Method and device for calculating electromagnetic transient characteristic value of power system based on frequency shift conversion

Abstract

The invention relates to a power system electromagnetic transient characteristic value calculation method and device based on frequency shift conversion. The method comprises the following steps: firstly, constructing an instantaneous value electromagnetic transient model of a complex space, carrying out frequency shift conversion to obtain a frequency shift electromagnetic transient model, and determining a balance point of a power system based on the frequency shift electromagnetic transient model; then, constructing a linear state-space equation at the balance point of the power system by adopting a discrete state-space modeling method based on the frequency-shift electromagnetic transient model; then, determining an amplification matrix based on the state matrix of the linearized state-space equation by adopting a rotation-amplification preprocessing spectral transformation technology; and finally, constructing a sparse matrix based on the amplification matrix, and calculating an electromagnetic transient characteristic value of the power system by adopting an Arnoldi sparse characteristic value algorithm based on implicit restart. The problems of extremely low calculation efficiency, easy memory overflow, difficult convergence, result error and the like existing in characteristic value calculation of the electromagnetic transient model state matrix are solved.

Description

Technical Field

[0001] The present application relates to the technical field of novel power system electromagnetic transient modeling, and in particular 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 renewable energy to power systems, the dynamic behavior of the system has become increasingly complex. The computational efficiency of traditional methods is difficult to cope with the high requirements of new power systems, especially when performing 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 characterize the dynamic process of the new power system. Compared with the electromechanical transient simulation model, the electromagnetic transient simulation model can accurately simulate the broadband dynamic process of the power system. Therefore, for the new power system, it is necessary to use the electromagnetic transient model to accurately simulate its 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 the 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 modeling in the electromagnetic transient model is a differential equation, the independence between the state variables in the network needs to be determined when using the traditional state variable analysis method. When the system scale increases, due to the complex topological connection relationship in the system, the elimination of non-independent state variables is particularly difficult. In addition, 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. The eigenvalue calculation of the state matrix of ultra-high-dimensional sparse electromagnetic transient models has problems such as convergence difficulties, errors in the results, extremely low calculation efficiency, easy memory overflow, and even prone to calculation failure.

[0004] Therefore, in the related technology, there is an urgent need for a method that can improve the accuracy of calculating the characteristic values ​​of the new power system. Summary of the invention

[0005] Based on this, it is necessary to provide a method and device for calculating the electromagnetic transient eigenvalues ​​of an electric power system based on frequency shift transformation, which can improve the calculation accuracy of the eigenvalues ​​of a new electric power system in order to address the above technical problems.

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

[0007] 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;

[0008] 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;

[0009] Determine an amplification matrix based on the state matrix of the linearized state space equation using a spectral transformation technique of rotation-amplification preprocessing;

[0010] 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.

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

[0012] 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.

[0013] Optionally, in one embodiment of the present application, 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:

[0014] 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;

[0015] 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.

[0016] Optionally, in one embodiment of the present application, the spectral transformation technology using rotation-amplification preprocessing determines the amplification matrix based on the state matrix of the linearized state space equation, including:

[0017] 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.

[0018] Optionally, in one embodiment of the present application, constructing a sparse matrix based on the magnification matrix includes:

[0019] A sparse matrix is ​​constructed based on the identity matrix and the magnification matrix using the Kronecker product.

[0020] Optionally, in one embodiment of the present application, the calculating of the electromagnetic transient eigenvalue of the power system by using the implicit restart-based Arnoldi sparse eigenvalue algorithm includes:

[0021] Construct Krylov subspace;

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

[0023] Calculate reprojection coefficients and update the product;

[0024] 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.

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

[0026] 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;

[0027] 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;

[0028] 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;

[0029] 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.

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

[0031] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the method described in each of the above embodiments are implemented.

