Method and device for calculating electromagnetic transient eigenvalue of power system based on frequency shift transformation

Abstract

The present application relates to a method and device for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation. The method includes: First, constructing an instantaneous value electromagnetic transient model in the complex space, performing frequency shift transformation to obtain a frequency shift electromagnetic transient model, and determining the equilibrium point of the power system based on the frequency shift electromagnetic transient model; After that, constructing a linearized state space equation at the equilibrium point of the power system by using a discrete state space modeling method based on the frequency shift electromagnetic transient model; After that, determining an amplification matrix based on the state matrix of the linearized state space equation by using a spectral transformation technique with rotation-amplification preprocessing; Finally, constructing a sparse matrix based on the amplification matrix, and calculating the electromagnetic transient eigenvalues of the power system by using an implicit restart Arnoldi sparse eigenvalue algorithm. It solves the problems such as extremely low calculation efficiency, easy memory overflow, difficult convergence, and error in the results of calculating the eigenvalues of the state matrix of the electromagnetic transient model.

Description

Technical Field

[0001] The present application relates to the technical field of electromagnetic transient modeling of new power systems, and particularly to a method and device for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation. Background Art

[0002] With the large-scale access of new energy in the power system, the dynamic behavior of the system has become increasingly complex. The calculation efficiency of traditional methods is difficult to meet the high requirements of new power systems, especially when facing challenges in eigenvalue analysis.

[0003] There are a large number of dynamic processes with small time scales and high frequencies in new power systems. Since the traditional electromechanical transient model is based on the quasi-steady state assumption, it is difficult to accurately describe the dynamic processes of new power systems. Compared with the electromechanical transient simulation model, the electromagnetic transient simulation model can accurately simulate the broadband dynamic processes of the power system. Therefore, for new power systems, it is necessary to use electromagnetic transient models to accurately simulate their broadband dynamic characteristics of multi-time scale coupling. However, the electromagnetic transient model of the power system is a dynamic model described by instantaneous values, and the system described by this model is a periodic motion system. For a periodic motion system such as the electromagnetic transient model of the power system, there is no equilibrium point. At the same time, since the network in the electromagnetic transient model is modeled as a differential equation, when using the traditional state variable analysis method, it is necessary to determine the independence between state variables in the network. When the system scale increases, due to the complex topological connection relationships in the system, it is particularly difficult to eliminate non-independent state variables. And the dimension of the state space equation of the electromagnetic transient model of the new power system is significantly higher than that of the electromechanical transient model of the traditional power system, and can even reach millions of dimensions. There are problems such as difficult convergence, error in results, extremely low calculation efficiency, easy memory overflow, etc. in the calculation of eigenvalues of the ultra-high-dimensional sparse electromagnetic transient model state matrix, and even calculation failures are likely to occur.

[0004] Therefore, in the related art, there is an urgent need for a method that can improve the accuracy of eigenvalue calculation for new power systems. Summary of the Invention

[0005] Based on this, in view of the above technical problems, it is necessary to provide a method and device for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation that can improve the accuracy of eigenvalue calculation for new power systems.

[0006] In a first aspect, the present application provides a method for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation. The method includes:

[0007] Construct an instantaneous value electromagnetic transient model in the complex space, perform frequency shift transformation to obtain a frequency shift electromagnetic transient model, and determine the equilibrium point of the power system based on the frequency shift electromagnetic transient model;

[0008] Construct the linearized state - space equation at the equilibrium point of the power system by using the discrete state - space modeling method based on the shifted - frequency electromagnetic transient model;

[0009] Determine the amplification matrix based on the state matrix of the linearized state - space equation by using the spectral transformation technique with rotation - amplification pre - processing;

[0010] Construct a sparse matrix based on the amplification matrix, and calculate the electromagnetic transient eigenvalues of the power system by using the implicit restart Arnoldi sparse eigenvalue algorithm.

[0011] Optionally, in an embodiment of the present application, the construction of the instantaneous - value electromagnetic transient model in the complex space includes:

[0012] Construct the orthogonal adjoint model of the power system, and superimpose it with the original power system model to obtain the instantaneous - value electromagnetic transient model in the complex space.

