Power system eigenvalue tracking method and device, electronic equipment and storage medium

Abstract

The application discloses a power system eigenvalue tracking method and device, electronic equipment and storage medium, and is used for solving the problem that the traditional Newton method is used to track eigenvalues and is prone to tracking failure when stability analysis is performed after small disturbance of a power system in related technologies. The method comprises the following steps: obtaining variable equations before and after disturbance of the power system, and deducing a matrix pair eigen equation based on the variable equations, wherein the matrix pair eigen equation comprises a matrix bundle before disturbance and a matrix bundle after disturbance, and the matrix bundle before disturbance corresponds to a plurality of solving subintervals; initial eigenvalues and initial eigenvectors of the matrix bundle before disturbance are calculated; the initial eigenvalues and the initial eigenvectors are combined with sparse matrix decomposition to sequentially perform adaptive step Newton method solving in each solving subinterval, so that target eigenvalues and target eigenvectors of the matrix bundle after disturbance are obtained.

Description

Technical Field

[0001] This invention relates to the field of small-disturbance stability analysis technology for power systems, and in particular to a method, apparatus, electronic device, and storage medium for tracking characteristic values ​​of power systems. Background Technology

[0002] With rapid economic and social development, people's daily electricity demands are placing increasingly higher requirements on the power system. Simultaneously, the integration of numerous new energy power generation devices, the rapid development of ultra-high-voltage AC / DC transmission, and the integration of various flexible transmission equipment have gradually transformed my country's power grid into a complex and diverse mega-system. To address the significant challenges posed by increasingly complex large-scale power system dynamic models to the safe and stable operation of the power system, it is necessary to ensure the stability of the power system under various forms of emergencies, especially small-disturbance stability. Eigenvalue analysis is one of the most widely used methods in small-disturbance stability analysis. This method primarily involves linearizing the power system at an equilibrium point, followed by eigenvalue analysis of the linearized model to obtain the stability properties of the original nonlinear system.

[0003] As the scale of power grids continues to expand, the dimensionality of power system dynamic models increases dramatically. High-dimensional state matrices lead to a significant reduction in computational reliability and efficiency, posing a major challenge to small-disturbance stability analysis methods. For the oscillation modes of power systems, it is generally only necessary to calculate the key eigenvalues ​​under the underdamped modes, rather than analyzing all modes of the system. Especially for large power systems, using key eigenvalue analysis can greatly improve computational speed and reliability.

[0004] In practical applications, when a power system is subjected to disturbances, its eigenvalues ​​will also shift. In such cases, key eigenvalues ​​can be tracked and calculated without needing to recalculate the system after the disturbance. Currently, Newton's method is mainly used for eigenvalue tracking. However, when using Newton's method to track eigenvalues, because the eigenvalues ​​of large systems are relatively dense, it is possible that Newton's method will track other eigenvalues, leading to eigenvalue tracking failure and incorrect results, thus hindering accurate eigenvalue analysis. Summary of the Invention

[0005] This invention provides a power system eigenvalue tracking method, apparatus, electronic device, and storage medium, which solves or partially solves the technical problem in existing related technologies where traditional Newton's method for tracking eigenvalues ​​is prone to failure when performing stability analysis of power systems after small disturbances.

[0006] This invention provides a power system eigenvalue tracking method, the method comprising:

[0007] Obtain the variable equations of the power system before and after the disturbance, and derive the matrix pair characteristic equations based on the variable equations. The matrix pair characteristic equations include the matrix bundle before the disturbance and the matrix bundle after the disturbance. The matrix bundle before the disturbance corresponds to several solution sub-intervals.

[0008] Calculate the initial eigenvalues ​​and initial eigenvectors of the matrix bundle before the perturbation;

[0009] Based on the initial eigenvalues ​​and the initial eigenvectors, and combined with sparse matrix decomposition, the adaptive step-size Newton method is sequentially applied to each of the solution sub-intervals to obtain the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle.

[0010] Optionally, the step of obtaining the variable equations before and after the power system disturbance, and deriving the matrix pair characteristic equations based on the variable equations, includes:

[0011] When a disturbance occurs in the power system, the dynamic network, network parameters, dynamic component model, and model parameters of the power system are obtained, and a corresponding mathematical model of the power system is constructed based on the dynamic network, network parameters, dynamic component model, and model parameters.

[0012] The mathematical model of the power system is linearized to obtain the variable equations of the power system before and after the disturbance, and the variable equations are expressed as the differential algebraic equations of the power system.

[0013] Characteristic analysis is performed on the differential algebraic equations to derive the characteristic equations of the matrix pairs, forming the pre-disturbance matrix bundle and post-disturbance matrix bundle of the power system.

[0014] Optionally, the pre-perturbation matrix bundle includes a pre-perturbation state matrix, and the post-perturbation matrix bundle includes a post-perturbation state matrix; the method further includes:

[0015] Based on the state matrix before the disturbance and the state matrix after the disturbance, a state increment before and after the disturbance is defined, and the entire solution interval is divided into several solution sub-intervals based on the state increment.

[0016] Optionally, the step of using the initial eigenvalues ​​and the initial eigenvectors, combined with sparse matrix decomposition, to sequentially perform adaptive step-size Newton's method in each of the solution sub-intervals to obtain the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle includes:

[0017] The initial eigenvalues ​​and the initial eigenvectors are used as initial values ​​for the solution;

[0018] For each of the plurality of solution sub-intervals, the Newton method is used iteratively to solve the solution in the target solution sub-interval by combining sparse matrix decomposition.

[0019] If the number of iterations is less than or equal to 2, then jump to the next sub-interval of the target sub-interval and continue the iterative solution;

[0020] If the number of iterations is greater than 2, the iteration step size of the target solution sub-interval is reduced according to the adaptive step size control method, and the iteration solution is continued according to the updated iteration step size until convergence is achieved.

[0021] When all target solution sub-intervals have been iteratively solved, the final solution result is output, which includes the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle.

