A power system dynamic equivalent model parameter identification method based on quasi-tridiagonal matrix inverse eigenvalue problem

Abstract

The application discloses a power system dynamic equivalent model parameter identification method based on quasi-tridiagonal matrix inverse eigenvalue problem, and belongs to the technical field of power system modeling. The method first acquires eigenvalues of key dominant oscillation modes of a power system; subsequently, structures a state matrix of an equivalent system into a quasi-tridiagonal matrix corresponding to elements and physical parameters of the equivalent system; establishes a structured inverse eigenvalue problem based on the quasi-tridiagonal matrix; and finally inversely calculates all physical parameters of the equivalent system by applying a special solving algorithm, so as to complete construction of a high-precision dynamic equivalent model. The application combines strict mathematical theory with engineering practice, overcomes defects of strong subjectivity and fuzzy physical meaning of parameters of a traditional equivalent method, realizes automation and precision of a parameter identification process, and significantly improves reliability and practicability of the equivalent model.

Description

Technical Field

[0001] This invention belongs to the field of power system modeling and simulation technology, specifically relating to a parameter identification method for a dynamic equivalent model of a power system, and particularly a method for high-precision inversion of equivalent model parameters using the inverse eigenvalue theory of quasi-tridiagonal matrices. Background Technology

[0002] Dynamic simulation and control of large-scale interconnected power grids are crucial for ensuring their safe and stable operation. Since the order of full-dimensional models is too high to meet the computational efficiency requirements of real-time analysis and control, it is necessary to dynamically equivalence the power grid, that is, to replace the external complex network with a low-order simplified model.

[0003] Currently, the widely used dynamic equivalent method, similar to the adjustment equivalent method, has the following inherent defects: First, its equivalent accuracy heavily relies on the human judgment of generator grouping, which is highly subjective, and requires regrouping under different operating modes, resulting in poor adaptability; Second, the physical meaning of the model parameters after equivalent modeling is ambiguous, making it difficult to directly correlate with the actual physical characteristics of the system, which is not conducive to subsequent controller design; Finally, such methods are mostly based on heuristic criteria and lack a rigorous mathematical theoretical foundation, and the dynamic response of the equivalent model, especially under non-rated operating points, may deviate significantly from the original system.

[0004] The inverse eigenvalue problem is a classic problem in numerical algebra, aiming to reconstruct a matrix from given spectral data. While existing mathematical research has provided several theories for matrix reconstruction, these results are largely confined to the realm of pure mathematics, and their solution algorithms are severely disconnected from the physical parameter identification problems in specific industrial scenarios such as power systems. In the field of power systems, there are currently no publicly available technical solutions that systematically apply the inverse eigenvalue problem of quasi-tridiagonal matrix structures to the identification of dynamic equivalent parameters.

[0005] Therefore, there is an urgent need in this field for a new method with a solid mathematical foundation, capable of automatically and accurately identifying equivalent model parameters, and with parameters having clear physical meaning, in order to overcome the shortcomings of traditional empirical methods. Summary of the Invention

[0006] (a) Technical problems to be solved This invention addresses the problems of existing dynamic equivalent models relying on empirical judgment, unclear physical meaning of parameters, poor adaptability, and lack of rigorous mathematical theoretical support. It provides a parameter identification method for dynamic equivalent models of power systems based on the inverse eigenvalue problem of quasi-tridiagonal matrices.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for parameter identification of dynamic equivalent models of power systems based on the inverse eigenvalue problem of quasi-tridiagonal matrices includes the following steps: S1: Obtain modal information of the power system: Through small-disturbance stability analysis or data identification based on a wide-area measurement system, obtain the characteristic values ​​Λ = {λ1, λ2,..., λk} corresponding to the k key dominant oscillation modes that need to be retained in the original power system; S2: Constructing the parameterized state matrix of the equivalent system: Based on the dynamically equivalent object, establish the state space model of the equivalent system, and structure the state matrix A of the model into a quasi-tridiagonal matrix form, where the non-zero elements in matrix A correspond one-to-one with the physical parameters to be identified in the equivalent system θ = {θ1, θ2, ..., θm}, and the physical parameters include the generator inertial time constant, damping coefficient and synchronous power coefficient; S3: Establish a structured inverse eigenvalue problem: Using the eigenvalue set Λ obtained in step S1 as known spectral data, and the pseudo-tridiagonal state matrix A(θ) constructed in step S2 and determined by the parameter θ as the target to be solved, establish an inverse eigenvalue problem: A(θ)V = VΛ, where V is the eigenvector matrix; S4: Solving the inverse problem and identifying parameters: Based on the theory of solving the inverse eigenvalue problem of a quasi-tridiagonal matrix, a numerical algorithm is constructed to solve the inverse eigenvalue problem established in step S3. The algorithm uniquely determines all elements in the quasi-tridiagonal matrix A(θ) by embedding the known eigenvalue Λ into a specific Jacobi matrix structure and solving the associated Sylvester equation, thereby solving the numerical solution of the physical parameter θ of the equivalent system. S5: Generate and verify the equivalent model: Substitute the physical parameters θ identified in step S4 into the state space model of the equivalent system to complete the construction of the dynamic equivalent model; verify the effectiveness and accuracy of the equivalent model by comparing the dynamic response curves of the equivalent model with those of the original full-dimensional system under typical disturbances.