[0013] Optionally, in an embodiment of the present application, the construction of the linearized state - space equation at the equilibrium point of the power system by using the discrete state - space modeling method based on the shifted - frequency electromagnetic transient model includes:

[0014] Use the numerical integration method to discretize the differential equations of the power system to obtain the discrete state - space equation of the electromagnetic transient model and the port - node current expression;

[0015] Construct the discrete state - space equation of the power system by using the node analysis method based on the discrete state - space equation of the electromagnetic transient model and the port - node current expression.

[0016] Optionally, in an embodiment of the present application, the determination of the amplification matrix based on the state matrix of the linearized state - space equation by using the spectral transformation technique with rotation - amplification pre - processing includes:

[0017] Construct an orthogonal rotation matrix, perform a rotation transformation on the state matrix based on the orthogonal rotation matrix, and multiply by an amplification factor to obtain the amplification matrix.

[0018] Optionally, in an embodiment of the present application, the construction of the sparse matrix based on the amplification matrix includes:

[0019] Construct a sparse matrix by using the Kronecker product based on the identity matrix and the amplification matrix.

[0020] Optionally, in an embodiment of the present application, the calculation of the electromagnetic transient eigenvalues of the power system by using the implicit restart Arnoldi sparse eigenvalue algorithm includes:

[0021] Construct a Krylov subspace;

[0022] Calculate the product of the sparse matrix and the state vector;

[0023] Calculate the reprojection coefficient and update the product;

[0024] Construct a Hessenberg matrix and solve it, update the Krylov subspace, and use the Newton iteration correction method to calculate the exact value of the damping ratio minimum or the rightmost part of the eigenvalues in the new power system electromagnetic transient model.

[0025] In a second aspect, the present application also provides a device for calculating the electromagnetic transient eigenvalues of a power system based on frequency shift transformation. The device includes:

[0026] An equilibrium point determination module, configured to construct an instantaneous value electromagnetic transient model in the complex space, perform frequency shift transformation to obtain a frequency shift electromagnetic transient model, and determine the power system equilibrium point based on the frequency shift electromagnetic transient model;

[0027] A linearized discrete state space equation construction module, configured to construct a linearized state space equation at the power system equilibrium point by using a discrete state space modeling method based on the frequency shift electromagnetic transient model;

[0028] An eigenvalue distribution sparsity increasing module, configured to determine an amplification matrix based on the state matrix of the linearized state space equation by using a spectral transformation technique of rotation-amplification preprocessing;

[0029] An eigenvalue calculation module, configured to construct a sparse matrix based on the amplification matrix and calculate the electromagnetic transient eigenvalues of the power system by using an implicit restart Arnoldi sparse eigenvalue algorithm.

[0030] In a third aspect, the present application also provides a computer device. The computer device includes a memory and a processor, the memory stores a computer program, and the processor executes the steps of the methods described in the above respective embodiments.

[0031] In a fourth aspect, the present application also provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the methods described in the above respective embodiments are implemented.

[0032] The above-mentioned method and device for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation first construct an instantaneous electromagnetic transient model in the complex space, perform frequency shift transformation to obtain a frequency-shifted electromagnetic transient model, and determine the equilibrium point of the power system based on the frequency-shifted electromagnetic transient model; then, construct a linearized state space equation at the equilibrium point of the power system by using the discrete state space modeling method based on the frequency-shifted electromagnetic transient model; then, use the spectral transformation technology with rotation-amplification preprocessing to determine the amplification matrix based on the state matrix of the linearized state space equation; finally, construct a sparse matrix based on the amplification matrix and calculate the electromagnetic transient eigenvalues of the power system by using the implicit restart Arnoldi sparse eigenvalue algorithm. That is to say, starting from obtaining the equilibrium point of the power system described by instantaneous values, the power system with periodic motion is transformed into a system with an equilibrium point, and the equilibrium point of the system and the electromagnetic transient model at the equilibrium point are obtained, effectively solving the problem that the electromagnetic transient model has no equilibrium point and laying a foundation for the subsequent analysis of the eigenvalues of the new power system. Secondly, a method for constructing a discrete state space equation of a new power system based on the node analysis method is proposed. Taking linearly independent historical current sources as state variables, a linearized discrete state space equation of the electromagnetic transient model of the new power system is constructed, and the state matrix of the system is obtained, which can effectively analyze the eigenvalues of the new power system. At the same time, an efficient eigenvalue calculation method based on sparse processing is proposed, which solves the problems such as extremely low calculation efficiency, easy memory overflow, difficult convergence, and error in the result of calculating the eigenvalues of the state matrix of the electromagnetic transient model. Description of the Drawings