[0022] Optionally, the step of combining sparse matrix decomposition with Newton's method for iterative solution in the target solution sub-interval includes:

[0023] Based on the initial eigenvalues ​​and the initial eigenvectors, write the perturbation-feature pair equations corresponding to the perturbation-perturbed matrix bundle;

[0024] For the perturbated feature pair equation, a normalization equation is set to ensure that the norm of the final solved target feature vector is not 0;

[0025] The Jacobian matrix is ​​determined based on the perturbation feature pair equation and the normalized equation.

[0026] The perturbed feature pair equation and the normalized equation are combined to form a well-posed nonlinear equation system.

[0027] Based on the initial values ​​of the solution, the well-posed nonlinear equations are modified using the Jacobian matrix to obtain the modified equations.

[0028] In the target solution sub-interval, the modified equation is solved iteratively using Newton's method. Simultaneously, during the iterative solution process, the Jacobian matrix is ​​decomposed into sparse factors using sparse matrix decomposition.

[0029] Optionally, each of the target solution sub-intervals corresponds to a state sub-increment. The step of reducing the iteration step size of the target solution sub-interval according to an adaptive step size control method, and continuing the iterative solution according to the updated iteration step size until convergence is achieved, includes:

[0030] Step S01: Select a portion of the state sub-increments as target state sub-increments according to a preset selection method to reduce the current iteration step size;

[0031] Step S02: Solve the iterative value output by the previous iteration using Newton's method to obtain an intermediate solution. Then, based on the reduced iteration step size, continue to iterate and solve the intermediate solution.

[0032] Step S03: If the number of iterations for the intermediate solution is less than or equal to 2, then repeat step S02 to continue iteratively solving the unsolved increment of the state sub-increment;

[0033] Step S04: If the number of iterations for the intermediate solution is greater than 2, then repeat steps S01 to S03 to continue iteratively solving the unsolved increments of the state sub-increment until the iterative solution of the target solution sub-interval converges.

[0034] Optionally, calculating the initial eigenvalues ​​and initial eigenvectors of the matrix bundle before perturbation includes:

[0035] The inverse power method is used to solve the matrix bundle before the perturbation to obtain the corresponding initial eigenvalues ​​and initial eigenvectors.

[0036] The present invention also provides a power system characteristic value tracking device, comprising:

[0037] The matrix pair characteristic equation calculation module is used to obtain the variable equations of the power system before and after the disturbance, and derive the matrix pair characteristic equations based on the variable equations. The matrix pair characteristic equations include a matrix bundle before the disturbance and a matrix bundle after the disturbance. The matrix bundle before the disturbance corresponds to several solution sub-intervals.

[0038] The initial feature pair calculation module is used to calculate the initial eigenvalues ​​and initial eigenvectors of the matrix bundle before perturbation;

[0039] The adaptive step-size Newton method solution module is used to perform adaptive step-size Newton method solution sequentially in each of the solution sub-intervals based on the initial eigenvalues ​​and the initial eigenvectors, combined with sparse matrix decomposition, to obtain the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle.

[0040] The present invention also provides an electronic device, the device comprising a processor and a memory:

[0041] The memory is used to store program code and transmit the program code to the processor;

[0042] The processor is configured to execute the power system eigenvalue tracking method as described above, according to instructions in the program code.

[0043] The present invention also provides a computer-readable storage medium for storing program code for executing the power system eigenvalue tracking method as described in any of the preceding claims.

[0044] As can be seen from the above technical solutions, the present invention has the following advantages: In view of the shortcomings of the prior art, an adaptive step-size Newton method for eigenvalue tracking of large-scale power systems is proposed. By adopting this method, the eigenvalues ​​and eigenvectors of the system after disturbance can be tracked quickly and accurately, while avoiding the possibility of tracking the wrong results in the traditional Newton method for eigenvalue tracking, thus enabling more efficient eigenvalue analysis of power systems. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 A flowchart illustrating the steps of a power system eigenvalue tracking method provided in this embodiment of the invention;

[0047] Figure 2 This is a schematic diagram of the overall process of a power system characteristic value tracking method provided in an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of the control structure of a SI-type PSS for a power system provided in an embodiment of the present invention;

[0049] Figure 4 This is a schematic diagram illustrating the relationship between the number of feature value tracking attempts and the iteration step size based on an adaptive step size control method, provided by an embodiment of the present invention.

[0050] Figure 5 This is a schematic diagram illustrating the trajectory tracking effect of a feature value according to an embodiment of the present invention;

[0051] Figure 6 This is a structural block diagram of a power system feature value tracking device provided in an embodiment of the present invention. Detailed Implementation

[0052] This invention provides a power system eigenvalue tracking method, apparatus, electronic device, and storage medium to solve or partially solve the technical problem in existing related technologies where traditional Newton's method for tracking eigenvalues ​​is prone to failure when performing stability analysis after a small disturbance in a power system.

[0053] To make the objectives, features, and advantages of this invention more apparent and understandable, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0054] As an example, in practical applications, when a power system is subjected to disturbances, its eigenvalues ​​will also shift. In this case, key eigenvalues ​​can be tracked and calculated without resolving the system after the disturbance. Currently, Newton's method is mainly used for eigenvalue tracking. However, when using Newton's method to track eigenvalues, because the eigenvalues ​​of large systems are relatively dense, it is possible that Newton's method will track other eigenvalues, leading to eigenvalue tracking failure and incorrect results, thus making accurate eigenvalue analysis impossible.

[0055] Therefore, one of the core inventive points of this invention is: in view of the shortcomings of the prior art, an adaptive step-size Newton method for tracking characteristic values ​​of large-scale power systems is proposed, which can accurately and quickly track characteristic values ​​when the system is disturbed. First, based on the differential-algebraic equations (DDAEs) of the power system, the matrix pair characteristic equations of the system are derived. Then, the generalized eigenvalues ​​and eigenvectors of the system matrix bundle before the disturbance are obtained using the inverse power method, and these are used as initial values ​​for the tracking calculation. Next, utilizing the operating characteristics of the power system, the problem of solving the eigenvalues ​​is equivalently transformed into solving a system of nonlinear equations. Based on the convergence of the solution norm, an adaptive step-size control method is adopted to avoid the possibility of the traditional Newton method tracking eigenvalues ​​and obtaining incorrect results, thus enabling more efficient eigenvalue analysis of the power system. Then, the changes in the state matrix are divided, and the adaptive step-size is determined within small intervals based on convergence. Finally, utilizing the sparsity of the power system model, the corrected equations are solved, enabling rapid and accurate tracking of the eigenvalues ​​and eigenvectors of the system after the disturbance. Since this process does not explicitly solve for the eigenvalues, this method has high computational efficiency in practical large-scale system applications.