[0008] Compared with the prior art, the present invention has the following significant advantages: 1. Rigorous theoretical foundation and strong innovation: This invention is the first to creatively apply the theoretical results of the "inverse eigenvalue problem of quasi-tridiagonal matrix" in the field of pure mathematics to solve the parameter identification problem in power system engineering. The technical means are not obvious and have outstanding substantive features.

[0009] 2. High identification accuracy and strong objectivity: This invention directly performs inversion based on the essential dynamic characteristics (eigenvalues) of the system, completely avoiding the errors caused by subjective grouping and engineering approximation in traditional methods. The parameter identification process is automatically completed by mathematical algorithms, and the results are accurate and objective.

[0010] 3. Clear physical meaning: The parameters obtained from the inversion directly correspond to key physical quantities such as inertial constant and damping coefficient in the equivalent model. The model has high transparency, making it easy for engineers to understand and use for subsequent stability analysis and controller design.

[0011] 4. High universality and practicality: The method of this invention does not depend on the specific topology or operating point of the system. As long as the key modal information of the system can be obtained, the corresponding equivalent model can be constructed. It is also applicable to power systems with a high proportion of new energy sources, and has good versatility and industrial application prospects. Attached Figure Description

[0012] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0013] Figure 2 This is a dynamic equivalent diagram of a power system.

[0014] Figure 3 This is a comparison diagram of the dynamic response of the equivalent model constructed using the method of this invention and the original system under disturbance.

[0015] Figure 4 This is a schematic diagram of the structure of the pseudo-tridiagonal state matrix A(θ) involved in the method of the present invention. Detailed Implementation

[0016] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. Example

[0017] The IEEE 39-node system was used as a test case.

[0018] S1: Establish a full-dimensional detailed model of the IEEE 39-bus system in power system simulation software, perform small-disturbance stability analysis, and extract the eigenvalues ​​λ1 = -0.15 + j3.5 and λ2 = -0.08 + j4.1 of two key modes related to inter-regional low-frequency oscillations.

[0019] S2: The system of 10 generators is equivalent to a 3-machine system (1 detailed machine and 2 equivalent machines). For a certain equivalent machine group, its classical second-order model is established, and its linearized state equation is expressed in fourth-order state-space form. Its state matrix A(θ) naturally presents a quasi-tridiagonal structure. The parameters to be determined are θ = [M, D, K1, K2], which correspond to the inertial time constant, damping coefficient and synchronization power coefficient, respectively.

[0020] S3: Using λ1 and λ2 obtained in S1 as partial spectral information, and combining them with the structural constraints of matrix A(θ), we establish the inverse eigenvalue problem.

[0021] S4: Using the solver designed in this invention (whose core algorithm is based on the theory of the inverse eigenvalue problem of a quasi-tridiagonal matrix), with input λ1 and λ2, the numerical solution of parameter θ is obtained as follows: M = 12.5 s, D = 2.1 pu, K1 = 1.8 pu / rad, K2 = 0.9 pu / rad.

[0022] S5: Construct an equivalent model from the identified parameters and perform a three-phase short-circuit time-domain simulation. The results are as follows: Figure 3 As shown, the power angle swing curve of the equivalent system is highly consistent with the response of the dominant machine group in the full-dimensional system, proving the effectiveness of the method of the present invention.

Claims

1. A method for parameter identification of dynamic equivalent models of power systems based on the inverse eigenvalue problem of quasi-tridiagonal matrices, characterized in that, Includes the following steps: Obtain the eigenvalues ​​of the key dominant oscillation modes of the power system; The state matrix of the equivalent system is structured into a quasi-tridiagonal matrix whose elements correspond to the physical parameters to be identified. Using the eigenvalues ​​as known quantities and the quasi-tridiagonal matrix as the quantities to be determined, a structured inverse eigenvalue problem is established. An algorithm for solving the inverse eigenvalue problem of a quasi-tridiagonal matrix is ​​applied to solve the elements of the quasi-tridiagonal matrix, thereby obtaining the physical parameters of the equivalent system. The final dynamic equivalent model is constructed using the physical parameters.

2. The method according to claim 1, characterized in that, The physical parameters include at least one of the equivalent generator's inertial time constant, damping coefficient, and synchronous power coefficient.

3. The method according to claim 1, characterized in that, The eigenvalues ​​of the key dominant oscillation modes are obtained by performing small-disturbance stability analysis on a full-dimensional power system model, or by processing field data collected by a wide-area measurement system.

4. The method according to claim 1, characterized in that, The algorithm for solving the inverse eigenvalue problem of a quasi-tridiagonal matrix includes the steps of embedding known eigenvalues ​​into a Jacobi matrix and determining the elements of the quasi-tridiagonal matrix by solving the Sylvester equation.

5. A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the method as described in any one of claims 1 to 4.

6. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor executes the program to implement the method as described in any one of claims 1 to 4.

Images