[0033] Figure 1 It is an application environment diagram of the method for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation in an embodiment;

[0034] Figure 2 It is a schematic flowchart of the method for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation in an embodiment;

[0035] Figure 3 It is a schematic diagram of the frequency-shifted electromagnetic transient simulation idea in an embodiment;

[0036] Figure 4 It is a schematic diagram of variables before and after frequency shift transformation in an embodiment;

[0037] Figure 5 It is a structural block diagram of the device for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation in an embodiment;

[0038] Figure 6 It is an internal structure diagram of a computer device in an embodiment. Detailed Embodiments

[0039] To make the objectives, technical solutions, and advantages of this application clearer and more understandable, the following further elaborates on this application in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely used to explain this application and are not intended to limit this application.

[0040] The method for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation provided by an embodiment of this application can be applied to an application environment as Figure 1 shown. Among them, the terminal 102 communicates with the server 104 through a network. The data storage system can store the data that the server 104 needs to process. The data storage system can be integrated on the server 104, or can be placed in the cloud or on other network servers. Among them, the terminal 102 can be, but is not limited to, various personal computers, laptop computers, smartphones, tablet computers, Internet of Things devices, and portable wearable devices. The Internet of Things devices can be smart speakers, smart TVs, smart air conditioners, smart in-vehicle devices, etc. The portable wearable devices can be smart watches, smart bracelets, head-mounted devices, etc. The server 104 can be implemented by an independent server or a server cluster composed of multiple servers.

[0041] In one embodiment, as Figure 2 shown, a method for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation is provided. Taking the application of this method to the Figure 1 server as an example for illustration, it includes the following steps:

[0042] S201: Construct an instantaneous value electromagnetic transient model in the complex space, perform frequency shift transformation to obtain a frequency shift electromagnetic transient model, and determine the power system equilibrium point based on the frequency shift electromagnetic transient model.

[0043] In an embodiment of this application, first, construct an instantaneous value electromagnetic transient model in the complex space, and then perform frequency shift transformation on the electromagnetic transient model in the complex space described by the instantaneous value, thereby obtaining a frequency shift electromagnetic transient model described by the envelope signal, as Figure 3 (c) shown. For the frequency shift electromagnetic transient model, when the system is in a steady state, the envelope signals of the state variables in the system are all direct current quantities and are no longer alternating quantities, as Figure 4 shown. At this time, at the steady-state operating point, the eigenvalues of the linearized state space equation constructed based on the frequency shift electromagnetic transient model will no longer be alternating quantities, and the set composed of the values of each variable in the system at steady state is the equilibrium point of the system.

[0044] Specifically, in an embodiment of this application, the construction of the instantaneous value electromagnetic transient model in the complex space includes:

[0045] Construct an orthogonal adjoint model of the power system, and superimpose it with the original power system model to obtain an instantaneous value electromagnetic transient model in the complex space.

[0046] In one embodiment of the present application, an orthogonal adjoint model of the system is first constructed, and an instantaneous value electromagnetic transient model in complex space is obtained by superimposing the original power system model and the orthogonal adjoint model, such as Figure 3 (b) as shown.

[0047] S203: Constructing a linearized state space equation at the balance point of the power system using a discrete state space modeling method based on the frequency-shifted electromagnetic transient model.

[0048] In the embodiment of the present application, a linearized state space model at the equilibrium point is constructed based on the frequency-shifted electromagnetic transient model. Existing studies have shown that when facing the state space modeling of electromagnetic transient state space of large-scale power systems, the traditional continuous state space modeling method is difficult to eliminate the linear correlation between the state variables of different components, and it is difficult to combine the state space models of each independent component to obtain the state space equation of the whole system. This method is based on the EMTP-type electromagnetic transient simulation model of power system equipment to construct the discrete state space equation of the electromagnetic transient model of power system equipment under general circumstances.