[0032] The above-mentioned method and device for calculating electromagnetic transient eigenvalues ​​of power system based on frequency shift transformation, first, 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; then, based on the frequency shift electromagnetic transient model, a discrete state space modeling method is used to construct the linearized state space equation at the balance point of the power system; then, a spectrum transformation technology with rotation-amplification preprocessing is used to determine the amplification matrix based on the state matrix of the linearized state space equation; finally, a sparse matrix is ​​constructed based on the amplification matrix, and the electromagnetic transient eigenvalue algorithm based on implicit restart Arnoldi is used to calculate the electromagnetic transient eigenvalue of the power system. In other words, starting from the balance point of the power system described by the instantaneous value, the periodic motion power system is converted into a system containing a balance point, and the balance point of the system and the electromagnetic transient model at the balance point are obtained, which effectively solves the problem that there is no balance point in the electromagnetic transient model, and lays a foundation for the subsequent analysis of the eigenvalues ​​of new power systems. Secondly, a new method for constructing discrete state space equations of power systems based on node analysis is proposed. With linearly independent historical current sources as state variables, the linearized discrete state space equations of the electromagnetic transient model of the new power system are 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 to solve the problems of extremely low calculation efficiency, easy memory overflow, difficult convergence, and errors in the results of eigenvalue calculation of the state matrix of the electromagnetic transient model. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is an application environment diagram of a method for calculating electromagnetic transient characteristic values ​​of a power system based on frequency shift conversion in one embodiment;

[0034] Figure 2 It is a flowchart of a method for calculating electromagnetic transient characteristic values ​​of a power system based on frequency shift conversion in one embodiment;

[0035] Figure 3 A schematic diagram of a frequency-shifted electromagnetic transient simulation concept in an embodiment;

[0036] Figure 4 A schematic diagram of variables before and after frequency shift conversion in one embodiment;

[0037] Figure 5 It is a structural block diagram of a device for calculating electromagnetic transient characteristic values ​​of a power system based on frequency shift conversion in one embodiment;

[0038] Figure 6 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0040] The method for calculating the electromagnetic transient characteristic value of a power system based on frequency shift transformation provided in the embodiment of the present application can be applied to Figure 1 In the application environment shown. Among them, the terminal 102 communicates with the server 104 through the 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 it can be placed on the cloud or other network servers. Among them, the terminal 102 can be but is not limited to various personal computers, laptops, smart phones, tablets, Internet of Things devices and portable wearable devices. The Internet of Things devices can be smart speakers, smart TVs, smart air conditioners, smart car-mounted devices, etc. Portable wearable devices can be smart watches, smart bracelets, head-mounted devices, etc. The server 104 can be implemented with an independent server or a server cluster consisting of multiple servers.

[0041] In one embodiment, Figure 2 As shown in the figure, a method for calculating the electromagnetic transient characteristic value of a power system based on frequency shift transformation is provided. Figure 1 The server in the example is used to illustrate the following steps:

[0042] S201: 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.

[0043] In the embodiment of the present application, first, a complex space instantaneous value electromagnetic transient model is constructed, and then the complex space electromagnetic transient model described by the instantaneous value is subjected to frequency shift transformation, thereby obtaining a frequency shift electromagnetic transient model described by an envelope signal, such as Figure 3 (c) As shown in Figure 2, for the frequency-shifted electromagnetic transient model, when the system is in a steady state, the envelope signals of the state variables in the system are all DC quantities, not AC quantities, such as Figure 4 At this time, at the steady-state operation point, the eigenvalue of the linearized state space equation constructed based on the frequency-shifted electromagnetic transient model will no longer be an alternating variable, and the set of values ​​of the system variables in the steady state is the equilibrium point of the system.

[0044] Specifically, in one embodiment of the present application, constructing the instantaneous value electromagnetic transient model of the complex space includes:

[0045] 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.

[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 the components, the discrete state space equations of the EMTP discretized network (i.e., the accompanying circuit network) of the power system are constructed. The method of discrete state space modeling of components follows the idea of ​​component discretization of EMTP-type simulations, represents all components in the form of historical current sources plus equivalent conductances, and constructs their discrete state equations. 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 based on the relationship between the node voltage equations. It should be noted that the effectiveness of the discrete state space modeling theory and its advantage over the traditional continuous state space modeling theory is that the historical current terms of each component are naturally linearly independent.

[0055] In one embodiment of the present application, 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:

[0056] 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;

[0057] 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.

