Power system participation factor analysis method and stability analysis method

Abstract

The invention discloses a participation factor analysis method and a stability analysis method of an electric power system, and belongs to the technical field of electric power system analysis control, and the participation factor analysis method of the electric power system comprises the steps: calculating the state energy of each state of a linear period time-varying system after linearization of the electric power system; calculating modal energy of each mode in the linear period time-varying system; and finally, taking the ratio of the two as a participation factor corresponding to the kth mode lambda k and the ith state xi (t). According to the mode, the correlation degree between each mode and each state can be accurately described. The module value of each element in the finally obtained participation factor matrix of the linear periodic time-varying system can represent the correlation degree between the corresponding state and mode of the element in the linear periodic time-varying system, and the element with the larger module value represents the higher correlation degree between the corresponding state and mode. And a theoretical basis can be provided for subsequent stability analysis and system controller pre-design.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system analysis and control, and more specifically, relates to a participation factor analysis method and a stability analysis method for a power system. Background Art

[0002] The small-disturbance stability of power systems has long been a focus of attention. Given the complex broadband oscillations in power systems, especially those in power electronics, a deep understanding of the correlations between states and modes is key to suppressing oscillations. Classical participation factor analysis, a key metric for measuring the mutual contribution between states and modes, has been a key focus of research since its initial introduction. However, current research primarily relies on time-invariant eigenvectors. Since the states and modal spaces of linear periodic time-varying systems are linked by time-varying eigenvectors, defining their mutual contribution is rarely explored in the literature.

[0003] Considering the different properties of linear periodic time-varying power systems compared to linear time-invariant systems, such as initial moment uncertainty and oscillation mode frequency shift, research based on the state / modal energy perspective helps to reveal the impact of these properties on the state-mode correlation characteristics.

[0004] The periodic time-varying nature of linear periodic time-varying eigenvectors poses new challenges. Whether the LTI state / modal energy formulation constructed based on time-invariant eigenvectors is applicable to linear periodic time-varying systems requires further exploration. Therefore, to meet the stability analysis requirements of power electronic systems with general time-varying characteristics, the development of a linear periodic time-varying power system participation factor analysis method based on the state-modal energy perspective is crucial. Summary of the Invention

[0005] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a participation factor analysis method and a stability analysis method for an electric power system, the purpose of which is to solve the technical problem that the prior art often uses a linear time-invariant system to model and analyze the electric power system, and is unable to accurately characterize the stability characteristics of a general periodic time-varying electric power system.

[0006] To achieve the above object, according to one aspect of the present invention, a method for analyzing participation factors of a power system is provided, comprising:

[0007] S1: Calculate the states x of the linear periodic time-varying system obtained after linearization of the power system i The state energy {η i (t)}, i = {1, 2, ..., n}, n is the total number of states;

[0008] S2: Based on the states x in the linear periodic time-varying system iThe state energy {η i (t)} and each mode λ in the linear periodic time-varying system k The modal energy {ξ k (t)} Calculate each mode λ in the linear periodic time-varying system k The modal energy {ξ k (t)}, k = {1, 2, ..., n};

[0009] S3: The kth mode λ in the linear periodic time-varying system k The modal energy ξ k (t) and the state energy η of the i-th state i The ratio of (t) is taken as the kth mode λ k With the i-th state x i (t) corresponds to the participation factor p ik , and then the participation factor matrix of the linear periodic time-varying system is obtained.

[0010] Furthermore, the S1 includes: using the formula Calculate the state energy η of the i-th state of the linear periodic time-varying system i (t).

[0011] Furthermore, the S2 includes: based on the mapping relationship between the state energy and the modal energy of each state in the linear periodic time-varying system

[0012]

[0013] Using the formula Calculate the modal energy {ξ k (t)}; where the state vector x(t)=[x1(t),…,x i (t),…,x n (t)], superscript T indicates transposition, r k(h) is the kth mode λ k Corresponding to the hth order frequency component of the right eigenvector, l k(-h) is the kth mode λ k Corresponding to the -hth order frequency component of the left eigenvector.