[0049] In order to obtain the EMTP-type electromagnetic transient model of electrical components, the system differential equation is first discretized using a numerical integration method (such as the trapezoidal method) and expressed in the form of a Norton equivalent circuit:

[0050]

[0051] Where i(t) is the component current; v(t) is the component voltage; i h (t) is the historical current source, which represents the quantity related to the state at time t-Δt in the discrete expression i(t) of the component current; A, B, C, and D are coefficient matrices. It can be found that i h The expression of (t) contains the variable at time t-Δt, which is naturally the same as the discrete state equation x(t) = ax(t-Δt) + bu(t-Δt). h (t) is a discrete state variable, and the discrete state equation of the element can be expressed as:

[0052] i h (t) = A d i h (t-Δt)+B d v(t-Δt)

[0053] Among them, A d , B d are coefficient matrices respectively. The specific expression can be deduced based on the Norton equivalent circuit form equation. The Norton equivalent circuit form equation and the component discrete state equation together constitute a generalized discrete state space equation expression for the power system equipment.

[0054] Next, based on the discrete state equations of components, the discrete state - space equations of the discretized network of the power system EMTP (i.e., the adjoint circuit network) are constructed. The method of component discrete state - space modeling follows the idea of component discretization in EMTP - type simulations. All components are represented in the form of historical current sources plus equivalent conductances, and their discrete state equations are constructed. In this method, in the network state - space equations, the historical terms in the discretized expressions of each component are still used as state variables, and the system state - space equations are constructed according to the relationship of nodal voltage equations. It should be noted that the effectiveness of the discrete state - space modeling theory and its advantages compared with the traditional continuous state - space modeling theory are that the historical current terms of each component are naturally linearly independent.

[0055] In an embodiment of the present application, the construction of the linearized state - space equation at the equilibrium point of the power system by using the discrete state - space modeling method based on the shifted - frequency electromagnetic transient model includes:

[0056] Use the numerical integration method to discretize the differential equations of the power system to obtain the discrete state - space equations of the electromagnetic transient model and the port nodal current expressions;

[0057] Based on the discrete state - space equations of the electromagnetic transient model and the port nodal current expressions, use the nodal analysis method to construct the discrete state - space equations of the power system.

[0058] In an embodiment of the present application, in an actual new - type power system, there are a large number of new - energy and HVDC transmission devices. Generally, these devices contain complex control systems, and the dimension of the state - variable vector of the control system of one device can be as high as dozens to hundreds of dimensions. If no dimension - reduction processing is carried out, the system equations will face the problem of the curse of dimensionality. In fact, in EMTP - type simulations, the solution of the control system and the electrical system is also decoupled, which can also be regarded as a kind of system dimension - reduction technology. Following the idea of EMTP - type simulation methods, an idea of reducing the order of the system discrete state - space equations is proposed. For a power - system device containing a control system, use the numerical integration method to discretize the differential equations of the power system to obtain the discrete state - space equations of the electromagnetic transient model and the port nodal current expressions. Specifically, at the equilibrium point, the continuous - time state - space equation of the electromagnetic transient model can generally be expressed as:

[0059]

[0060] where \(x(t)\) is the vector of internal state variables of the device, \(i(t)\) and \(v(t)\) are the port current and voltage, and \(A_2\), \(B_2\), \(C_2\) are coefficient matrices. Taking the trapezoidal method as an example, discretize the continuous - time state - space equation of the electromagnetic transient model to derive the discrete state - space equation of the device's electromagnetic transient model:

[0061] i h i(t) = A d2 i h (t - Δt) + B d2 v(t - Δt)

[0062] wherein, i h (t) is the historical current source, and A d2 and B d2 are the coefficient matrices of the discrete state equations of the components.

[0063] Meanwhile, the expression of the port node current of the device is derived (regarded as the output equation):

[0064] i(t) = C d2 i h (t) + D d2 v(t)

[0065] wherein, C d2 and D d2 are the coefficient matrices of the output equation.

[0066] In the discrete state space equation of the system, the dimension of all component state variables is the same as the number of branches in its electrical network, which is much smaller than the original state equation. The complex dynamics of the component control system are implicit in its low-dimensional discrete state space equation. Additionally, when performing discrete state space modeling, the system is modeled in the abc phase domain to make full use of elements such as the nodal admittance matrix in the EMTP simulation program. After all components are expressed in the form of the discrete state space equation of the device electromagnetic transient model and the expression of the port node current of the device, the discrete state space equation of the entire system is constructed using the nodal analysis method.

