An EIGD time-delay power system stability analysis method and device

Abstract

The application belongs to the technical field of power systems, and discloses an EIGD time-delay power system stability analysis method and device, wherein the method comprises the following steps: a linear model of the time-delay power system is established, and the differential equation in the model is converted into an abstract Cauchy problem by using an infinitesimal generator; a group of discrete points is selected for each time-delay interval of the time-delay power system, a discrete function space is established according to the discrete points, and the time-delay variable is discretized to generate a low-order partial infinitesimal generator discretization matrix; displacement and inverse transformation are performed on the discretization matrix to obtain an inverse matrix, and the characteristic value of the system is obtained according to the inverse matrix; the characteristic value is checked by using the Newton method to obtain the accurate characteristic value and the characteristic vector, and the stability of the time-delay power system is analyzed and judged. The method solves the problem of large matrix LU decomposition calculation amount in the existing EIGD time-delay power system characteristic value sparse calculation method based on the DDAE model.

Description

Technical Field

[0001] This application relates to the field of power system technology, and in particular to an EIGD time-delay power system stability analysis method and apparatus. Background Technology

[0002] With the continuous expansion of the Internet, wide-area measurement systems based on phasor measurement units have been widely used in power systems. However, wide-area measurement signals generally suffer from communication delays during acquisition, routing, transmission, processing, and execution. For example, the communication delay of a wide-area damped control system based on synchronous measurement varies from tens to hundreds of milliseconds, while the communication delay and sampling-induced delay of a frequency control system can reach several seconds. These delays significantly impact the performance of wide-area controllers and pose risks to the stable operation of power systems. Therefore, the impact of wide-area communication delays must be considered in the small-disturbance stability analysis and controller design of power systems involving wide-area control.

[0003] Currently, the stability studies of time-delay systems mainly employ two methods: time-domain methods and frequency-domain methods. Time-domain analysis primarily utilizes the Lyapunov-Krasovskii functional to propose sufficient conditions for determining the asymptotic stability of the system. Time-domain analysis methods can effectively handle varying time delays. Recent research has focused on using Jensen and Wiringer inequalities in functional derivative estimation to reduce quadratic integral terms into integral inequalities, thereby reducing decision variables and lowering the conservatism of the criterion. In the frequency domain, the characteristic equation of a time-delay power system contains time-delay-related exponential terms, and the system has infinitely many eigenvalues. To facilitate analysis, methods such as the Padé approximation and Rekasius transform are commonly used to eliminate exponential time-delay terms. Another type of frequency-domain analysis method is the eigenvalue method based on spectral discretization, which directly calculates eigenvalues ​​without performing any transformations on the transcendental characteristic equation of the time-delay power system.

[0004] The basic principle of the eigenvalue method based on spectral discretization is to transform the rightmost or minimum damping ratio eigenvalues ​​of a time-delay power system into partial eigenvalues ​​of a high-dimensional discretized matrix of two semigroup operators (including infinitesimal generators and solution operators). Chinese invention patent publication CN108647906A proposes an eigenvalue algorithm for large-scale time-delay power systems based on explicit infinitesimal generator discretization (EIGD). This algorithm discretizes only the time-delay state variables to calculate the eigenvalues ​​of the time-delay power system, thereby determining the system's stability. However, the small-disturbance stability analysis of time-delay power systems using this method is based on a delayed differential equation (DDE) model. The DDE model requires the elimination of the system's algebraic equations, which can easily introduce more state variables, limiting the improvement of computational efficiency. Researchers have proposed a sparse calculation method for eigenvalues ​​of EIGD time-delay power systems based on the Delayed Differential-Algebraic Equation (DDAE) model. The DDAE model retains the algebraic equations and directly discretizes the time-delay variables, thereby efficiently calculating the key eigenvalues ​​of the time-delay power system.

[0005] The inventors of this application have discovered that existing sparse calculation methods for eigenvalues ​​of time-delay power systems based on the DDAE model for EIGD suffer from a large computational burden due to the existence of singular matrices in the discretized submatrices of the infinitesimal generator matrix, which limits further improvements in the algorithm's computational efficiency. Summary of the Invention

[0006] This application provides an EIGD-based method and apparatus for stability analysis of time-delay power systems, addressing the problem of large computational load in existing EIGD eigenvalue sparse calculation methods for time-delay power systems based on the DDAE model, which suffer from singular matrices in the discretized submatrices of infinitesimal generators. To provide a basic understanding of some aspects of the disclosed embodiments, a brief summary is given below. This summary is not intended as a general commentary, nor is it intended to identify key / important components or describe the scope of protection of these embodiments. Its sole purpose is to present some concepts in a simple form as a prelude to the detailed description that follows.