[0014] Furthermore, the formula is used in S2 Calculate the modal energy {ξ k (t)}, including: using Calculate the modal energy {ξ k (t)}; where lk (t) is the kth mode λ of the linear periodic time-varying system k The corresponding left eigenvector, r k (t) is the kth mode λ of the linear periodic time-varying system k The corresponding right eigenvector.

[0015] Furthermore, the S3 includes: using formula p ik ={r ik (t)l ki (t)}0 Calculate the kth mode λ k With the i-th state x i Participation factor p of (t) ik , and then the participation factor matrix of the linear periodic time-varying system is obtained.

[0016] Furthermore, the participation factor matrix of the linear periodic time-varying system is obtained in S3, including: using P LTP ={p ik}={R(t)⊙L T (t)}0 represents the participation factor matrix P of the linear periodic time-varying system LTP ; where ⊙ represents the Hadamard product, {}0 represents the average value of the expression in the brackets within one cycle, R(t) is the right eigenvector matrix of the linear periodic time-varying system, and L T (t) is the transpose of the left eigenvector matrix of the linear periodic time-varying system.

[0017] According to another aspect of the present invention, a method for analyzing the stability of an electric power system is provided, comprising: obtaining a participation factor matrix of the linear periodic time-varying system using the above-mentioned participation factor analysis method of the electric power system; and performing stability analysis using the participation factor matrix of the linear periodic time-varying system.

[0018] According to another aspect of the present invention, there is provided a stability analysis device for a power system, comprising:

[0019] The state energy calculation module is used to calculate the states x of the linear periodic time-varying system obtained after the power system is linearized. i The state energy {η i (t)}, i = {1, 2, ..., n}, n is the total number of states;

[0020] A modal energy calculation module is used for calculating the modal energy of each state x in the linear periodic time-varying system. i The state energy {η i (t)} and each mode λ in the linear periodic time-varying system k The modal energy {ξ k(t)} Calculate each mode λ in the linear periodic time-varying system k The modal energy {ξ k (t)}, k = {1, 2, ..., n};

[0021] The participation factor calculation module is used to calculate the kth mode λ in the linear periodic time-varying system. k The modal energy ξ k (t) and the state energy η of the i-th state i The ratio of (t) is taken as the kth mode λ k With the i-th state x i (t) corresponds to the participation factor p ik , and then obtain the participation factor matrix of the linear periodic time-varying system;

[0022] The stability analysis module is used to perform stability analysis using the participation factor matrix of the linear periodic time-varying system.

[0023] According to another aspect of the present invention, a stability analysis system for a linear periodic time-varying power system is provided, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the power system stability analysis method when executing the computer program.

[0024] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the power system stability analysis method are implemented.

[0025] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0026] The present invention provides a method for analyzing the participation factors of a power system, which calculates the various states x of a linear periodic time-varying power system. i The state energy {η i (t)}, and then calculate the various modes λ in the linear periodic time-varying system k The modal energy {ξ k (t)}; finally, the ratio of the two is taken as the kth mode λ k With the i-th state x i (t) corresponds to the participation factor p ik , this method can accurately describe each mode λ k With each state x iThe modulus of each element in the participation factor matrix of the linear periodic time-varying system can characterize the degree of correlation between the state and mode corresponding to the element in the linear periodic time-varying system. The larger the modulus, the higher the correlation between the corresponding state and mode. This can provide a theoretical basis for subsequent stability analysis and system controller pre-design. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a flow chart of a method for analyzing participation factors of a power system provided in Example 1 of the present invention;

[0028] Figure 2 This is a flow chart of a method for analyzing the stability of a power system provided in Example 1 of the present invention. DETAILED DESCRIPTION

[0029] 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.

