A method for analyzing cross-scale interactions in power systems under transient disturbances

Abstract

The present invention discloses a method for analyzing cross-scale interactions of power systems under transient disturbances, belonging to the field of power system control technology. A second-order Taylor expansion is performed at an off-equilibrium point on the nonlinear differential equations of the x-domain state variables of the power system under transient disturbances, so as to sequentially transform the nonlinear differential equations of the x-domain state variables into the y-domain, z-domain, and m-domain to obtain an analytical expression of the m-domain state variables. Compared to the first-order Taylor expansion, the second-order Taylor expansion includes a second-order nonlinear term matrix, which can more accurately characterize the strong nonlinear dynamic behavior of the power system. Furthermore, the analytical expression of the m-domain state variables is sequentially inversely transformed into the z-domain, y-domain, and x-domain to obtain an analytical expression of the x-domain state variables of the power system under transient disturbances. Since the analytical expression of the x-domain state variables includes a constant term, an independent frequency term, and a coupled frequency term, it describes the multi-time-scale characteristics of the power system at the off-equilibrium point.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system control, and more specifically, relates to an analysis method for cross-scale interaction of power systems under transient disturbances. Background Art

[0002] In recent years, the penetration rate of renewable energy has continued to increase, and the problem of broadband oscillations with unknown mechanisms has led to the large-scale deployment of renewable energy units. In new power systems based on power electronics, the physical and control structures of power electronic equipment differ significantly from those of traditional synchronous units. This has led to significant changes in the composition and operational structure of power systems, and profound changes in the transient dynamic behavior of the system under disturbances. The fundamental characteristic that distinguishes power electronic equipment from electromagnetic equipment is multiscale control. Understanding the dynamic characteristics of equipment under multiscale control is a key issue in the study of the stability of power electronic power systems.

[0003] Currently, modal analysis is mainly used to analyze the stability of power systems under small disturbances. However, in systems with a high proportion of new energy, the system exhibits strong nonlinear characteristics. Under the same disturbance, the power system is at a non-equilibrium point during the transient process.

[0004] That is, the modal analysis method based on first-order Taylor expansion cannot perform cross-scale interaction analysis on the non-equilibrium points of the power system under transient disturbances. Summary of the Invention

[0005] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a method for analyzing cross-scale interactions of power systems under transient disturbances, the purpose of which is to solve the technical problem that the modal analysis method based on first-order Taylor expansion cannot perform cross-scale interaction analysis of power systems under transient disturbances.

[0006] To achieve the above objectives, according to one aspect of the present invention, a method for analyzing cross-scale interactions of power systems under transient disturbances is provided, comprising:

[0007] S1: Construct a nonlinear differential equation of the x-domain state variable with physical meaning for the power system under transient disturbance, perform a second-order Taylor expansion on the differential equation of the x-domain state variable at a non-equilibrium point, and then perform a linear coordinate transformation to obtain a differential equation of the y-domain state variable containing a second-order nonlinear term; perform a normal form nonlinear transformation on the differential equation of the y-domain state variable to eliminate the nonlinear term and convert it into a differential equation of the z-domain state variable;

[0008] S2: Transfer the differential equation of the z-domain state variable to the decoupled domain m to obtain an analytical expression of the m-domain state variable;

[0009] S3: Inversely transforming the analytical expression of the m-domain state variable into the z-domain, y-domain, and x-domain in sequence, so as to convert the m-domain, which does not contain actual physical meaning, into the x-domain, which has actual physical meaning, to obtain the analytical expression of the x-domain state variable of the power system under the transient disturbance, wherein the analytical expression of the x-domain state variable is expanded to include a constant term, an independent frequency term, and a coupled frequency term;

[0010] S4: Analyze the independent frequency terms and the coupled frequency terms to determine cross-scale characteristics of the power system under transient disturbances.