[0007] According to a first aspect of the embodiments of this application, an EIGD time-delay power system stability analysis method is provided, comprising:

[0008] A linearized model of the time-delay power system is established, and the differential equations in the linearized model are transformed into an abstract Cauchy problem using infinitesimal generators.

[0009] For each time delay interval of the time-delay power system, a set of discrete points are selected, a discrete function space is established based on the discrete points, and the time delay variables are discretized in the discrete function space to generate a partial infinitesimal generator discretization matrix of the low-order time-delay power system.

[0010] The infinitesimal generator discretization matrix is ​​shifted and inversely transformed to obtain the inverse matrix, and the eigenvalues ​​of the time-delay power system are obtained based on the inverse matrix.

[0011] The eigenvalues ​​are verified using Newton's method to obtain the precise eigenvalues ​​and eigenvectors of the time-delay power system, and the stability of the time-delay power system is analyzed and judged based on the precise eigenvalues ​​and eigenvectors.

[0012] In one embodiment, the step of establishing a linearized model of the time-delay power system and transforming the differential equations in the linearized model into an abstract Cauchy problem using infinitesimal generators further includes:

[0013] The small-disturbance stability analysis model of a time-delay power system is described by an augmented form of a set of time-delay differential equations.

[0014] In one embodiment, the linearized model of the time-delay power system in this method takes the form of:

[0015]

[0016] In the formula, and These represent the state variables and algebraic variables of the time-delay power system, respectively; d = n + l, where d is the dimension of Δz, n is the dimension of Δz, and l is the dimension of Δy; Δz r(p) =e r(p) Δz represents the r(p)th element of Δz. Let r(p) be the unit vector. Let Δz be the time-delay variable. r(p) (t-τ p The coefficient vector of τ, p = 1, 2, ..., q; p >0 and different time delay constants;

[0017] In the formula, E and J are both d-dimensional square matrices.

[0018]

[0019] in,

[0020] In one embodiment, the step of establishing a linearized model of the time-delay power system and transforming the differential equations in the linearized model into an abstract Cauchy problem using infinitesimal generators further includes:

[0021] The state variables and algebraic variables of the time-delay power system are divided into time-delay-related terms and time-delay-independent terms, respectively, so that the differential equations can be rewritten based on the division of state variables and algebraic variables.

[0022] In one embodiment, the step of dividing the state variables and algebraic variables of the time-delay power system into time-delay-related terms and time-delay-independent terms, respectively, and rewriting the differential equation based on the division of state variables and algebraic variables, further includes:

[0023] The state variable Δx is classified into non-time-delay state variables. and time-delay state variables Right now

[0024] Δx=[(Δx (1) ) T ,(Δx (2) ) T ] T n1 + n2 = n;

[0025] The algebraic variable Δy is divided into non-time-delay algebraic variables. and time-delay algebraic variables Right now

[0026] Δy=[(Δy (1) ) T ,(Δy (2) ) T ] T , l1+l2=l.

[0027] In one embodiment, the method further includes the following steps: selecting a set of discrete points for each time delay interval of the time-delay power system, establishing a discrete function space based on the discrete points, and discretizing the time-delay variables in the discrete function space to generate a partial infinitesimal generator discretization matrix of the low-order time-delay power system:

[0028] For each time delay interval

[0029] [-τ p [0](p=1,2,…,q)

[0030] Select a set of discrete points

[0031]

[0032] Where α k U is the Nth order second-kind Chebyshev polynomial NThe zero point of (·), i.e.

[0033]

[0034] In one embodiment, the method further includes the following steps: selecting a set of discrete points for each time delay interval of the time-delay power system, establishing a discrete function space based on the discrete points, and discretizing the time-delay variables in the discrete function space to generate a partial infinitesimal generator discretization matrix of the low-order time-delay power system:

[0035] The discretization matrix of the partially infinitesimal generators of the generated time-delay power system is in the form of double Scur complement.

[0036] In one embodiment, the step of performing shift and inverse transformation on the infinitesimal generator discretization matrix to obtain the inverse matrix, and obtaining the eigenvalues ​​of the time-delay power system based on the inverse matrix, further includes:

[0037] The inverse matrix is ​​calculated using the implicit restart Arnoldi algorithm, and then the eigenvalues ​​of the time-delay power system are obtained.