[0056] Reference Figure 1 The diagram illustrates a flowchart of a power system eigenvalue tracking method according to an embodiment of the present invention, which may specifically include the following steps:

[0057] Step 101: Obtain the variable equations of the power system before and after the disturbance, and derive the matrix pair characteristic equations based on the variable equations. The matrix pair characteristic equations include the matrix bundle before the disturbance and the matrix bundle after the disturbance. The matrix bundle before the disturbance corresponds to several solution sub-intervals.

[0058] As can be seen from the foregoing, when using eigenvalue analysis to analyze the small-disturbance stability of a power system, the main principle is to linearize the power system at an equilibrium point, and then perform eigenvalue analysis on the linearized model to obtain the stability properties of the original nonlinear system.

[0059] In practical applications, when a small disturbance occurs, the dynamic network and network parameters of the power system, as well as the dynamic component model and model parameters, can be obtained. Then, a mathematical model of the power system is established based on the obtained data. This model is then linearized to obtain the power system's differential algebraic equations (DDAEs). Since solving these DDAEs requires considering the state variables at both the current and past times, they can also be viewed as equations representing the power system before and after the disturbance. Based on these DDAEs, the corresponding matrix pair characteristic equations can be derived, forming the matrix bundle (J, T) before and after the disturbance.

[0060] Therefore, in the specific implementation, the variable equations of the power system before and after the disturbance are obtained, and based on the variable equations, the characteristic equation of the matrix pair is derived, which can be:

[0061] First, when a disturbance occurs in the power system, the dynamic network, network parameters, dynamic component model, and model parameters of the power system are obtained, and a corresponding mathematical model of the power system is constructed based on the dynamic network, network parameters, dynamic component model, and model parameters.

[0062] Secondly, the mathematical model of the power system is linearized to obtain the variable equations before and after the power system is disturbed. The variable equations are expressed as the differential algebraic equations of the power system.

[0063] Furthermore, the differential-algebraic equations (DDAEs) of a power system can be viewed as a set of state-space equations used to describe the evolution of the system state over time. State-space equations typically consist of two parts: state equations and output equations. The state equations describe the evolution of the system state and can be written in matrix form; therefore, they can also be called state transition equations. The output equations describe the relationship between the system outputs. The specific expression of the state-space equations can be represented as follows:

[0064]

[0065] In the formula, Both represent deviation variables consisting of n state variables and m algebraic variables. Corresponding to the output equation, x corresponds to the state equation. as well as Both are coefficient matrices. J corresponds to the state equation and represents the state matrix. T corresponds to the output equation and represents the output matrix.

[0066] For the matrix bundle (J, T) before and after the perturbation and It can be seen that in power systems, eigenvalue tracking is mainly achieved by solving for the system state changes, which further enables small-disturbance stability analysis of the system. Therefore, accurately solving the system state matrix is ​​the key to successfully tracking the eigenvalues.

[0067] In related technologies, the system state matrix is ​​the analytical solution of the state transition equation, which can be used to calculate the state of the system at any time. Each element of the system state matrix (eigenvalue and corresponding eigenvector) represents the rate of change of the system state at different times. These rates of change can be used to evaluate the stability and response speed of the system.

[0068] Next, a characteristic analysis is performed on the above differential-algebraic equations to derive the characteristic equations of the matrix pairs, forming the pre-disturbance matrix bundle (J, T) and post-disturbance matrix bundle of the power system.

[0069] Furthermore, the pre-perturbation matrix bundle (J, T) can include the pre-perturbation state matrix J and the post-perturbation matrix bundle. It can include the post-perturbation state matrix. For the state matrix J before the perturbation, if J has a small increment ΔJ, then for the state matrix after the perturbation... have In order to achieve the small-interval adaptive step-size control iterative solution based on Newton's method provided in this embodiment of the invention, the state increment ΔJ can be divided into i solution sub-intervals (that is, the entire solution interval is divided into i solution sub-intervals based on the state increment), such that... Let the sub-increment of the r-th subinterval be...

[0070] In the specific implementation, a state increment before and after the perturbation can be defined based on the state matrix before and after the perturbation, and the entire solution interval can be divided into several solution sub-intervals based on the state increment, thereby dividing the change value of the state matrix. This allows for the adaptive step size of the solution to be determined based on convergence within a small interval.

[0071] Step 102: Calculate the initial eigenvalues ​​and initial eigenvectors of the matrix bundle before perturbation;

[0072] Then, the generalized eigenvalues ​​λ (initial eigenvalues) and eigenvectors u (initial eigenvectors) of the matrix bundle (J, T) before perturbation can be obtained by inverse power method. The generalized eigenvalues ​​λ and eigenvectors u can form the generalized eigenpair (λ, u) of the matrix bundle (J, T) before perturbation.

[0073] Step 103: Based on the initial eigenvalues ​​and the initial eigenvectors, and combined with sparse matrix decomposition, perform adaptive step-size Newton's method to solve each of the solution sub-intervals in turn to obtain the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle.

[0074] Specifically, the process of obtaining the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle by performing adaptive step-size Newton's method in each solution sub-interval, based on the initial eigenvalues ​​and initial eigenvectors and combined with sparse matrix decomposition, can include the following steps:

[0075] Step S1031: Use the initial eigenvalues ​​and initial eigenvectors as initial values ​​for the solution;

[0076] When solving for eigenvalues, calculations can be performed based on Newton's method. Generally, when using Newton's method for iterative solutions, it is necessary to consider the initial values ​​of the unknowns, the calculation of the Jacobian matrix, and the corresponding iterative steps.