[0067] S205: Determine the amplification matrix based on the state matrix of the linearized state space equation using the spectral transformation technique with rotation-amplification preprocessing.

[0068] In the embodiments of the present application, since the dimension of the state space equation of the electromagnetic transient model of the new power system is much higher than that of the corresponding state space equation of the traditional electromechanical transient simulation model, the eigenvalue calculation generally uses an implicit sparse calculation method. When calculating some eigenvalues with the largest modulus of the discrete state matrix using the sparse eigenvalue algorithm, the calculation convergence speed depends on the sparsity of the eigenvalue distribution of the discretized matrix of the solution operator (the relative distance between eigenvalues). Therefore, the spectral transformation technique with rotation-amplification preprocessing is used to increase the sparsity of the discrete state space eigenvalue distribution.

[0069] Specifically, in an embodiment of the present application, the determining of the amplification matrix based on the state matrix of the linearized state space equation using the spectral transformation technique with rotation-amplification preprocessing includes:

[0070] Construct an orthogonal rotation matrix, perform a rotation transformation on the state matrix based on the orthogonal rotation matrix, and multiply by an amplification factor to obtain an amplification matrix.

[0071] In an embodiment of the present application, first, an orthogonal rotation matrix Q is constructed, and a rotation transformation is performed on the state matrix A of the system, which can make the eigenvalues more dispersed in the frequency domain and enhance the influence of important eigenvalues. The rotation transformation process is shown in the following formula:

[0072] A′ = Q T AQ

[0073] Then, a new amplification matrix A is constructed by multiplying the rotated state matrix A′ by the amplification factor λ scaled :

[0074] A scaled = λA′

[0075] Through the above rotation-amplification preprocessing, the calculation of some eigenvalues with the largest modulus of the discrete state matrix is greatly accelerated, which can achieve the purpose of optimizing the sparse distribution characteristics of eigenvalues and accelerating the convergence rate of sparse eigenvalue calculation.

[0076] S207: Construct a sparse matrix based on the amplification matrix, and calculate the electromagnetic transient eigenvalues of the power system by using the implicit restart Arnoldi sparse eigenvalue algorithm.

[0077] In an embodiment of the present application, the constructing a sparse matrix based on the amplification matrix includes:

[0078] Construct a sparse matrix by using the Kronecker product based on the identity matrix and the amplification matrix.

[0079] In an embodiment of the present application, based on the sparse characteristics of the system augmented discrete state matrix, methods such as the Kronecker product are used to implement the sparse calculation of the product operation of the discrete state matrix and the vector. For A scaled and the coefficient matrix B of the discrete state space equation, its Kronecker product is defined as:

[0080]

[0081] Select an identity matrix I m to expand the dimension, and use the Kronecker product to construct a new sparse matrix:

[0082] C = A scaled ×I m

[0083] Then, the sparse calculation is realized by multiplying the matrix C and the state vector:

[0084] y = C·vec(x k)

[0085] Among them, vec(x k ) represents an n×1 column vector.

[0086] In an embodiment of the present application, the calculation of the electromagnetic transient eigenvalues of the power system by using the implicitly restarted Arnoldi sparse eigenvalue algorithm includes:

[0087] Construct a Krylov subspace;

[0088] Calculate the product of the sparse matrix and the state vector;

[0089] Calculate the reprojection coefficient and update the product;

[0090] Construct a Hessenberg matrix and solve it, update the Krylov subspace, and use the Newton iteration correction method to calculate the exact values of the eigenvalues with the smallest damping ratio or the rightmost part in the new electromagnetic transient model of the power system.

[0091] In an embodiment of the present application, based on the implicitly restarted Arnoldi sparse eigenvalue algorithm, effectively calculate the partial eigenvalues with the largest modulus value in the discretized state matrix. First, use the initial vector v1 to construct a Krylov subspace:

[0092] κ k (A, v1) = span{v1, Av1, A 2 v1,..., A k-1 v1}

[0093] Among them, A is the abbreviation of the sparse matrix A scaled and A 2 is the product of two matrices A·A, and A k-1 is the (k - 1)th power of the matrix A.

[0094] In each iteration, calculate the product of the sparse matrix and the state vector:

[0095] w = Cv j = (A scaled × I m )v j

[0096] Among them, v j is the state vector.