[0038] In one embodiment, the step of performing shift and inverse transformation on the infinitesimal generator discretization matrix to obtain the inverse matrix, and obtaining the eigenvalues ​​of the time-delay power system based on the inverse matrix, further includes:

[0039] In the process of calculating the inverse matrix, the product of the inverse vectors of the inverse matrix is ​​solved by iterative method to obtain the eigenvalues ​​of the time-delay power system.

[0040] In one embodiment, the step of obtaining the eigenvalues ​​of the time-delay power system by iteratively solving the product of the inverse vectors of the inverse matrix during the calculation of the inverse matrix further includes:

[0041] The subspace method is used to calculate the eigenvalues ​​of the maximum set number of moduli of the discretized matrix of the solution subpart, including the matrix-vector product in the process of iteratively forming Krylov subvectors.

[0042] In one embodiment, the method, which uses the subspace method to calculate the eigenvalues ​​of the maximum set number of moduli of the discretized sub-matrix, including the matrix-vector product step in the iterative formation of Krylov sub-vectors, further includes:

[0043] The power method is used to calculate the matrix-vector product.

[0044] In one embodiment, the method, which uses the subspace method to calculate the eigenvalues ​​of the maximum set number of moduli of the discretized sub-matrix, including the matrix-vector product step in the iterative formation of Krylov sub-vectors, further includes:

[0045] The matrix inverse-vector product is represented as an augmented matrix, and the matrix inverse-vector product is calculated using the inverse power method.

[0046] In one embodiment, the method further includes the step of verifying eigenvalues ​​using Newton's method to obtain precise eigenvalues ​​and eigenvectors of the time-delay power system, and analyzing and judging the stability of the time-delay power system based on the precise eigenvalues ​​and eigenvectors:

[0047] After obtaining the eigenvalues ​​of the time-delay power system, the precise eigenvalues ​​are obtained by sequentially performing spectral mapping, inverse displacement-inverse transformation, and Newton's check.

[0048] According to a second aspect of the embodiments of this application, an EIGD time-delay power system stability analysis device is provided.

[0049] In one embodiment, the apparatus includes: a linear model building module, a discrete matrix generation module, an eigenvalue acquisition module, and a stability analysis module; wherein,

[0050] The linear model building module is used to build a linearized model of a time-delay power system, and uses infinitesimal generators to transform the differential equations in the linearized model into an abstract Cauchy problem.

[0051] The discrete matrix generation module is used to select a set of discrete points for each time delay interval of the time-delay power system, establish a discrete function space based on the discrete points, and discretize the time-delay variables in the discrete function space to generate a low-order partial infinitesimal generator discretization matrix of the time-delay power system.

[0052] The eigenvalue acquisition module is used to perform shift and inverse transformation on the discretized matrix of infinitesimal generators to obtain the inverse matrix, and to obtain the eigenvalues ​​of the time-delay power system based on the inverse matrix.

[0053] The stability analysis module is used to verify the eigenvalues ​​using Newton's method to obtain the precise eigenvalues ​​and eigenvectors of the time-delay power system, and to analyze and judge the stability of the time-delay power system based on the precise eigenvalues ​​and eigenvectors.

[0054] According to a third aspect of the embodiments of this application, a computer device is provided.

[0055] In some embodiments, the computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the method as described in the first aspect.

[0056] According to a fourth aspect of the embodiments of this application, a computer-readable storage medium is provided.

[0057] In some embodiments, a computer program is stored on a computer-readable storage medium; the computer program is executed by a processor to implement the steps of the method as described in the first aspect.

[0058] The technical solutions provided in this application embodiment may include the following beneficial effects:

[0059] On the one hand, the small-disturbance stability analysis of time-delay power systems in this application is based on the DDAE model, avoiding the introduction of more state variables when eliminating algebraic equations using the DDE model. On the other hand, by representing the partially infinitesimal discretized matrix as a "double Scur complement" structure, and using this form to obtain the expression for the product of the displacement inverse matrix and the vector of the infinitesimal generator discretized matrix, the sparsity of the discretized matrix and the system state matrix can be fully utilized. The product of this matrix and vector can be solved using the power method and the inverse power method, which significantly improves the computational efficiency of the eigenvalue calculation method for low-order EIGD time-delay power systems, and further improves the efficiency of stability analysis.