[0011] In one embodiment, the S1 includes:

[0012] Construct the power system model under transient disturbance The differential equation of x-domain state variables with Taylor second-order expansion at non-equilibrium point

[0013] Substitute x=Uy into get

[0014] Set y = z + G(z), and take the derivative of y = z + G(z) to get Bring it in get

[0015] Set (I+DG(z)) -1 =I-DG(z) Obtain z=P-DG(z)P+Λz+ΛG(z)+F(z)-(DG(z))Λz+O(3);

[0016] Where P = U -1 B, O(3) is the third-order and higher-order term, D is the Jacobian matrix operator, U is the right eigenvector matrix of x, H j is the Hessian matrix of the jth state variable, Λ is the characteristic root of matrix A λ1,λ2,···,λ n The diagonal matrix formed;

[0017] Let F(z)=(DG(z))Λz-ΛG(z) and calculate and the differential equations for the z-domain state variables It is the coefficient matrix of z after merging -DG(z)P+Λz.

[0018] In one embodiment, S2 includes: converting the differential equation of the state variable in the z domain into the m domain by transforming z=Rm to obtain the differential equation of the state variable in the m domain: R is The right eigenvector matrix composed of the right eigenvector and the generalized right eigenvector; The analytical expression of the m-domain state variable is obtained by integration.

[0019] In one embodiment, in S3: when the matrix When there are no repeated roots, The jth analytical expression of the x-domain state variable of the power system under transient disturbance is Among them, the j-th state variable x j Contains the constant term C j0 , independent frequency terms and the coupling frequency term η1, η2…η n yes Characteristic root.

[0020] In one embodiment, in S3:

[0021] For the matrix The i-th repeated characteristic root η si The multiplicity is e si , then the corresponding analytical solution is:

[0022]

[0023] For the matrix Non-repeated characteristic roots, the corresponding analytical solution is:

[0024] When the matrix When there are i repeated roots, the jth analytical expression of the x-domain state variable of the power system under transient disturbance is: Among them, the j-th state variable x j Contains the constant term C ji0 , independent frequency terms and the coupling frequency term yes Characteristic root, dmax is the maximum multiplicity of all repeated roots.

[0025] In one embodiment, the S4 includes:

[0026] The characteristic roots in the independent frequency terms and the characteristic roots corresponding to the coupled frequency terms are analyzed to obtain cross-scale characteristics of the power system under transient disturbances.

[0027] According to another aspect of the present invention, there is provided an analysis device for cross-scale interaction of a power system under transient disturbances, comprising:

[0028] A construction module is used to construct a Taylor-expanded differential equation of the x-domain state variable of the power system under transient disturbances, perform a linear coordinate transformation on the differential equation of the x-domain state variable to obtain a differential equation of the y-domain state variable containing a second-order nonlinear term; perform a normal form nonlinear transformation on the differential equation of the y-domain state variable to eliminate the nonlinear term, and convert it into a differential equation of the z-domain state variable;

[0029] A decoupling module, configured to transfer the differential equation of the z-domain state variable to the domain m of first-order decoupling to obtain an analytical expression of the m-domain state variable;

[0030] a transformation module, configured to sequentially transform the analytical expressions of the m-domain state variables into the z-domain, y-domain, and x-domain, so as to convert the m-domain, which does not contain actual physical meaning, into the x-domain, which has actual physical meaning, to obtain analytical expressions of the x-domain state variables of the power system under transient disturbances, wherein the analytical expressions of the x-domain state variables are expanded to include a constant term, an independent frequency term, and a coupled frequency term;

[0031] An analysis module is used to analyze the independent frequency terms and the coupled frequency terms to determine the cross-scale characteristics of the power system under transient disturbances.

[0032] According to another aspect of the present invention, a control system for an electric power system is provided, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0033] According to another aspect of the present invention, 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 of the above method are implemented.