[0058] In one embodiment of the present application, the actual new power system includes a large number of new energy sources, direct current transmission and other equipment. Generally speaking, these devices contain complex control systems, and the dimension of the state variable vector of the control system of a device is as high as tens to hundreds of dimensions. If dimensionality reduction is not performed, the system equation will face the problem of dimensionality disaster. 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 system dimensionality reduction technology. Following the idea of ​​EMTP-type simulation methods, an idea of ​​reducing the order of discrete state space equations of the system is proposed. For a power system device containing a control system, the numerical integration method is used to discretize the differential equations of the power system to obtain the discrete state space equations of the electromagnetic transient model and the port node 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] Among them, x(t) is the internal state variable vector of the equipment, i(t) and v(t) are the port current and voltage, A2, B2, C2 are coefficient matrices, and the continuous time state space equation of the electromagnetic transient model is discretized by taking the trapezoidal method as an example, and the discrete state space equation of the electromagnetic transient model of the equipment can be derived:

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

[0062] Among them, i h (t) is the historical current source, A d2 , B d2 is the coefficient matrix of the discrete state equation of the component.

[0063] At the same time, the expression of the port node current of the device is derived (considered as the output equation):

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

[0065] Among them, C d2 , D d2 is the output equation coefficient matrix.

[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 is implicit in its low-dimensional discrete state space equation. In addition, when modeling the discrete state space, the system is modeled in the abc phase domain to make full use of elements such as the node admittance matrix in the EMTP simulation program. When all components are expressed in the form of discrete state space equations of the electromagnetic transient model of the equipment and expressions of the port node currents of the equipment, the node analysis method is used to construct the discrete state space equations of the entire system.

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

[0068] In the embodiment 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 the state space equation corresponding to the traditional electromechanical transient simulation model, its eigenvalue calculation generally adopts an implicit sparse calculation method. When the sparse eigenvalue algorithm is used to calculate the partial eigenvalues ​​with the largest modulus value of the discrete state matrix, the calculation convergence speed depends on the sparsity of the eigenvalue distribution of the discretization matrix of the solution operator (the relative distance between the eigenvalues). Therefore, the spectral transformation technology of the rotation-amplification preprocessing is used to increase the sparsity of the eigenvalue distribution of the discrete state space.

[0069] Specifically, in one embodiment of the present application, the spectrum transformation technology using rotation-amplification preprocessing determines the amplification matrix based on the state matrix of the linearized state space equation, including:

[0070] 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.

[0071] In one embodiment of the present application, an orthogonal rotation matrix Q is first constructed to perform a rotation transformation 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, the new magnification matrix A is constructed by multiplying the state matrix A′ after the rotation transformation by the magnification factor λ scaled :

[0074] A scaled =λA′

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

[0076] S207: constructing a sparse matrix based on the amplified matrix, and calculating the electromagnetic transient eigenvalues ​​of the power system using an implicit restart-based Arnoldi sparse eigenvalue algorithm.

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

[0078] A sparse matrix is ​​constructed based on the identity matrix and the magnification matrix using the Kronecker product.

[0079] In one embodiment of the present application, based on the sparse characteristics of the system augmented discrete state matrix, a method such as Kronecker product is used to implement sparse calculation of the product operation of the discrete state matrix and the vector. scaled and the coefficient matrix B of the discrete state space equation, whose Kronecker product is defined as:

[0080]

[0081] Choose an identity matrix I m To expand the dimension, construct a new sparse matrix using the Kronecker product:

[0082] C=A scaled ×I m

[0083] Sparse calculation is then achieved by multiplying the matrix C with the state vector:

[0084] y=C·vec(x k)

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

[0086] In one embodiment of the present application, the calculation of the electromagnetic transient eigenvalue of the power system by using the implicit restart-based Arnoldi sparse eigenvalue algorithm includes:

[0087] Construct Krylov subspace;

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

[0089] Calculate reprojection coefficients and update the product;

[0090] 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.

[0091] In one embodiment of the present application, based on the implicit restart Arnoldi sparse eigenvalue algorithm, the largest partial eigenvalue in the module value of the discretized state matrix is ​​effectively calculated. First, the Krylov subspace is constructed using the initial vector v1:

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

[0093] Where A is a sparse matrix A scaled Abbreviation of A 2 is the product of two matrices A·A, A k-1 is the k-1th power of matrix A.

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

[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=wh ij v i

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

[0101] Then construct the Hessenberg matrix as follows:

[0102]

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

[0104] det(H k -λI)=0

[0105] Among them, λ is the eigenvalue to be found, and I is the unit matrix.