[0060] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0061] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0062] Figure 1 This is a flowchart of the EIGD time-delay power system stability analysis method provided in the embodiments of this application;

[0063] Figure 2 This is a structural diagram of the EIGD time-delay power system stability analysis device provided in the embodiments of this application;

[0064] Figure 3 This is a schematic diagram of the structure of a computer device according to an exemplary embodiment. Detailed Implementation

[0065] The following description and accompanying drawings fully illustrate specific embodiments described herein to enable those skilled in the art to practice them. Some embodiments may include or substitute parts and features of other embodiments. The scope of the embodiments herein encompasses the entire scope of the claims and all available equivalents thereof. Throughout this document, the terms “first,” “second,” etc., are used only to distinguish one element from another without requiring or implying any actual relationship or order between the elements. Indeed, a first element can also be referred to as a second element, and vice versa. Furthermore, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a structure, apparatus, or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a structure, apparatus, or device. Without further limitation, an element defined by the phrase “comprising one…” does not exclude the presence of other identical elements in the structure, apparatus, or device that includes said element. The various embodiments described herein are presented in a progressive manner, with each embodiment focusing on its differences from other embodiments; similar or identical parts between embodiments can be referred to interchangeably.

[0066] In this document, unless otherwise stated, the term "multiple" means two or more.

[0067] Figure 1 A flowchart of the EIGD time-delay power system stability analysis method of this application is shown, as follows: Figure 1 As shown:

[0068] S1: Establish a linearized model of the time-delay power system, and use infinitesimal generators to transform the differential equations in the linearized model into an abstract Cauchy problem.

[0069] In practical implementation, a linearized mathematical model of the time-delay power system is established, in which the small-disturbance stability analysis model of the time-delay power system is described by an augmented form of the time-delay differential equation system.

[0070] Specifically, the system state variables and algebraic variables are divided into time-delay related terms and time-delay unrelated terms, respectively. Based on the division of system variables, the system differential equations are rewritten.

[0071] Furthermore, by utilizing infinitesimal generators, the formulas in the linearized mathematical model of the time-delay power system are transformed into an abstract Cauchy problem. Based on this, solving for the eigenvalues ​​of the linearized model is transformed into solving for infinitesimal generators. eigenvalues.

[0072] In some embodiments of this application, the linearized time-delay power system model is as follows:

[0073]

[0074] In the formula, and These are the state variables and algebraic variables of the time-delay power system, respectively; d = n + l, where d is the dimension of Δz, n is the dimension of Δz, and l is the dimension of Δy; Δz r(p) =e r(p) Δz represents the r(p)th element of Δz. Let r(p) be the unit vector. Let Δz be the time-delay variable. r(p) (t-τ p The coefficient vector of τ, p = 1, 2, ..., q; p >0 and different time delay constants;

[0075] In the formula, E and J are both d-dimensional square matrices.

[0076]

[0077] in,

[0078] In some embodiments of this application, the state variable Δx is divided into non-time-delay state variables. and time-delay state variables Right now

[0079] Δx=[(Δx (1) ) T ,(Δx (2) ) T ] T , n1+n2=n; (3)

[0080] The algebraic variable Δy is divided into non-time-delay algebraic variables. and time-delay algebraic variables Right now

[0081] Δy=[(Δy (1) ) T ,(Δy (2) ) T ] T , l1+l2=l (4)

[0082] In practical implementation, based on the division of Δx and Δy, the aforementioned E and J can be written in the following block form:

[0083]

[0084]

[0085] In the formula,

[0086] Please continue reading Figure 1 .

[0087] S2: Select a set of discrete points for each time delay interval of the time-delay power system, establish a discrete function space based on the discrete points, and discretize the time-delay variables in the discrete function space to generate a partial infinitesimal generator discretization matrix of the low-order time-delay power system.

[0088] In practical implementation, for each time delay interval

[0089] [-τ p [0](p=1,2,…,q)

[0090] Select a set of discrete points

[0091]

[0092] in, α is one of a set of discrete points; k U is the Nth order second-kind Chebyshev polynomial N The zero point of (·), i.e.

[0093]

[0094] In the discrete space, pseudospectral discretization is performed only on the time-delay-related parts, thereby generating a partial infinitesimal generator discretization matrix for the low-order time-delay power system. in, The dimension is n+Nq.

[0095] In some embodiments of this application, the generated partially discretized matrix It is in the form of "double Scur complement":

[0096]

[0097]

[0098] In the formula, It can be represented in the following form:

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] In the formula, This represents the Kronecker product operation; I Nq It is an identity matrix of dimension N*q;

[0106] In the formula, Let p be a constant matrix, p = 1, 2, ..., q.