[0034] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0035] (1) Compared with the traditional normal form method that can only be applied to the equilibrium point, the present invention provides an analytical method for the cross-scale interaction of the power system under transient disturbances. The nonlinear differential equation of the x-domain state variable with physical meaning of the power system under transient disturbances is subjected to a second-order Taylor expansion at the non-equilibrium point, so as to transform the nonlinear differential equation of the x-domain state variable into the y-domain, z-domain and m-domain in turn to obtain the analytical expression of the m-domain state variable. Compared with the first-order Taylor expansion, the second-order Taylor expansion of the system contains the Jacobian matrix of the first-order Taylor expansion and the second-order nonlinear term matrix, so it can more accurately characterize the strong nonlinear dynamic behavior of the power system. Further, the analytical expression of the m-domain state variable is reversely transformed into the z-domain, y-domain and x-domain in turn, so as to transform the m-domain that does not contain actual physical meaning into the x-domain with actual physical meaning, and obtain the analytical expression of the x-domain state variable of the power system under transient disturbances. Since the analytical expression of the x-domain state variable includes a constant term, an independent frequency term and a coupled frequency term, it describes the multi-time scale characteristics of the power system at the non-equilibrium point. That is, this application overcomes the problem that the normal form of non-equilibrium points is not applicable, and extends the normal form method to high-order nonlinear power systems, providing strong support for the stability analysis of the system after disturbance. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a flow chart of a method for analyzing cross-scale interactions of a power system under transient disturbances provided in Example 1 of the present invention;

[0037] Figure 2 1 is a flow chart of sequentially transforming the nonlinear differential equation of the x-domain state variable into the y-domain, z-domain, and m-domain, provided by Example 1 of the present invention;

[0038] Figure 3 This is a flow chart of sequentially inversely transforming the nonlinear differential equation of the m-domain state variable into the z-domain, y-domain, and x-domain, as provided in Example 1 of the present invention. DETAILED DESCRIPTION

[0039] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0040] Example 1

[0041] like Figure 1 As shown, this embodiment provides an analysis method for cross-scale interaction of power systems under transient disturbances, including: S1-S4.

[0042] S1: Construct a nonlinear differential equation of the x-domain state variables with physical meaning for the power system under transient disturbances, perform Taylor expansion on the differential equation of the x-domain state variables at the non-equilibrium point, and then perform linear coordinate transformation to obtain the differential equation of the y-domain state variables containing second-order nonlinear terms; perform a normal form nonlinear transformation on the differential equation of the y-domain state variables to eliminate the nonlinear terms and convert it into a differential equation of the z-domain state variables.

[0043] S2: Transfer the differential equations of the z-domain state variables to the decoupled domain m to obtain the analytical expressions of the m-domain state variables.

[0044] S3: The analytical expressions of the m-domain state variables are sequentially transformed back into the z-domain, y-domain, and x-domain to convert the m-domain, which does not contain actual physical meaning, into the x-domain, which has actual physical meaning. The analytical expressions of the x-domain state variables of the power system under transient disturbances are obtained. The analytical expressions of the x-domain state variables are expanded to include constant terms, independent frequency terms, and coupled frequency terms.

[0045] S4: Analyze independent frequency terms and coupled frequency terms to determine the cross-scale characteristics of the power system under transient disturbances.

[0046] In one embodiment, S1 includes: constructing a power system model under transient disturbance The differential equation of x-domain state variables with Taylor second-order expansion at non-equilibrium point Substitute x=Uy into get Set y = z + G(z), and take the derivative of y = z + G(z) to get Bring it in get Furthermore, we set (I+DG(z)) -1 =I-DG(z) get P=U -1 B, O(3) is the third-order and higher-order term, D is the Jacobian matrix operator, U is the right eigenvector matrix of x, H j is the Hessian matrix of the jth state variable, Λ is the characteristic root of matrix A λ1,λ2,···,λ n The diagonal matrix is ​​formed; let F(z)=(DG(z))Λz-ΛG(z) to calculate and the differential equations for the z-domain state variables is the coefficient matrix of z after the combination of -DG(z)P+Λz. Further, S2 includes: converting the differential equation of the state variable in the z domain to the m domain by transforming z=Rm, and obtaining the differential equation of the state variable in the m domain: R is The right eigenvector matrix composed of the right eigenvector and the generalized right eigenvector; The analytical expression of the m-domain state variable is obtained by integration.

[0047] Among them, the traditional normal form method analyzes at the equilibrium point, when P=0, and can obtain the decoupled differential equation. However, the present invention analyzes at the non-equilibrium point, so P≠0, and needs to solve the following equation: Therefore, the z domain is converted to the m domain by transforming z = Rm, and the state variables in the m domain are decoupled: Where Q = R -1 P, for There are two cases, with and without repeated roots, which are discussed below.