[0097] Calculate the reprojection coefficient and update the product w. The specific formula is as follows:

[0098]

[0099] w = w - h ij v i

[0100] where h ij is the reprojection coefficient, and v i is the i-th basis vector in the Krylov subspace.

[0101] Next, construct the Hessenberg matrix as follows:

[0102]

[0103] The upper triangular form of the Hessenberg matrix simplifies the complexity of eigenvalue solving. Utilizing this structure can significantly improve the efficiency of numerical calculations. By solving the eigenvalue problem of H k :

[0104] det(H k - λI) = 0

[0105] where λ is the eigenvalue to be solved, and I is the identity matrix.

[0106] Select the first m eigenvalues and the corresponding eigenvectors as the new initial vector v j+1 , update the Krylov subspace for the next round of iteration. Then, using the Newton iteration correction method, calculate the exact values of the damping ratio minimum or the rightmost part eigenvalues in the electromagnetic transient model of the new power system.

[0107] According to the calculation results of the discrete eigenvalues, the stability of the new power system can be analyzed more accurately. The discrete eigenvalues obtained by the optimization method are more accurate in calculating the two parameters of the variable participation factor and the component participation degree. When characterizing the participation degree of different electrical equipment in the oscillation mode, it is easy to identify the source of system oscillation. At the same time, the accurate calculation of the discrete eigenvalues of the new power system can better reflect the oscillation frequency of the system, and has a better fitting effect on the simulation results of time-domain simulation, etc.

[0108] In the above method for calculating the electromagnetic transient eigenvalues of a power system based on frequency shift transformation, first, an instantaneous value electromagnetic transient model in the complex space is constructed, and frequency shift transformation is performed to obtain a frequency shift electromagnetic transient model. Based on the frequency shift electromagnetic transient model, the equilibrium point of the power system is determined. Then, based on the frequency shift electromagnetic transient model, a linearized state space equation at the equilibrium point of the power system is constructed using the discrete state space modeling method. Then, a magnification matrix is determined based on the state matrix of the linearized state space equation using the spectral transformation technology with rotation-amplification preprocessing. Finally, a sparse matrix is constructed based on the magnification matrix, and the electromagnetic transient eigenvalues of the power system are calculated using the implicit restart Arnoldi sparse eigenvalue algorithm. That is to say, starting from obtaining the equilibrium point of the power system described by instantaneous values, the power system with periodic motion is transformed into a system containing an equilibrium point, and the equilibrium point of the system and the electromagnetic transient model at the equilibrium point are obtained, effectively solving the problem that the electromagnetic transient model has no equilibrium point and laying a foundation for the subsequent analysis of the eigenvalues of the new power system. Secondly, a method for constructing a discrete state space equation of a new power system based on the nodal analysis method is proposed. Taking linearly independent historical current sources as state variables, a linearized discrete state space equation of the electromagnetic transient model of the new power system is constructed, and the state matrix of the system is obtained, which can effectively analyze the eigenvalues of the new power system. At the same time, an efficient eigenvalue calculation method based on sparse processing is proposed, solving the problems such as extremely low calculation efficiency, easy memory overflow, difficult convergence, and error in the results in calculating the eigenvalues of the state matrix of the electromagnetic transient model.

[0109] It should be understood that although the steps in the flowcharts involved in the above embodiments are shown in sequence according to the arrows, these steps do not necessarily need to be executed in the order indicated by the arrows. Unless there is a clear description in this article, the execution of these steps has no strict order limit, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above embodiments may include multiple steps or multiple stages. These steps or stages do not necessarily need to be executed at the same time, but can be executed at different times. The execution order of these steps or stages does not necessarily need to be sequential, but can be executed alternately or in turn with at least a part of the steps or stages in other steps or other steps.

[0110] Based on the same inventive concept, an embodiment of the present application further provides a device for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation for implementing the method for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation involved above. The implementation solutions provided by this device to solve problems are similar to those recorded in the above method. Therefore, the specific limitations in one or more embodiments of the device for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation provided below can refer to the limitations on the method for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation in the above text, and will not be repeated here.