[0107]

[0108] In the formula,

[0109] In the formula, K x The coefficient matrix is ​​composed of the coefficient vectors kp. 1′ N = [1, -1, ..., -(-1)] N ] T ;

[0110] Please continue reading Figure 1 .

[0111] S3: Perform shift and inverse transformations on the discretized matrix of infinitesimal generators to obtain the inverse matrix, and obtain the eigenvalues ​​of the time-delay power system based on the inverse matrix.

[0112] In specific implementation, The displacement processing technique is applied, and then the approximate matrix after displacement processing is obtained. After inverse transformation, the inverse matrix is ​​obtained. This transforms some of the system's eigenvalues ​​with smaller moduli into eigenvalues ​​with larger moduli.

[0113] Furthermore, the implicitly restarted Arnoldi algorithm (IRA) is used to calculate the inverse matrix obtained in step (4). In the solution process, an iterative method is used to solve for the product of the matrix inverse vectors. Ultimately, the eigenvalue λ can be obtained.

[0114] In some embodiments of this application, for large-scale time-delay power systems, the dimension of the partially infinitesimal generator discretization matrix is ​​enormous. Therefore, it is necessary to use the subspace method to calculate a set number of eigenvalues ​​λ" with the largest modulus of the solution subdiscretization matrix, where the main operation is the matrix-vector product in the iterative formation of Krylov subvectors.

[0115] Suppose that in the k-th iteration, it is necessary to calculate with vector The product of . That is The steps are as follows:

[0116] S301:

[0117] Will

[0118]

[0119] Substitute have to,

[0120]

[0121] S302:

[0122] Calculate matrix-vector product using the power method

[0123] S303:

[0124] Inverse of matrix - vector product Represented as an augmented matrix;

[0125] S304:

[0126] Calculating the matrix inverse-vector product using the inverse power method

[0127] S305:

[0128] Get v k The solution.

[0129] In step S302, the matrix-vector product is calculated using the power method as follows:

[0130]

[0131] in, This is an intermediate variable. `lu` represents the sparse triangular decomposition operation; `\` represents the left division operation, where left division of one matrix by another is equivalent to multiplying the inverse of the first matrix by the second. To The sparse triangular decomposition yields a lower triangular matrix and an upper triangular matrix, both of dimension l. To When performing sparse triangular decomposition, the left and right multiplications of the permutation matrix are performed, with each dimension being l.

[0132] In step S303, the matrix inverse-vector product can be expressed as an augmented matrix in the form of:

[0133]

[0134] In step S304, the matrix inverse-vector product is calculated using the inverse power method as follows:

[0135]

[0136] in, It is an intermediate variable. To The sparse triangular decomposition yields lower and upper triangular matrices of dimension n+Nq.

[0137] in, To When performing sparse triangular decomposition, the left and right multiplications of the permutation matrix are of dimension n+Nq; S is an (n+Nq)×l dimensional matrix. For D * The sparse triangular decomposition yields a lower triangular matrix and an upper triangular matrix, both of dimension l. For D * When performing sparse triangular decomposition, the left and right multiplications are performed on the permutation matrix, both of dimension l.

[0138] S4: Verify the eigenvalues ​​using Newton's method to obtain the precise eigenvalues ​​and eigenvectors of the time-delay power system, and analyze and judge the stability of the time-delay power system based on the precise eigenvalues ​​and eigenvectors.

[0139] Specifically, by using Newton's method to verify the eigenvalues ​​calculated in step S3, if they satisfy the convergence condition, the precise eigenvalues ​​λ and eigenvectors of the time-delay power system can be obtained.

[0140] In some embodiments of this application, after calculating λ", the characteristic value λ of the time-delay power system is obtained by sequentially performing spectral mapping, inverse displacement-inverse transform, and Newton's check. Before Newton's check, the approximate value of λ is calculated using the following formula:

[0141]

[0142] The precise characteristic value λ of the time-delay power system can be obtained through Newton's verification. Finally, the stability of the time-delay power system can be analyzed and judged based on the precise characteristic value and eigenvector.

[0143] To verify the effectiveness of the EIGD time-delay power system stability analysis method based on the DDAE model proposed in this application, this application presents an exemplary analysis based on an ultra-high voltage interconnected power grid. The exemplary analysis was performed in Matlab and on a desktop computer with 8GB RAM and a 3.4GHz CPU.