[0077] For handling unknowns, the generalized eigenvalue λ and eigenvector u obtained through the aforementioned steps can be used as the initial values ​​for the solution. When the equilibrium point of the system does not change much, using λ and u as initial values ​​can basically guarantee that the solution is near the true solution.

[0078] Step S1032: For each of the several target solution sub-intervals, combine sparse matrix decomposition and use Newton's method to iteratively solve the target solution sub-interval;

[0079] Furthermore, the implementation process of iteratively solving the target solution subinterval using Newton's method, combined with sparse matrix decomposition, can include the following steps:

[0080] Step S321: Based on the initial eigenvalues ​​and initial eigenvectors, write the perturbation eigenpair equations corresponding to the perturbation matrix bundle;

[0081] For the generalized characteristic pair (λ,u) of the pre-perturbation matrix bundle (J,T), it satisfies: Ju=λTu. Furthermore, combining this with the preceding information, for the pre-perturbation state matrix J, if J has a small increment ΔJ, then for the post-perturbation state matrix… have Thus, the original generalized feature pair (λ, u) may be perturbed into a new feature pair. At this point, the equations for the perturbed eigenpairs corresponding to the perturbed matrix bundle can be listed:

[0082] Step S322: For the perturbation feature pair equation, set a normalization equation. The normalization equation is used to ensure that the norm of the final target feature vector is not 0.

[0083] Because of the aforementioned formula There are n equations, but n+1 unknowns. To obtain the final solution, we need to add an equation to get the equation that needs to be solved. The specific settings are as follows:

[0084]

[0085]

[0086] Among them, equation To normalize the equation, u H This represents the conjugate transpose of the eigenvector u. The normalization equation is used to ensure that the solved eigenvector u is normalized. norm Not zero.

[0087] Step S323: Determine the Jacobian matrix based on the perturbation feature pair equation and the normalized equation;

[0088] In vector analysis, the Jacobian matrix is ​​a matrix formed by arranging first-order partial derivatives in a certain way, and its determinant is called the Jacobian determinant. In this embodiment of the invention, based on the perturbation-induced feature pair equation and the normalized equation, the Jacobian matrix can be determined as follows:

[0089]

[0090] in, The first l rows of x represent the increment of the feature vector u during the iteration process. Let x be the (l+1)th row, representing the increment of the eigenvalue λ during the iteration process. and For the system after disturbance eigenvalues ​​and eigenvectors.

[0091] Step S324: Combine the perturbation-induced characteristic pair equations and the normalized equations into a well-posed nonlinear equation system.

[0092] It can be viewed as a well-posed nonlinear equation system, described as follows: This allows us to utilize the operating characteristics of the power system to equivalently transform the problem of solving eigenvalue problems into the calculation of solutions to a system of nonlinear equations.

[0093] Step S325: Based on the initial values ​​of the solution equations, and in conjunction with the Jacobian matrix, modify the well-posed nonlinear equations to obtain the modified equations;

[0094] Specifically, the corrected equations corresponding to the well-posed nonlinear equation system are as follows:

[0095]

[0096] Step S326: In the target solution sub-interval, Newton's method is used to iteratively solve the modified equation. At the same time, during the iterative solution process, sparse matrix decomposition is used to perform sparse factor decomposition on the Jacobian matrix.

[0097] When using Newton's method to track eigenvalues, the eigenvalues ​​of large power systems are relatively dense. If the state increment ΔJ is too large (the size here can be measured by the norm of the eigenvector), Newton's method may track other eigenvalues. Therefore, when using Newton's method to solve for eigenvalues, the deviation of the state matrix must be fully considered.

[0098] In practical applications, for the i-th solution sub-interval, if its corresponding state increment ΔJ i If the value of ΔJ is relatively small, Newton's method generally converges after two iterations. If convergence is not achieved after more than two iterations, then ΔJ can be considered to be relatively small. i The value is relatively large, so ΔJ needs to be reduced. i For example, take ΔJ i The value of ΔJ can be halved to reduce the iteration step size, or the selection of ΔJ can be determined based on the iteration value obtained from the previous iteration. i The corresponding proportional increment is used as the state increment for this solution. Then, Newton's method is used to solve the iterative value output by the previous iteration to obtain an intermediate solution. Then, based on the intermediate solution, the accurate eigenvalue is tracked again.

[0099] The aforementioned solution method is called adaptive step-size control. Instead of directly solving for the exact value, it uses a step-by-step solution to obtain the accurate eigenvalues. Based on the convergence of the solution norm, adaptive step-size control avoids the possibility of the traditional Newton's method tracking eigenvalues ​​and obtaining erroneous results. This allows for more efficient eigenvalue analysis of power systems. Furthermore, since this process does not explicitly solve for the eigenvalues, it offers high computational efficiency in large-scale system applications.

[0100] Considering the state increment ΔJ, we can combine each solution sub-interval with the corresponding state sub-increment ΔJ. i For well-posed nonlinear equations With appropriate adjustments and combining the corrected equations obtained through the preceding steps, the following equations can be solved in each iteration:

[0101]

[0102]

[0103] in, make Then, the adaptive step-size Newton method can be used for iteration.

[0104] In light of the foregoing, during the iterative solution process, since the coefficient matrices J and T are sparse matrices and the initial eigenvector u is a sparse vector, in order to avoid tracking other eigenvalues ​​when using Newton's method to solve for eigenvalues, the deviation of the state matrix must be fully considered during the solution process. That is, the sparse LU decomposition technique needs to be used to decompose the Jacobian matrix into sparse factors.

[0105] Among them, the sparse LU decomposition technique refers to the following: For solving a system of linear equations of the form Ax=B, matrices A and B are also sparse. Sparse LU decomposition of matrix A yields [L,U,P,Q]=lu(A), that is, P×A×Q=L×U, where L is a unit lower triangular matrix, U is an upper triangular matrix, P is a row permutation matrix, and Q is a column permutation matrix.