[0111] In one embodiment, as Figure 5 shown, a device 500 for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation is provided, including: an equilibrium point determination module 501, a linearized discrete state space equation construction module 503, an eigenvalue distribution sparsity increasing module 505, and an eigenvalue calculation module 507, where:

[0112] The equilibrium point determination module 501 is configured to construct an instantaneous value electromagnetic transient model in the complex space, perform frequency shift transformation to obtain a frequency shift electromagnetic transient model, and determine the power system equilibrium point based on the frequency shift electromagnetic transient model.

[0113] The linearized discrete state space equation construction module 503 is configured to construct a linearized state space equation at the power system equilibrium point by using a discrete state space modeling method based on the frequency shift electromagnetic transient model.

[0114] The eigenvalue distribution sparsity increasing module 505 is configured to determine an amplification matrix based on the state matrix of the linearized state space equation by using a spectral transformation technique of rotation-amplification preprocessing.

[0115] The eigenvalue calculation module 507 is configured to construct a sparse matrix based on the amplification matrix and calculate the electromagnetic transient eigenvalues of the power system by using an implicit restart Arnoldi sparse eigenvalue algorithm.

[0116] In one embodiment of the present application, the equilibrium point determination module is further configured to:

[0117] Construct an orthogonal adjoint model of the power system, and superimpose it with the original power system model to obtain an instantaneous value electromagnetic transient model in the complex space.

[0118] In one embodiment of the present application, the linearized discrete state space equation construction module is further configured to:

[0119] Discretize the power system differential equation by using a numerical integration method to obtain a discrete state space equation of the electromagnetic transient model and a port node current expression;

[0120] Based on the discrete state - space equation of the electromagnetic transient model and the port - node current expression, the node analysis method is used to construct the discrete state - space equation of the power system.

[0121] In one embodiment of the present application, the eigenvalue distribution sparsity increasing module is further configured to:

[0122] Construct an orthogonal rotation matrix, perform a rotation transformation on the state matrix based on the orthogonal rotation matrix, and multiply by an amplification factor to obtain an amplified matrix.

[0123] In one embodiment of the present application, the eigenvalue calculation module is further configured to:

[0124] Construct a sparse matrix using the Kronecker product based on the identity matrix and the amplified matrix.

[0125] In one embodiment of the present application, the eigenvalue calculation module is further configured to:

[0126] Construct a Krylov subspace;

[0127] Calculate the product of the sparse matrix and the state vector;

[0128] Calculate the reprojection coefficient and update the product;

[0129] Construct and solve a Hessenberg matrix, update the Krylov subspace, and use the Newton iteration correction method to calculate the exact values of the damping ratios that are the smallest or the eigenvalues in the right - most part in the electromagnetic transient model of the new power system.

[0130] Each module in the above - mentioned power system electromagnetic transient eigenvalue calculation device based on frequency - shift transformation can be implemented in whole or in part by software, hardware, and their combination. The above - mentioned modules can be embedded in the processor of the computer device in hardware form or be independent of it, or can be stored in the memory of the computer device in software form, so as to facilitate the processor to call and execute the operations corresponding to the above - mentioned modules.

[0131] In one embodiment, a computer device is provided. The computer device can be a terminal, and its internal structure diagram can be as Figure 6As shown in the figure. The computer device includes a processor, a memory, a communication interface, a display screen, and an input device connected via a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The communication interface of the computer device is used to communicate with external terminals in a wired or wireless manner, and the wireless manner can be implemented through WIFI, mobile cellular networks, NFC (Near Field Communication), or other technologies. When the computer program is executed by the processor, it implements a method for calculating electromagnetic transient eigenvalues of a power system based on frequency shift transformation. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a button, trackball, or touchpad provided on the outer shell of the computer device, or an external keyboard, touchpad, or mouse, etc.

[0132] Those skilled in the art can understand that Figure 6 the structure shown in the figure is only a block diagram of some structures related to the solution of this application, and does not constitute a limitation on the computer device to which the solution of this application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0133] In one embodiment, a computer device is provided, including a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are implemented.

[0134] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by the processor, the steps in the above method embodiments are implemented.

[0135] In one embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by the processor, the steps in the above method embodiments are implemented.

[0136] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0137] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memories. Non-volatile memories can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memories can include random access memory (RAM) or external cache memory, etc. 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. The databases involved in the embodiments provided in the present application can include at least one of relational databases and non-relational databases. Non-relational databases can include distributed databases based on blockchain, etc., without limitation. The processors involved in the embodiments provided in the present application can be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, data processing logics based on quantum computing, etc., without limitation.