[0144] The parameters of the North China-Central China UHV interconnected power grid under a certain level of year are: 3220 generators, 62952 busbars, and 20 DC lines. The feedback delay and control delay of the two control loops are τ0 and τ0, respectively. f1 =220ms, τ c1 =150ms, τ f2 =250ms, τ c2 =100ms.

[0145] The dimensions of the system state variables and algebraic variables are n = 134378 and l = 243781, respectively.

[0146] To verify the effectiveness of the method proposed in this application, the computational efficiency of the method proposed in this application is compared with that of the existing EIGD time-delay power system eigenvalue calculation method based on the DDAE model. The table below shows the time required for the two methods to calculate the eigenvalues ​​of the time-delay system when the parameters are exactly the same.

[0147] Tests 1-4 show the wide-area feedback signals as the speed difference between DH#1 and GE#1 units, and between DH#7 and HQ#2 units. Tests 5-8 show the wide-area feedback signals as the tie-line power deviation.

[0148] As shown in the table below, when the wide-area feedback signal is the speed difference between units, the time consumed by the method of this application embodiment is 81% to 91% of the time consumed by the existing method. When the wide-area feedback signal is the tie-line power deviation, the running time of the method of this application embodiment is reduced by 32% to 65% compared with the existing method. As shown in the table below, after applying the efficient eigenvalue sparse calculation method proposed in this application embodiment, the time required to calculate the eigenvalues ​​of the time-delay system is greatly reduced.

[0149]

[0150] It should be understood that although the steps in the flowchart are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order constraint on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the diagram may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0151] Please see Figure 2One embodiment of this application provides an EIGD time-delay power system stability analysis device, including a linear model establishment module 10, a discrete matrix generation module 20, an eigenvalue acquisition module 30, and a stability analysis module 40; wherein,

[0152] The linear model building module 10 is used to build a linearized model of the time-delay power system and uses infinitesimal generators to transform the differential equations in the linearized model into an abstract Cauchy problem.

[0153] Discrete matrix generation module 20 is used to select a set of discrete points for each time delay interval of the time delay power system, establish a discrete function space based on the discrete points, and discretize the time delay variables in the discrete function space to generate a low-order partial infinitesimal generator discretization matrix of the time delay power system.

[0154] The eigenvalue acquisition module 30 is used to perform shift and inverse transformation on the infinitesimal generator discretization matrix to obtain the inverse matrix, and to obtain the eigenvalues ​​of the time-delay power system based on the inverse matrix.

[0155] The stability analysis module 40 is used to verify the eigenvalues ​​using Newton's method to obtain the precise eigenvalues ​​and eigenvectors of the time-delay power system, and to analyze and judge the stability of the time-delay power system based on the precise eigenvalues ​​and eigenvectors.

[0156] Specific limitations regarding the aforementioned EIGD time-delay power system stability analysis device can be found in the above description of the limitations of the EIGD time-delay power system stability analysis method, and will not be repeated here. Each module in the aforementioned EIGD time-delay power system stability analysis device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0157] In another embodiment of this application, a computer device is provided, which may be a server, and its internal structure diagram may be as follows. Figure 3 As shown, the computer device includes a processor, memory, and a network interface connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database stores static and dynamic information data. The network interface communicates with external terminals via a network connection. When the computer program is executed by the processor, it implements the steps in the above method embodiments.

[0158] Those skilled in the art will understand that Figure 3 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0159] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the steps in the method embodiments described above.