[0106] Then x can be expressed by the sparse LU factor as x = Q × U -1 ×L -1 ×P×B, where The first l rows of x, i.e. For the (l+1)th row of x, that is We can obtain the following formula:

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] Where lu(*) denotes sparse LU factorization, in which case, and Both indicate that the system is perturbed during eigenvalue tracking. eigenvalues, and Both indicate that the system is perturbed during eigenvalue tracking. The eigenvectors, where k and k+1 both represent the iteration numbers, then The eigenvalue corresponding to the (k+1)th iteration The corresponding new estimate, The eigenvector corresponding to the (k+1)th iteration The corresponding new estimate.

[0114] By utilizing the sparsity of the power system model and solving the modified equations, the eigenvalues ​​and eigenvectors of the system after the disturbance can be quickly and accurately tracked.

[0115] Step S1033: If the number of iterations is less than or equal to 2, then jump to the next sub-interval of the target sub-interval and continue the iterative solution;

[0116] During the solution process, for each sub-interval, if convergence can be achieved within 2 iterations, the process jumps to the next sub-interval and continues iteratively.

[0117] Step S1034: If the number of iterations is greater than 2, the iteration step size of the target solution sub-interval is reduced according to the adaptive step size control method, and the iteration solution is continued according to the updated iteration step size until convergence is achieved;

[0118] For any subinterval, if convergence is not achieved within two iterations, it indicates that the corresponding state increment ΔJ i If the value is small, then after reducing the iteration step size of this sub-interval, we can continue iteratively solving until convergence is achieved.

[0119] In a specific implementation, each sub-interval of the objective solution can be viewed as corresponding to a state sub-increment. Combining the relevant content from the aforementioned embodiments, the process of reducing the iteration step size of the objective solution sub-interval using an adaptive step size control method, and continuing iterative solution according to the updated iteration step size until convergence is achieved, can include the following steps:

[0120] Step S01: Select a portion of the state sub-increments as target state sub-increments according to a preset selection method to reduce the current iteration step size;

[0121] Step S02: Use Newton's method to solve for the iterative value output by the previous iteration to obtain an intermediate solution. Then, based on the reduced iteration step size, continue to iterate and solve for the intermediate solution.

[0122] Step S03: If the number of iterations for the intermediate solution is less than or equal to 2, then repeat step S02 to continue iteratively solving the unsolved increments of the state sub-increment.

[0123] Step S04: If the number of iterations for the intermediate solution is greater than 2, repeat steps S01 to S03 to continue iterating over the unsolved increments of the state sub-increment until the iterative solution of the target solution sub-interval converges.

[0124] Step S1035: When all target solution sub-intervals have been iteratively solved, output the final solution result, which includes the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle.

[0125] When ΔJ r =0 (all partitioned solution subspaces have been solved), meaning the state matrix J has become 0. (The eigenvalue is then traced from J to...) And when convergence occurs, the iteration ends, at which point the result is obtained. and That is, the system after the disturbance The target feature values ​​and target feature vectors.

[0126] To better illustrate this, we select the state sub-increment ΔJ. i Taking the reduction of the iteration step size as an example, an iterative process using the adaptive step size Newton's method is provided as follows:

[0127] (1) Given the initial values ​​λ and u of the unknowns, set the allowable error ε, and set the sorting of the sub-intervals to i = 1;

[0128] (2) Let If ΔJ r =0, then stop the iteration and jump to (6); otherwise, jump to (3);

[0129] (3) For the i-th sub-interval to be solved, set the iteration number k = 0 and perform the following iteration:

[0130] a. If If the solution error is within the allowable range and the convergence condition is met, then the loop will exit.

[0131] b. According to the formula We obtain the Jacobian matrix;

[0132] c. Combining well-posed nonlinear equations and the corrected equation By solving the system of equations To solve for the increments of the unknowns λ and u and

[0133] d. Solving for unknowns and New estimates:

[0134] e. Set k = k + 1. If k = 2, then exit the loop.

[0135] (4) If Newton's method converges when k = 2, set i = i + 1 and jump to step (2);

[0136] (5) If Newton's method does not converge when k = 2, set ΔJ i =0.5ΔJ i And jump to step (2).

[0137] (6) The eigenvalue is traced from J to Output the final solution result and At this time, it was obtained and That is, the system after the disturbance The target feature values ​​and target feature vectors.

[0138] In this embodiment of the invention, an adaptive step-size Newton method for eigenvalue tracking of large-scale power systems is proposed. First, based on the differential algebraic equations (DDAEs) of the power system, the matrix pair characteristic equations of the system are derived. Then, the generalized eigenvalues ​​and eigenvectors of the system matrix bundle before the disturbance are obtained using the inverse power method, and these are used as initial values ​​for the tracking calculation. Then, utilizing the operating characteristics of the power system, the problem of solving the eigenvalues ​​is equivalently transformed into solving a system of nonlinear equations. Based on the convergence of the solution norm, an adaptive step-size control method is adopted to avoid the possibility of tracking erroneous results in the traditional Newton method, thus enabling more efficient eigenvalue analysis of the power system. Next, the change values ​​of the state matrix are divided, and the adaptive step-size for solving is determined based on the convergence within small intervals. Finally, utilizing the sparsity of the power system model, the corrected equations are solved, thereby enabling fast and accurate tracking of the eigenvalues ​​and eigenvectors of the system after the disturbance.

[0139] For better explanation, refer to Figure 2 This diagram illustrates the overall flow of a power system eigenvalue tracking method according to an embodiment of the present invention. It should be noted that this example only briefly describes the general flow of the adaptive step-size Newton method iteration for large-scale power system eigenvalue tracking. Detailed explanations of each step can be obtained by referring to the relevant content in the foregoing embodiments. It is understood that the present invention does not impose any limitations on this.

[0140] Step 1: Obtain the dynamic network, network parameters, dynamic component model, and model parameters of the power system; establish the mathematical model of the power system; then, after linearization, obtain the differential algebraic equations (DDAEs) of the power system before and after the disturbance; further, obtain the corresponding characteristic matrix pair equations, forming the matrix bundle (J,T) before and after the disturbance.