[0138] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0139] The above-described embodiments merely represent several implementation manners of the present application. Their descriptions are relatively specific and detailed, but they should not be construed as limiting the patent scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A method for calculating electromagnetic transient characteristic values ​​of power system based on frequency shift conversion, characterized in that: The method comprises: Constructing an instantaneous value electromagnetic transient model in complex space, performing frequency shift transformation to obtain a frequency shift electromagnetic transient model, and determining a balance point of the power system based on the frequency shift electromagnetic transient model; Based on the frequency-shifted electromagnetic transient model, a discrete state space modeling method is used to construct a linearized state space equation at the balance point of the power system; Determine an amplification matrix based on the state matrix of the linearized state space equation using a spectral transformation technique of rotation-amplification preprocessing; A sparse matrix is ​​constructed based on the amplified matrix, and an implicit restart-based Arnoldi sparse eigenvalue algorithm is used to calculate the electromagnetic transient eigenvalues ​​of the power system.

2. The method for calculating the electromagnetic transient characteristic value of the power system based on frequency shift transformation according to claim 1 is characterized in that: The construction of the instantaneous value electromagnetic transient model in complex space includes: An orthogonal adjoint model of the power system is constructed and superimposed on the original power system model to obtain an instantaneous electromagnetic transient model in complex space.

3. The method for calculating electromagnetic transient characteristic values ​​of a power system based on frequency shift transformation according to claim 1, characterized in that: The method of constructing the linearized state space equation at the balance point of the power system based on the frequency-shifted electromagnetic transient model using a discrete state space modeling method includes: The power system differential equations are discretized using numerical integration methods to obtain the discrete state space equations of the electromagnetic transient model and the port node current expressions; Based on the discrete state space equation of the electromagnetic transient model and the port node current expression, the discrete state space equation of the power system is constructed by adopting the node analysis method.

4. The method for calculating electromagnetic transient characteristic values ​​of a power system based on frequency shift transformation according to claim 1, characterized in that: The spectrum transformation technology using rotation-amplification preprocessing determines the amplification matrix based on the state matrix of the linearized state space equation, including: An orthogonal rotation matrix is ​​constructed, and a state matrix is ​​rotated and transformed based on the orthogonal rotation matrix, and then multiplied by a magnification factor to obtain a magnification matrix.

5. The method for calculating the electromagnetic transient characteristic value of a power system based on frequency shift transformation according to claim 1, characterized in that: The constructing a sparse matrix based on the magnified matrix comprises: A sparse matrix is ​​constructed based on the identity matrix and the magnification matrix using the Kronecker product.

6. The method for calculating the electromagnetic transient characteristic value of a power system based on frequency shift transformation according to claim 1, characterized in that: The method of calculating the electromagnetic transient eigenvalue of the power system by using the implicit restart Arnoldi sparse eigenvalue algorithm includes: Construct Krylov subspace; Calculating the product of the sparse matrix and the state vector; Calculate reprojection coefficients and update the product; The Heisenberg matrix is ​​constructed and solved, the Krylov subspace is updated, and the Newton iterative correction method is used to calculate the exact value of the eigenvalue of the smallest or rightmost part of the damping ratio in the new power system electromagnetic transient model.

7. A device for calculating electromagnetic transient characteristic values ​​of a power system based on frequency shift conversion, characterized in that: The device comprises: A balance point determination module is used to construct an instantaneous value electromagnetic transient model in complex space, perform frequency shift transformation, obtain a frequency shift electromagnetic transient model, and determine the balance point of the power system based on the frequency shift electromagnetic transient model; A linearized discrete state space equation construction module, used to construct a linearized state space equation at the balance point of the power system based on the frequency-shifted electromagnetic transient model using a discrete state space modeling method; An eigenvalue distribution sparsity increasing module, used for determining an amplification matrix based on the state matrix of the linearized state space equation by using a spectral transformation technique of rotation-amplification preprocessing; The eigenvalue calculation module is used to construct a sparse matrix based on the amplified matrix, and calculate the electromagnetic transient eigenvalues ​​of the power system by using an implicit restart Arnoldi sparse eigenvalue algorithm.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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