[0160] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0161] This application is not limited to the structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A stability analysis method for EIGD time-delay power systems, characterized in that, include: A linearized model of a time-delay power system is established. Infinitesimal generators are used to transform the differential equations in the linearized model into an abstract Cauchy problem. The small-disturbance stability analysis model of the time-delay power system is described by an augmented form of a system of time-delay differential equations. The state variables and algebraic variables of the time-delay power system are respectively divided into time-delay-related terms and time-delay-independent terms. The differential equations are then rewritten based on this division, including: dividing the state variable Δx into non-time-delay state variables. and time-delay state variables ,Right now ,n1+n2=n; The algebraic variable Δy is divided into non-delay algebraic variables. and time-delay algebraic variables ,Right now ，l1+l2=l； The linearization model of the time-delay power system is in the form of: ； In the formula, , and These represent the state variables and algebraic variables of the time-delay power system, respectively; d = n + l, where d is the dimension of Δz, n is the dimension of Δz, and l is the dimension of Δy; Δz r(p)= e r(p) Δz represents the r(p)th element of Δz. Let r(p) be the unit vector. Time-delay variables The coefficient vector, p=1, 2, …, q; τ p >0 and different time delay constants; In the formula, E and J are both d-dimensional square matrices. ； Among them, E 11 , E 12 , ; ; For each time delay interval of the time-delay power system, a set of discrete points is selected. A discrete function space is established based on these discrete points, and the time-delay variables are discretized within this space to generate a low-order partial infinitesimal generator discretization matrix for the time-delay power system, including: For each time delay interval (p=1, 2, …, q) Select a set of discrete points ； in, α is one of a set of discrete points; k For the Nth order Chebyshev polynomial of the second kind U N The zero point of (·), i.e. k=1, 2, …, N+1; the discretized matrix of the partially infinitesimal generators of the time-delay power system is in double Schur complement form; The infinitesimal generator discretization matrix is ​​subjected to shift and inverse transformation to obtain the inverse matrix, and the eigenvalues ​​of the time-delay power system are obtained based on the inverse matrix. The eigenvalues ​​are verified using Newton's method to obtain the precise eigenvalues ​​and eigenvectors of the time-delay power system, and the stability of the time-delay power system is analyzed and judged based on the precise eigenvalues ​​and eigenvectors.

2. The EIGD time-delay power system stability analysis method according to claim 1, characterized in that, The step of performing shift and inverse transformations on the discretized matrix of the infinitesimal generator to obtain the inverse matrix, and obtaining the eigenvalues ​​of the time-delay power system based on the inverse matrix, further includes: The inverse matrix is ​​calculated using the implicit restart Arnoldi algorithm, and then the eigenvalues ​​of the time-delay power system are obtained.

3. The EIGD time-delay power system stability analysis method according to claim 2, characterized in that, The step of performing shift and inverse transformations on the discretized matrix of the infinitesimal generator to obtain the inverse matrix, and obtaining the eigenvalues ​​of the time-delay power system based on the inverse matrix, further includes: In the process of calculating the inverse matrix, the product of the inverse vectors of the inverse matrix is ​​solved by an iterative method to obtain the eigenvalues ​​of the time-delay power system.

4. The EIGD time-delay power system stability analysis method according to claim 3, characterized in that, In the process of calculating the inverse matrix, the step of obtaining the eigenvalues ​​of the time-delay power system by iteratively solving the product of the inverse vectors of the inverse matrix further includes: The eigenvalues ​​of the maximum set number of moduli of the discrete sub-matrix are calculated using the subspace method, including matrix-vector multiplication in the process of iteratively forming Krylov subvectors.

5. The EIGD time-delay power system stability analysis method according to claim 4, characterized in that, The calculation of the eigenvalues ​​of the maximum set number of moduli of the discretized sub-matrix using the subspace method, including the matrix-vector multiplication step in the iterative formation of Krylov sub-vectors, further includes: The matrix-vector product is calculated using the power method.

6. The EIGD time-delay power system stability analysis method according to claim 5, characterized in that, The calculation of the eigenvalues ​​of the maximum set number of moduli of the discretized sub-matrix using the subspace method, including the matrix-vector multiplication step in the iterative formation of Krylov sub-vectors, further includes: The matrix inverse-vector product is represented as an augmented matrix, and the matrix inverse-vector product is calculated using the inverse power method.

7. The EIGD time-delay power system stability analysis method according to claim 1, characterized in that, The step of verifying the eigenvalues ​​using Newton's method to obtain the precise eigenvalues ​​and eigenvectors of the time-delay power system, and analyzing and judging the stability of the time-delay power system based on the precise eigenvalues ​​and eigenvectors, further includes: After obtaining the characteristic values ​​of the time-delay power system, the precise characteristic values ​​are obtained by sequentially performing spectral mapping, inverse displacement-inverse transformation, and Newton verification.