[0141] Step 2: Use the inverse power method to obtain the generalized eigenvalues ​​λ and eigenvectors u of the original system matrix bundle (J,T) before the disturbance;

[0142] Step 3: For the state matrix J before the disturbance, if there exists a state increment ΔJ, ΔJ can be divided into i small intervals (i.e., solving for sub-intervals) such that... make Perform adaptive step-size Newton's method iteration;

[0143] Step 4: Solve the problem using the adaptive step-size Newton method in each small interval. If convergence is achieved within two iterations, jump to the next small interval and continue iteratively. If convergence is not achieved, reduce the iteration step size between the small intervals and continue iteratively based on the updated iteration step size. Since the coefficient matrices J and T are sparse matrices and u is a sparse vector, it is necessary to combine sparse LU decomposition technology with iterative solution during the eigenvalue tracking process.

[0144] Step 5: When ΔJ r =0, meaning the state matrix J before the disturbance has changed to the state matrix before the disturbance. And when convergence is achieved, the iteration ends, at which point the result is... and These are the eigenvalues ​​and eigenvectors of the system after the disturbance.

[0145] For ease of understanding, the embodiments of the present invention are described below through specific examples.

[0146] To verify the accuracy and computational efficiency of the adaptive step-size Newton method for eigenvalue tracking in large-scale power systems proposed in this invention, the method was tested on a Hainan power grid system in this embodiment. The tolerance error ε for the Newton iteration was 10. -6 In addition, for better comparison, all tests in this example were performed on the same computer.

[0147] For the Hainan power grid system, the gain parameter variation K of the SI-type PSS is... p For example (where the parameter increment ΔK) p Test from 0 to -6, refer to Figure 3 The diagram shows a schematic of the control structure of a SI-type PSS for a power system provided by an embodiment of the present invention.

[0148] Among them, the PSS (Power System Stabilizer) is a function of the excitation system used to suppress active power oscillations. Its main function is to provide additional control signals to the voltage regulator. Figure 3 The SI-type PSS structure shown is the SI-type model structure used in the "PSD-ST Transient Stability Program User Manual" compiled by the China Electric Power Research Institute. In the field of power systems, PSD (Power System Department, a power system simulation software) is currently widely used in various State Grid power companies, dispatch centers, etc. Since the example used in this invention is the actual power grid, this model is adopted. For detailed explanation of the SI-type model, please refer to the "PSD-ST Transient Stability Program User Manual", which will not be elaborated here.

[0149] For the eigenvalue tracking process, the eigenvalues ​​and their eigenvectors can first be obtained using the inverse power method, with a tolerance of 10. -8 Specifically, the eigenvalue after correction by the inverse power method is 0.4408+j1.8060.

[0150] Modify parameter K in PSS p The perturbation matrix bundle of the power system is obtained. Next, the adaptive step-size Newton method for eigenvalue tracking of large-scale power systems proposed in this invention is used for tracking and solving. The iteration step size for each step is as follows: Figure 4 As shown, Figure 4 This can well illustrate the change in the adaptive step size. In each solution sub-interval, if convergence fails after two iterations, the step size is adaptively reduced.

[0151] pass Figure 4 The relationship between the number of eigenvalue tracking attempts and the iteration step size based on the adaptive step size control method can be derived. From the overall trend, the iteration step size decreases as the number of tracking attempts increases. The change in iteration step size is greatest when the number of tracking attempts is less than 10, indicating that the adaptive step size control method plays the most significant role in the iteration process of Newton's method. With the increase in the number of tracking attempts, within a certain range (approximately 10-25 as shown in the figure), the iteration step size can remain at a stable value of about 0.01. This indicates that within the range of 10-25 tracking attempts, using a current step size of 0.01 for iteration can quickly reach the convergence condition, reduce computation time, and minimize iteration error. After iterative solving, the eigenvalue -1.356+j6.629 of the new system was finally tracked after 64 iterations.

[0152] For example, the trajectory tracking effect of the feature values ​​in the above example is shown in the figure. Figure 5As shown in the figure, the trajectory tracked by the adaptive step-size Newton method is largely the same as the trajectory of the eigenvalue change, indicating that it can effectively track the eigenvalues ​​of the system after disturbance. This proves that the adaptive step-size Newton method for eigenvalue tracking of large-scale power systems provided in this embodiment of the invention is an effective method capable of accurately and quickly tracking the eigenvalues ​​of the system after disturbance.

[0153] Reference Figure 6 The diagram illustrates a structural block diagram of a power system characteristic value tracking device according to an embodiment of the present invention, which may specifically include:

[0154] The matrix pair characteristic equation calculation module 601 is used to obtain the variable equations of the power system before and after the disturbance, and derive the matrix pair characteristic equations based on the variable equations. The matrix pair characteristic equations include a matrix bundle before the disturbance and a matrix bundle after the disturbance. The matrix bundle before the disturbance corresponds to several solution sub-intervals.

[0155] The initial feature pair calculation module 602 is used to calculate the initial eigenvalues ​​and initial eigenvectors of the matrix bundle before perturbation;

[0156] The adaptive step-size Newton method solution module 603 is used to perform adaptive step-size Newton method solution in each of the solution sub-intervals according to the initial eigenvalues ​​and the initial eigenvectors, combined with sparse matrix decomposition, to obtain the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle.

[0157] In one optional embodiment, the matrix pair characteristic equation calculation module 601 includes:

[0158] The power system mathematical model construction module is used to obtain the dynamic network, network parameters, dynamic component model and model parameters of the power system after a disturbance occurs, and to construct the corresponding power system mathematical model based on the dynamic network, network parameters, dynamic component model and model parameters.

[0159] The linearization module is used to linearize the mathematical model of the power system to obtain the variable equations of the power system before and after the disturbance, and the variable equations are expressed as the differential algebraic equations of the power system.

