTP system from time 0 to time t, and Φ(t,τ) is the state transition matrix of the LTP system from time τ to time t.

[0040] Before obtaining γ(t), we need to first obtain the analytical form of γ(0). Therefore, according to the steady-state periodic trajectory y ss The periodicity of (t) gives the solution condition γ(0) = γ(T). Assume that the LTP system has no eigenvalue equal to Then the matrix (I-Φ(T,0)) is reversible. By setting t=T in equation (5), we can solve γ(0) and γ(T) according to the boundary conditions:

[0041]

[0042] S2, calculate the partial derivative of the system matrix A(t) with respect to the parameter of interest α(t). More specifically, the parameter α(t) can be used to determine the partial derivative of the system matrix A(t) in two ways: ss (α),α) have an impact: one is indirect impact, which mainly considers the time-varying parameters of the power system affecting the steady-state solution y ss (α) further affects the system matrix of the LTP system, such as the operating parameters of the power system. In this case, the parameters are implicit in A(y ss (α)), and use the symbol A I The other is direct influence, which mainly considers the case where the parameters do not affect the steady-state solution, such as the control parameters of the power system. In this case, the parameters are explicitly contained in A(α(t)) and are represented by the symbol A E Indicates. Based on the parameters A I With A E The influence of the two parts, the functional derivative of the system matrix with respect to the time-varying parameters can be written as:

[0043]

[0044] Then, the time-varying parameter α(t) of the power system is analyzed to determine the dominant eigenvalue λ of the LTP system. i Analysis of the influence of: For the dominant eigenvalue λ of interest i , calculate the dominant eigenvalue λ of interest according to the following steps S3-S4 i λ i Partial derivative of the parameter of interest α(t):

[0045] S3, calculating the eigenvalue Λ of the LTP system and the corresponding time-varying left eigenvector and time-varying right eigenvector R(t), L(t).

[0046] First, the periodic state transfer matrix Φ(T,0) is numerically solved. The system eigenvalue Λ and the values ​​of the eigenvector R(0) and L(0) at 0 and T can be obtained by eigendecomposing Φ(T,0):

[0047] Φ(T,0)=R(T)e ΛT L(0)=R(0)e ΛT L(0) (8)

[0048] Among them, R(0)=R(T), L(0)=L(T).

[0049] Select the dominant eigenvalue λ of interest iand its left and right eigenvectors r i (t), l i (t), r i (t) is the i-th column of R(t), l i (t) is the i-th column of L(t). According to the calculation formula of the right eigenvector The right eigenvector of a period can be numerically solved;

[0050] The left eigenvector is similar to the left eigenvector l. i The calculation formula for (t) is Numerically solve for the left eigenvector of a period.

[0051] S4, using the system matrix A(t) to calculate the partial derivative, left and right eigenvectors l of the parameter of interest α(t) i (t), r i (t) Calculate the attention pattern λ i (i.e. the dominant eigenvalue λ i ) is the partial derivative of the parameter of interest α(t) (i.e., the parameter to be analyzed, the time-varying parameter).

[0052] Calculate the dominant eigenvalue λ of the interest i The partial derivative with respect to the time-varying parameter α(t).

[0053] Dominant eigenvalue λ i is a functional of the time-varying parameter α(t), so the dominant eigenvalue λ can be i The first-order variation δλ i writing:

[0054] δλ i =λ i [α(t)+δα(t)]-λ i [α(t)] (9)

[0055] Here, δα represents a small change in the parameter.

[0056] The system matrix A(t) with time-varying parameters is mapped to the time-invariant LTP eigenvalues, so the variation of the LTP eigenvalues ​​δλ i is time-invariant. Indicates that, Indicates the form of change of the parameter under study, such as sinusoidal change sin(ωt), ε is the coefficient describing small changes. Then, the dominant eigenvalue λ i Expressed using system matrices and eigenvectors:

[0057]

[0058] In order to make the expression simpler, A(t) and r are omitted.i (t) and l i (t) Information about time t, A(t), r i (t) and l i (t) is abbreviated as A, r i 、l i .