8. An EIGD time-delay power system stability analysis device, characterized in that, It includes a linear model building module, a discrete matrix generation module, an eigenvalue acquisition module, and a stability analysis module; among which, The linear model building module is used to establish a linearized model of the time-delay power system. It utilizes infinitesimal generators to transform the differential equations in the linearized model into an abstract Cauchy problem. The small-disturbance stability analysis model of the time-delay power system is described by an augmented form of a system of time-delay differential equations. The state variables and algebraic variables of the time-delay power system are respectively divided into time-delay-related terms and time-delay-independent terms. The differential equations are then rewritten based on this division, including: dividing the state variable Δx into non-time-delay state variables. and time-delay state variables ,Right now ,n1+n2=n; The algebraic variable Δy is divided into non-delay algebraic variables. and time-delay algebraic variables ,Right now ，l1+l2=l； The linearization model of the time-delay power system is in the form of: ； In the formula, These represent the state variables and algebraic variables of the time-delay power system, respectively; d = n + l, where d is the dimension of Δz, n is the dimension of Δz, and l is the dimension of Δy; Δz r(p)= e r(p) Δz represents the r(p)th element of Δz. Let r(p) be the unit vector. Time-delay variables The coefficient vector, p=1, 2, …, q; τ p >0 and different time delay constants; In the formula, E and J are both d-dimensional square matrices. ； in, ; A discrete matrix generation module is used to select a set of discrete points for each time delay interval of the time-delay power system, establish a discrete function space based on the discrete points, and discretize the time-delay variables in the discrete function space to generate a low-order partially infinitesimal generator discretization matrix of the time-delay power system, including: For each time delay interval ； Select a set of discrete points ； in, α is one of a set of discrete points; k For the Nth order Chebyshev polynomial of the second kind U N The zero point of (·), i.e. , k=1, 2, …, N+1; the discretization matrix of the partially infinitesimal generators of the time-delay power system is in double Schur complement form; The eigenvalue acquisition module is used to perform shift and inverse transformation on the infinitesimal generator discretization matrix to obtain the inverse matrix, and to obtain the eigenvalues ​​of the time-delay power system based on the inverse matrix. The stability analysis module is used to verify the eigenvalues ​​using Newton's method to obtain the precise eigenvalues ​​and eigenvectors of the time-delay power system, and to analyze and judge the stability of the time-delay power system based on the precise eigenvalues ​​and eigenvectors.

9. The EIGD time-delay power system stability analysis device according to claim 8, characterized in that, The discretization matrix of the infinitesimal generator is subjected to shift and inverse transformation to obtain the inverse matrix, and the eigenvalues ​​of the time-delay power system are obtained based on the inverse matrix, further including: The inverse matrix is ​​calculated using the implicit restart Arnoldi algorithm, and then the eigenvalues ​​of the time-delay power system are obtained.

10. The EIGD time-delay power system stability analysis device according to claim 9, characterized in that, The discretization matrix of the infinitesimal generator is subjected to shift and inverse transformation to obtain the inverse matrix, and the eigenvalues ​​of the time-delay power system are obtained based on the inverse matrix, further including: In the process of calculating the inverse matrix, the product of the inverse vectors of the inverse matrix is ​​solved by an iterative method to obtain the eigenvalues ​​of the time-delay power system.

11. The EIGD time-delay power system stability analysis device according to claim 10, characterized in that, In calculating the inverse matrix, the product of the inverse vectors of the inverse matrix is ​​obtained by iteratively solving to obtain the eigenvalues ​​of the time-delay power system, further including: The eigenvalues ​​of the maximum set number of moduli of the discrete sub-matrix are calculated using the subspace method, including matrix-vector multiplication in the process of iteratively forming Krylov subvectors.

12. The EIGD time-delay power system stability analysis device according to claim 11, characterized in that, The calculation of the eigenvalues ​​of the maximum set number of moduli of the discretized sub-matrix using the subspace method includes matrix-vector multiplication in the iterative formation of Krylov sub-vectors, and further includes: The matrix-vector product is calculated using the power method.

13. The EIGD time-delay power system stability analysis device according to claim 12, characterized in that, The calculation of the eigenvalues ​​for the maximum set number of moduli of the discretized sub-matrix using the subspace method includes matrix-vector multiplication in the iterative formation of Krylov sub-vectors, and further includes: The matrix inverse-vector product is represented as an augmented matrix, and the matrix inverse-vector product is calculated using the inverse power method.

14. The EIGD time-delay power system stability analysis device according to claim 8, characterized in that, The eigenvalues ​​are verified using Newton's method to obtain the precise eigenvalues ​​and eigenvectors of the time-delay power system. The stability of the time-delay power system is then analyzed and judged based on the precise eigenvalues ​​and eigenvectors, further including: After obtaining the characteristic values ​​of the time-delay power system, the precise characteristic values ​​are obtained by sequentially performing spectral mapping, inverse displacement-inverse transformation, and Newton verification.

15. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-7.

16. A computer-readable storage medium, characterized in that, It stores a computer program thereon; the computer program is executed by a processor to implement the method as described in any one of claims 1-7.

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