[0030] Example 1

[0031] This embodiment provides a method for analyzing participation factors of a power system. Figure 1 As shown, it includes: S1: Calculate the various states x of the linear periodic time-varying system obtained after the power system is linearized i The state energy {η i (t)}, i = {1, 2, ..., n}, n is the total number of the states; S2: based on the states x in the linear periodic time-varying system i The state energy {η i (t)} and each mode λ in the linear periodic time-varying system k The modal energy {ξ k (t)} Calculate each mode λ in the linear periodic time-varying system k The modal energy {ξ k (t)}, k={1,2,...,n}; S3: the kth mode λ in the linear periodic time-varying system k The modal energy ξ k (t) and the state energy η of the i-th state i The ratio of (t) is taken as the kth mode λ k With the i-th state x i (t) corresponds to the participation factor pik , and then the participation factor matrix of the linear periodic time-varying system is obtained.

[0032] As an optional implementation, the S1 includes: using the formula Calculate the state energy η of the i-th state of the linear periodic time-varying system i (t).

[0033] Specifically, since the state energy does not contain the information of the system matrix A, the quadratic form used to define the state energy is It is general and also applicable to linear periodic time-varying systems. From this, the state energy η of the linear periodic time-varying system can be directly obtained. i (t)Expression.

[0034] As an optional implementation, S2 includes: based on the mapping relationship between the state energy and the modal energy of each state in the linear periodic time-varying system:

[0035]

[0036] Using the formula

[0037]

[0038] Calculate the modal energy {ξ k (t)}; where the state vector x(t)=[x1(t),…,x i (t),…,x n (t)], superscript T indicates transposition, r k(h) is the kth mode λ k Corresponding to the hth order frequency component of the right eigenvector, l k(-h) is the kth mode λ k Corresponding to the -hth order frequency component of the left eigenvector. Further, the formula is used in S2 Calculate the modal energy {ξ k (t)}, including: using

[0039]

[0040] Calculate the modal energy {ξ k (t)}; where l k (t) is the kth mode λ of the linear periodic time-varying system k The corresponding left eigenvector, r k (t) is the kth mode λ of the linear periodic time-varying system k The corresponding right eigenvector.

[0041] Specifically, in order to study the form of the modal energy of the linear periodic time-varying system, we first calculate the state energy η i (t) is decomposed into:

[0042]

[0043] Among them, the identity matrix I can be expressed as the product of the left and right eigenvectors, and then:

[0044]

[0045] The formula contains terms related to the initial time t', corresponding to the modal energy excited at different initial times. The uncertainty brought by this initial time can be taken into account by introducing the expectation operator. At the same time, in order to consider the mode frequency shift characteristics caused by the time-varying characteristics of the eigenvector, the eigenvector in the above formula is decomposed into a Fourier series representation, and the part related to t' is rewritten. The decomposition form of the state energy sum can be rewritten as:

[0046]

[0047] Based on the mapping relationship between the state energy and modal energy of the linear periodic time-varying system The mode λ in a linear periodic time-varying system can be directly defined k The modal energy is represented by the symbol ξ k (t) means:

[0048]

[0049] Among them, {}0 means taking the average value of the expression in the brackets within one period.

[0050] Verifiable, since h corresponds to mode λ k The different orders of (λ k +jhω), we can further convert λ k The modal energy of is decomposed into different orders, and its h-th order modal energy is expressed as ξ k(h) (t):

[0051]

[0052] h-order modal energy ξ k(h) The sum of (t) is equal to the mode λ k The modal energy ξ k (t):

[0053]

[0054] As an optional implementation, the S3 includes: using formula pik ={r ik (t)l ki (t)}0 Calculate the kth mode λ k With the i-th state x i Participation factor p of (t) ik , and then obtain the participation factor matrix of the linear periodic time-varying system. Further, using

[0055] P LTP ={p ik}={R(t)⊙L T (t)}0

[0056] The participation factor matrix P of the linear periodic time-varying system is represented by LTP ; where ⊙ represents the Hadamard product, {}0 represents the average value of the expression in the brackets within one cycle, R(t) is the right eigenvector matrix of the linear periodic time-varying system, and L T (t) is the transpose of the left eigenvector matrix of the linear periodic time-varying system.