[0059] According to the properties of LTP eigenvectors and combined with the definition of functional derivatives, the dominant eigenvalue λ i The partial derivative with respect to time-varying parameters can be expressed as:

[0060]

[0061] The dominant eigenvalue λ i The partial derivative of the time-varying parameter is used as the dominant eigenvalue λ i The sensitivity of the time-varying parameter α(t) to the dominant eigenvalue λ is determined by determining the effect of the change of the time-varying parameter α(t) on the dominant eigenvalue λ. i The magnitude and direction of the influence (that is, according to the quantitative calculation of the dominant eigenvalue λ when the time-varying parameter changes) i The magnitude and direction of the change) are used to perform stability analysis on the power system, such as optimizing control parameters, identifying key influencing factors, and evaluating system robustness.

[0062] For example, if it is necessary to analyze and optimize the instability mode of the power system, the eigenvalue and its left and right eigenvectors corresponding to the instability mode are selected, and the sensitivity of the instability mode to the main parameter set in the system is calculated according to the calculation method of calculating the sensitivity of the eigenvalue to the time-varying parameters described in the present invention. According to the calculation results, the instability mode is stabilized by adjusting the power system operating parameters or control parameters with greater influence.

[0063] If it is necessary to identify the key influencing factors of the power system, the sensitivity of the mode of interest to the system parameter set is calculated according to the calculation method of the sensitivity of the characteristic value to the time-varying parameters described in the present invention. The sensitivity characterizes the sensitivity of the characteristic value to the parameter changes. Therefore, the parameter set with greater sensitivity in the calculation result is the key influencing factor affecting the dominant mode of the power system.

[0064] An embodiment of the present invention provides an electronic device, comprising: a computer-readable storage medium and a processor;

[0065] The computer-readable storage medium is used to store executable instructions;

[0066] The processor is configured to read the executable instructions stored in the computer-readable storage medium and execute the method described in any one of the above embodiments.

[0067] An embodiment of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to execute the method described in any one of the above embodiments.

[0068] An embodiment of the present invention provides a computer program product, including a computer program or instructions, which implements the method described in any of the above embodiments when executed by a processor.

[0069] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A LTP system eigenvalue sensitivity analysis method considering the time-varying characteristics of parameters for power system stability analysis, characterized in that: include: The dynamic equation of the power system f in y ss (t) as the system matrix A(t) of the LTP system, and the implicit expression part A of the time-varying parameter α(t) of the power system in the system matrix A(t) is used. I and display expression part A E and calculate the partial derivative of the system matrix A(t) with respect to the time-varying parameter α(t) in, A、α、 A(t), α(t), The abbreviation of is the variation of α(t), y is the time domain trajectory of the power system, y ss (t) is the steady-state periodic trajectory of the power system; Calculate the dominant eigenvalue λ of the system matrix A(t) of the LTP system i The corresponding left and right eigenvectors r i (t), l i (t); Calculate the dominant eigenvalue λ i Partial derivative with respect to the time-varying parameter α(t) Take it as the dominant eigenvalue λ i The sensitivity of the time-varying parameter α(t) to the dominant eigenvalue λ is determined by determining the effect of the change of the time-varying parameter α(t) on the dominant eigenvalue λ. i The magnitude and direction of the impact are determined to perform stability analysis on the power system.

2. The method according to claim 1, wherein and the dominant eigenvalue λ of the system matrix A(t) of the LTP system i The corresponding right eigenvector and the dominant eigenvalue λ of the system matrix A(t) of the LTP system i The corresponding left eigenvector I is the identity matrix.

3. The method according to claim 1 or 2, wherein: The implicit expression part A of the time-varying parameter α(t) of the power system in the system matrix A(t) is I including the operating parameters of the power system; The time-varying parameter α(t) of the power system is expressed in the system matrix A(t) as E Including control parameters of the power system.

4. The method according to claim 1, wherein The dominant eigenvalue λ i Partial derivative with respect to the time-varying parameter α(t) 5. An electronic device, characterized in that: include: Computer-readable storage media and processor; The computer-readable storage medium is used to store executable instructions; The processor is configured to read the executable instructions stored in the computer-readable storage medium and execute the method according to any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to execute the method according to any one of claims 1 to 4.

7. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

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