[0160] The matrix pair characteristic equation derivation module is used to perform characteristic analysis on the differential algebraic equation, derive the matrix pair characteristic equation, and form the pre-disturbance matrix bundle and post-disturbance matrix bundle of the power system.

[0161] In one optional embodiment, the pre-perturbation matrix bundle includes a pre-perturbation state matrix, the post-perturbation matrix bundle includes a post-perturbation state matrix, and the device further includes:

[0162] The sub-interval partitioning module is used to define a state increment before and after the disturbance based on the state matrix before the disturbance and the state matrix after the disturbance, and to divide the entire solution interval into several solution sub-intervals based on the state increment.

[0163] In one optional embodiment, the adaptive step-size Newton method solution module 603 includes:

[0164] The initial value definition module for the solution is used to use the initial eigenvalues ​​and the initial eigenvectors as initial values ​​for the solution.

[0165] The target solution sub-interval iterative solution module is used to perform iterative solution using Newton's method in conjunction with sparse matrix decomposition for each of the plurality of solution sub-intervals.

[0166] The iterative solution jump processing module is used to jump to the next solution sub-interval of the target solution sub-interval and continue iterative solution if the number of solution iterations is less than or equal to 2.

[0167] An adaptive step size control module is used to reduce the iteration step size of the target solution sub-interval according to the adaptive step size control method if the number of solution iterations is greater than 2, and continue to perform iterative solution according to the updated iteration step size until convergence is achieved.

[0168] The iterative solution result output module is used to output the final solution result when all target solution sub-intervals have been iteratively solved. The final solution result includes the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle.

[0169] In one optional embodiment, the target solution sub-interval iterative solution module includes:

[0170] The perturbation-post feature pair equation writing module is used to write the perturbation-post feature pair equations corresponding to the perturbation-post matrix bundle based on the initial eigenvalues ​​and the initial eigenvectors.

[0171] The normalization equation setting module is used to set a normalization equation for the perturbed feature pair equation, and the normalization equation is used to ensure that the norm of the final solved target feature vector is not 0;

[0172] The Jacobian matrix determination module is used to determine the Jacobian matrix based on the perturbation feature pair equation and the normalized equation.

[0173] A well-posed nonlinear equations definition module is used to combine the perturbed feature pair equations and the normalized equations into a well-posed nonlinear equations.

[0174] The equation correction module is used to correct the well-posed nonlinear equation system based on the initial value of the solution and the Jacobian matrix to obtain the corrected equation.

[0175] The Newton method combined with the sparse decomposition iterative solution module is used to iteratively solve the modified equation using the Newton method in the target solution sub-interval. At the same time, during the iterative solution process, the Jacobian matrix is ​​decomposed into sparse factors using the sparse matrix decomposition method.

[0176] In one optional embodiment, each of the target solution sub-intervals corresponds to a state sub-increment, and the adaptive step size control module includes:

[0177] The current iteration step size reduction module is used to execute step S01: select a portion of the state sub-increments as target state sub-increments according to a preset selection method, so as to reduce the current iteration step size;

[0178] The intermediate solution iterative solution module is used to execute step S02: using Newton's method to solve the iterative value output by the previous iteration to obtain an intermediate solution, and then continuing to iteratively solve the intermediate solution based on the reduced iteration step size;

[0179] The iterative solution first repeating module is used to execute step S03: if the number of iterative solutions to the intermediate solution is less than or equal to 2, then step S02 is repeated to continue iteratively solving the unsolved increment of the state sub-increment;

[0180] The iterative solution second repeating module is used in step S04: if the number of iterative solutions to the intermediate solution is greater than 2, then steps S01 to S03 are repeated to continue iteratively solving the unsolved increment of the state sub-increment until the iterative solution of the target solution sub-interval reaches convergence.

[0181] In one alternative embodiment, the initial feature calculation module 602 is specifically used for:

[0182] The inverse power method is used to solve the matrix bundle before the perturbation to obtain the corresponding initial eigenvalues ​​and initial eigenvectors.

[0183] As the device embodiment is basically similar to the method embodiment, it is described in a relatively simple way. For relevant details, please refer to the description of the method embodiment above.

[0184] This invention also provides an electronic device, which includes a processor and a memory:

[0185] The memory is used to store program code and transfer the program code to the processor;

[0186] The processor is used to execute the power system feature value tracking method of any embodiment of the present invention according to the instructions in the program code.

[0187] This invention also provides a computer-readable storage medium for storing program code for executing the power system characteristic value tracking method of any embodiment of the invention.

[0188] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0189] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between apparatuses or units through some interfaces, and may be electrical, mechanical, or other forms.

[0190] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0191] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0192] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0193] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for tracking eigenvalues ​​in a power system, characterized in that, include: Obtain the variable equations of the power system before and after the disturbance, and derive the matrix pair characteristic equations based on the variable equations. The matrix pair characteristic equations include the matrix bundle before the disturbance and the matrix bundle after the disturbance. The matrix bundle before the disturbance corresponds to several solution sub-intervals. Calculate the initial eigenvalues ​​and initial eigenvectors of the matrix bundle before the perturbation; Based on the initial eigenvalues ​​and the initial eigenvectors, and combined with sparse matrix decomposition, the adaptive step-size Newton method is sequentially applied to each of the solution sub-intervals to obtain the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle. The step of obtaining the variable equations before and after the power system disturbance, and deriving the matrix pair characteristic equations based on the variable equations, includes: When a disturbance occurs in the power system, the dynamic network, network parameters, dynamic component model, and model parameters of the power system are obtained, and a corresponding mathematical model of the power system is constructed based on the dynamic network, network parameters, dynamic component model, and model parameters. The mathematical model of the power system is linearized to obtain the variable equations of the power system before and after the disturbance, and the variable equations are expressed as the differential algebraic equations of the power system. Characteristic analysis is performed on the differential algebraic equations to derive the characteristic equations of the matrix pairs, forming the pre-disturbance matrix bundle and post-disturbance matrix bundle of the power system. The step of obtaining the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle by sequentially performing adaptive step-size Newton's method in each of the solution sub-intervals based on the initial eigenvalues ​​and initial eigenvectors, combined with sparse matrix decomposition, includes: The initial eigenvalues ​​and the initial eigenvectors are used as initial values ​​for the solution; For each of the plurality of solution sub-intervals, the Newton method is used iteratively to solve the solution in the target solution sub-interval by combining sparse matrix decomposition. If the number of iterations is less than or equal to 2, then jump to the next sub-interval of the target sub-interval and continue the iterative solution; If the number of iterations is greater than 2, the iteration step size of the target solution sub-interval is reduced according to the adaptive step size control method, and the iteration solution is continued according to the updated iteration step size until convergence is achieved. When all target solution sub-intervals have been iteratively solved, the final solution result is output, which includes the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle.