[0057] Using the linear periodic time-varying system state energy η i (t) and modal energy ξ k (t) form, and further use the mapping relationship between them as the characterization state x i (t) and mode λ k When considering the state x i (t) contributes to the pattern, set the rest of the states to 0, and then we can get:

[0058] ξ k η i ={r ik (t)l ki (t)}0=p ik

[0059] Among them, r ik (t) is the element in the i-th row and k-th column of the right eigenvector matrix R(t), l ki (t) is the element in the kth row and ith column of the left eigenvector matrix L(t), and the coefficient p ik ={r ik (t)l ki (t)}0 is used to evaluate the correlation characteristics between the i-th state and the k-th eigenvalue.

[0060] Furthermore, i,k=1,2,...,n, the participation factor matrix of the linear periodic time-varying system is obtained as:

[0061] P LTP ={p ik} i,k＝1,2,...，n= {R(t)⊙L T (t)}0

[0062] Where ⊙ represents the Hadamard product, which is defined as the multiplication of corresponding elements of the matrix, that is, (A⊙B) ik =a ik b ik The modulus value of each element in the P matrix can represent the degree of correlation between the state and mode corresponding to the element in the linear periodic time-varying system. The larger the modulus value of the element, the higher the correlation between the corresponding state and mode.

[0063] Example 2

[0064] like Figure 2 As shown, this embodiment provides a method for analyzing the stability of an electric power system, comprising: obtaining a participation factor matrix of the linear periodic time-varying system using the participation factor analysis method for the electric power system provided in Example 1; and performing stability analysis using the participation factor matrix of the linear periodic time-varying system. Specifically, the modulus value of each element in the participation factor matrix P of the linear periodic time-varying system can characterize the degree of correlation between the state and mode corresponding to the element in the linear periodic time-varying system, and the larger the modulus value, the higher the correlation between the corresponding state and mode. The modulus value of each element in the P matrix can be used to perform stability analysis and control design of the linear periodic time-varying system.

[0065] Example 3

[0066] This embodiment provides a stability analysis device for a power system, including: a state energy calculation module, a modal energy calculation module, a participation factor calculation module, and a stability analysis module.

[0067] The state energy calculation module is used to calculate the states x of the linear periodic time-varying system obtained after the power system is linearized. i The state energy {η i (t)}, i = {1, 2, ..., n}, n is the total number of states;

[0068] A modal energy calculation module is used for calculating the modal energy of each state x in the linear periodic time-varying system. i The state energy {η i (t)} and each mode λ in the linear periodic time-varying system k The modal energy {ξ k (t)} Calculate each mode λ in the linear periodic time-varying system k The modal energy {ξ k (t)}, k = {1, 2, ..., n};

[0069] The participation factor calculation module is used to calculate the kth mode λ in the linear periodic time-varying system. k The modal energy ξ k (t) and the state energy η of the i-th state i The ratio of (t) is taken as the kth mode λ k With the i-th state x i (t) corresponds to the participation factor p ik , and then obtain the participation factor matrix of the linear periodic time-varying system;

[0070] The stability analysis module is used to perform stability analysis using the participation factor matrix of the linear periodic time-varying system.

[0071] Example 4

[0072] This embodiment provides a stability analysis system for a linear periodic time-varying power system, including a memory and a processor. The memory stores a computer program, and the processor executes the steps of the power system stability analysis method provided in Example 2 when executing the computer program.

[0073] Example 5

[0074] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the power system stability analysis method provided in Embodiment 2 are performed.