[0106] Select the first m eigenvalues ​​and corresponding eigenvectors as the new initial vector v j+1 , update the Krylov subspace for the next round of iteration, and then use the Newton iterative correction method 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.

[0107] According to the calculation results of 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 variable participation factor and component participation. When characterizing the degree of participation of different electrical equipment in the oscillation mode, it is easy to identify the source of the oscillation of the system. 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 have a better fitting effect on the simulation results of time domain simulation, etc.

[0108] In the above-mentioned method for calculating the electromagnetic transient eigenvalue of the power system based on frequency shift transformation, first, an instantaneous value electromagnetic transient model of complex space is constructed, and frequency shift transformation is performed to obtain the frequency shift electromagnetic transient model, and the balance point of the power system is determined based on the frequency shift electromagnetic transient model; then, a linearized state space equation at the balance point of the power system is constructed based on the frequency shift electromagnetic transient model by using a discrete state space modeling method; then, a spectrum transformation technique with rotation-amplification preprocessing is used to determine the amplification matrix based on the state matrix of the linearized state space equation; finally, a sparse matrix is ​​constructed based on the amplification matrix, and the electromagnetic transient eigenvalue of the power system is calculated by using the implicit restart Arnoldi sparse eigenvalue algorithm. In other words, starting from the equilibrium point of the power system described by the instantaneous value, the periodic motion power system is converted into a system containing the equilibrium point, and the equilibrium point of the system and the electromagnetic transient model at the equilibrium point are obtained, which effectively solves the problem that there is no equilibrium point in the electromagnetic transient model, and lays a foundation for the subsequent analysis of the eigenvalues ​​of the new power system. Secondly, a new method for constructing discrete state space equations of power systems based on node analysis is proposed. With linearly independent historical current sources as state variables, the linearized discrete state space equations of the electromagnetic transient model of the new power system are 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 to solve the problems of extremely low calculation efficiency, easy memory overflow, difficult convergence, and errors in the results of eigenvalue calculation of the state matrix of the electromagnetic transient model.

[0109] It should be understood that, although the various steps in the flowcharts involved in the above-mentioned embodiments are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above-mentioned embodiments can include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0110] Based on the same inventive concept, the embodiment of the present application also provides a device for calculating electromagnetic transient characteristic values ​​of a power system based on frequency shift transformation for implementing the method for calculating electromagnetic transient characteristic values ​​of a power system based on frequency shift transformation. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above method, so the specific limitations in the embodiments of one or more devices for calculating electromagnetic transient characteristic values ​​of a power system based on frequency shift transformation provided below can be referred to the limitations of the method for calculating electromagnetic transient characteristic values ​​of a power system based on frequency shift transformation in the above text, and will not be repeated here.

[0111] In one embodiment, Figure 5 As shown, a device 500 for calculating electromagnetic transient eigenvalues ​​of a power system based on frequency shift transformation is provided, comprising: a balance 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, wherein:

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

[0113] The linearized discrete state space equation construction module 503 is used to construct 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.

[0114] The eigenvalue distribution sparsity increasing module 505 is used to determine the amplification matrix based on the state matrix of the linearized state space equation by using the spectrum transformation technology of rotation-amplification preprocessing.

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

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

[0117] 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.

[0118] In one embodiment of the present application, the linearized discrete state space equation building module is also used to:

[0119] 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;

[0120] 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.

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

[0122] 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.

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

[0124] A sparse matrix is ​​constructed based on the identity matrix and the magnification matrix using the Kronecker product.

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

[0126] Construct Krylov subspace;

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

[0128] Calculate reprojection coefficients and update the product;

[0129] 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.

[0130] Each module in the above-mentioned power system electromagnetic transient characteristic value calculation device based on frequency shift conversion can be fully or partially implemented by software, hardware and their combination. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the corresponding operations of each of the above modules.

[0131] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 6As shown. The computer device includes a processor, a memory, a communication interface, a display screen and an input device connected through 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 a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, a mobile cellular network, NFC (near field communication) or other technologies. When the computer program is executed by the processor, a method for calculating the electromagnetic transient characteristic value of a power system based on frequency shift conversion is implemented. 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 covered on the display screen, or a key, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse.

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

[0133] In one embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

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

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

[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 used 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 skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and 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-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, 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 memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

[0138] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, 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, they should be considered to be within the scope of this specification.

[0139] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached 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 is 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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