2. The power system eigenvalue tracking method according to claim 1, characterized in that, The pre-perturbation matrix bundle contains a pre-perturbation state matrix, and the post-perturbation matrix bundle contains a post-perturbation state matrix. The method further includes: Based on the state matrix before the disturbance and the state matrix after the disturbance, a state increment before and after the disturbance is defined, and the entire solution interval is divided into several solution sub-intervals based on the state increment.

3. The power system eigenvalue tracking method according to claim 1, characterized in that, The method of combining sparse matrix decomposition with Newton's method for iterative solution in the target solution sub-interval includes: Based on the initial eigenvalues ​​and the initial eigenvectors, write the perturbation-feature pair equations corresponding to the perturbation-perturbed matrix bundle; For the perturbated feature pair equation, a normalization equation is set to ensure that the norm of the final solved target feature vector is not 0; The Jacobian matrix is ​​determined based on the perturbation feature pair equation and the normalized equation. The perturbed feature pair equation and the normalized equation are combined to form a well-posed nonlinear equation system. Based on the initial values ​​of the solution, the well-posed nonlinear equations are modified using the Jacobian matrix to obtain the modified equations. In the target solution sub-interval, the modified equation is solved iteratively using Newton's method. Simultaneously, during the iterative solution process, the Jacobian matrix is ​​decomposed into sparse factors using sparse matrix decomposition.

4. The power system eigenvalue tracking method according to claim 1, characterized in that, Each of the aforementioned target solution sub-intervals corresponds to a state sub-increment. The step of reducing the iteration step size of the target solution sub-interval according to an adaptive step size control method, and continuing the iterative solution according to the updated iteration step size until convergence is achieved, includes: Step S01: Select a portion of the state sub-increments as target state sub-increments according to a preset selection method to reduce the current iteration step size; Step S02: Solve the iterative value output by the previous iteration using Newton's method to obtain an intermediate solution. Then, based on the reduced iteration step size, continue to iterate and solve the intermediate solution. Step S03: If the number of iterations for the intermediate solution is less than or equal to 2, then repeat step S02 to continue iteratively solving the unsolved increment of the state sub-increment; Step S04: If the number of iterations for the intermediate solution is greater than 2, then repeat steps S01 to S03 to continue iteratively solving the unsolved increments of the state sub-increment until the iterative solution of the target solution sub-interval converges.

5. The power system characteristic value tracking method according to claim 1 or 2, characterized in that, The calculation of the initial eigenvalues ​​and initial eigenvectors of the matrix bundle before perturbation includes: The inverse power method is used to solve the matrix bundle before the perturbation to obtain the corresponding initial eigenvalues ​​and initial eigenvectors.

6. A power system characteristic value tracking device, characterized in that, include: The matrix pair characteristic equation calculation module is used to obtain the variable equations of the power system before and after the disturbance, and derive the matrix pair characteristic equations based on the variable equations. The matrix pair characteristic equations include a matrix bundle before the disturbance and a matrix bundle after the disturbance. The matrix bundle before the disturbance corresponds to several solution sub-intervals. The initial feature pair calculation module is used to calculate the initial eigenvalues ​​and initial eigenvectors of the matrix bundle before perturbation; The adaptive step-size Newton method solution module is used to perform adaptive step-size Newton method solution in each of the solution sub-intervals according to the initial eigenvalues ​​and the initial eigenvectors, combined with sparse matrix decomposition, to obtain the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle. The matrix pair characteristic equation calculation module includes: The power system mathematical model construction module is used to obtain the dynamic network, network parameters, dynamic component model and model parameters of the power system after a disturbance occurs, and to construct the corresponding power system mathematical model based on the dynamic network, network parameters, dynamic component model and model parameters. The linearization module is used to linearize the mathematical model of the power system to obtain the variable equations of the power system before and after the disturbance, and the variable equations are expressed as the differential algebraic equations of the power system. The matrix pair characteristic equation derivation module is used to perform characteristic analysis on the differential algebraic equation, derive the matrix pair characteristic equation, and form the pre-disturbance matrix bundle and post-disturbance matrix bundle of the power system. The adaptive step-size Newton's method solution module includes: The initial value definition module for the solution is used to use the initial eigenvalues ​​and the initial eigenvectors as initial values ​​for the solution. The target solution sub-interval iterative solution module is used to perform iterative solution using Newton's method in conjunction with sparse matrix decomposition for each of the plurality of solution sub-intervals. The iterative solution jump processing module is used to jump to the next solution sub-interval of the target solution sub-interval and continue iterative solution if the number of solution iterations is less than or equal to 2. An adaptive step size control module is used to reduce the iteration step size of the target solution sub-interval according to the adaptive step size control method if the number of solution iterations is greater than 2, and continue to perform iterative solution according to the updated iteration step size until convergence is achieved. The iterative solution result output module is used to output the final solution result when all target solution sub-intervals have been iteratively solved. The final solution result includes the target eigenvalues ​​and target eigenvectors of the perturbed matrix bundle.

7. An electronic device, characterized in that, The device includes a processor and a memory: The memory is used to store program code and transmit the program code to the processor; The processor is used to execute the power system characteristic value tracking method according to any one of claims 1-5 according to the instructions in the program code.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store program code for executing the power system characteristic value tracking method according to any one of claims 1-5.

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