[0075] 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 method for analyzing participation factors of a power system, characterized in that: include: S1: Calculate the states x of the linear periodic time-varying system obtained after linearization of the power system i The state energy {η i (t)}, i = {1, 2, ..., n}, n is the total number of states; S2: Based on the states x in the linear periodic time-varying system i The state energy {η i (t)} and each mode λ in the linear periodic time-varying system k The modal energy {ξ k (t)} Calculate each mode λ in the linear periodic time-varying system k The modal energy {ξ k (t)}, k = {1, 2, ..., n}; S3: The kth mode λ in the linear periodic time-varying system k The modal energy ξ k (t) and the state energy η of the i-th state i The ratio of (t) is taken as the kth mode λ k With the i-th state x i (t) corresponds to the participation factor p ik , and then the participation factor matrix of the linear periodic time-varying system is obtained.

2. The method for analyzing participation factors of a power system according to claim 1, wherein: Said S1 comprises: using the formula Calculate the state energy η of the i-th state of the linear periodic time-varying system i (t).

3. The method for analyzing participation factors of a power system according to claim 1, wherein: The S2 includes: Based on the mapping relationship between the state energy and modal energy of each state in the linear periodic time-varying system Using the formula Calculate the modal energy {ξ k (t)}; Wherein, the state vector x(t)=[x1(t),…,x i (t),…,x n (t)], superscript T indicates transposition, r k(h) is the kth mode λ k Corresponding to the hth order frequency component of the right eigenvector, l k(-h) is the kth mode λ k Corresponding to the -hth order frequency component of the left eigenvector.

4. The method for analyzing participation factors of a power system according to claim 3, wherein: The formula used in S2 is Calculate the modal energy {ξ k (t)}, including: using Calculate the modal energy {ξ k (t)}; where l k (t) is the kth mode λ of the linear periodic time-varying system k The corresponding left eigenvector, r k (t) is the kth mode λ of the linear periodic time-varying system k The corresponding right eigenvector.

5. The method for analyzing participation factors of a power system according to claim 1, wherein: The S3 includes: using the formula p ik ={r ik (t)l ki (t)}0 Calculate the kth mode λ k With the i-th state x i Participation factor p of (t) ik , and then the participation factor matrix of the linear periodic time-varying system is obtained, where {}0 means taking the average value of the expression in the brackets within one period.

6. The method for analyzing participation factors of a power system according to claim 5, wherein: The participation factor matrix of the linear periodic time-varying system is obtained in S3, including: Using P LTP ={p ik }={R(t)⊙L T (t)}0 represents the participation factor matrix P of the linear periodic time-varying system LTP ; Where ⊙ represents the Hadamard product, R(t) is the right eigenvector matrix, and L T (t) is the transpose of the left eigenvector matrix.

7. A method for analyzing the stability of a power system, characterized in that: include: Obtaining a participation factor matrix of the linear periodic time-varying system using the participation factor analysis method of the linear periodic time-varying system according to any one of claims 1 to 6; The stability analysis is performed using the participation factor matrix of the linear periodic time-varying system.

8. A stability analysis device for a power system, characterized in that: include: The state energy calculation module is used to calculate the states x of the linear periodic time-varying system obtained after the power system is linearized. i The state energy {η i (t)}, i = {1, 2, ..., n}, n is the total number of states; A modal energy calculation module is used for calculating the modal energy of each state x in the linear periodic time-varying system. i The state energy {η i (t)} and each mode λ in the linear periodic time-varying system k The modal energy {ξ k (t)} Calculate each mode λ in the linear periodic time-varying system k The modal energy {ξ k (t)}, k = {1, 2, ..., n}; The participation factor calculation module is used to calculate the kth mode λ in the linear periodic time-varying system. k The modal energy ξ k (t) and the state energy η of the i-th state i The ratio of (t) is taken as the kth mode λ k With the i-th state x i (t) corresponds to the participation factor p ik , and then obtain the participation factor matrix of the linear periodic time-varying system; The stability analysis module is used to perform stability analysis using the participation factor matrix of the linear periodic time-varying system.

9. A stability analysis system for a linear periodic time-varying power system, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the power system stability analysis method according to claim 7 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the power system stability analysis method according to claim 7 is implemented.

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