[0048] Figure 2 The flowchart for converting the state variable x to the m-domain is shown. First, a linear coordinate transformation is performed to obtain the y-domain, where the first-order terms are decoupled. However, the y-domain still contains second-order nonlinear terms. A normalized nonlinear transformation is then performed to eliminate the nonlinear terms, resulting in a conversion to the z-domain. However, at this point, an analytical solution cannot be directly obtained in the z-domain at the nonequilibrium point. Therefore, the z-domain is converted to the m-domain, where the first-order terms are decoupled. An analytical expression in the m-domain is then obtained.

[0049] Figure 3 A flowchart for converting state variables from the m-domain to the x-domain is presented. After obtaining the m-domain analytical expression, a series of inverse transformations are performed to convert the m-domain, which lacks physical meaning, into the x-domain. Analysis of the time-domain solutions of the x-domain state variables reveals the system's multi-timescale characteristics and cross-scale phenomena.

[0050] In one embodiment, in S3: when the matrix When there are no repeated roots, The jth analytical expression of the x-domain state variable of the power system under transient disturbance Among them, the j-th state variable x j Contains the constant term C j0 , independent frequency terms and the coupling frequency term η1,η2…η n yes Characteristic root.

[0051] The j-th state variable x j Contains constant terms, independent frequency terms and coupled frequency terms. The coefficients before each term are C j0 , C ji , C jklThe constant term is caused by the non-zero derivatives of the state variables at the non-equilibrium point. In the normal form analysis method considering the second-order Taylor expansion at the non-equilibrium point, the coupled frequency terms will exhibit cross-scale phenomena, thus including cross-scale characteristics in the dynamic process of the system (i.e., the non-equilibrium point). In addition, because the z-domain equations contain the Jacobian matrix DG2(z) of the nonlinear transformation of the normal form, the frequencies of the independent frequency terms of the second-order expansion at the non-equilibrium point are different from those of the first-order Taylor expansion.

[0052] In one embodiment, in S3: for the matrix The i-th repeated characteristic root η si The multiplicity is e si , then the corresponding analytical solution is:

[0053]

[0054] For the matrix Non-repeated characteristic roots, the corresponding analytical solution is:

[0055] When the matrix When there are i repeated roots, the jth analytical expression of the x-domain state variable of the power system under transient disturbance is:

[0056] Among them, the j-th state variable x j Contains the constant term C ji0 , independent frequency terms and the coupling frequency term yes Characteristic root, dmax is the maximum multiplicity of all repeated roots.

[0057] Taking the m-domain 2-root solution as an example, the time domain analytical solution of the state quantity x can be obtained using z = Rm. The solution is in the form of: In a system with two state variables, the state variable x i It contains constant term, independent frequency term and coupled frequency term, whose coefficients are C i0 ,(C i1 +tC i1t ),(C i11 +tC i11t ), the system exhibits new cross-scale characteristics. The constant term is caused by the non-zero derivatives of the state variables at non-equilibrium points. The amplitudes of the independent and coupled frequency terms include the time variable t. This is due to the special case of repeated roots in the z-domain after the introduction of the nonlinear transformation. The exponential decay is faster than the growth of the variable t, so when the real part of the characteristic root is less than 0, the modes still converge.

[0058] In one embodiment, S4 includes: analyzing characteristic roots in the independent frequency terms and characteristic roots corresponding to the coupled frequency terms to obtain cross-scale characteristics of the power system under transient disturbances.

[0059] The specific implementation of the present invention is described by taking a system with two state variables as an example. Regarding the present invention without repeated roots, the description is carried out using object 1; regarding the present invention with repeated roots, the description is carried out using object 2.

[0060] The differential equation of the x-domain state variable of plant 1 is: Expanding on the non-equilibrium point (1, 0.5), the disturbance of the system state variable x is (0.1, 0), and we get:

[0061]

[0062] Convert to the y domain and obtain:

[0063] Further nonlinear transformation is performed to obtain: Then the transformation to the z domain becomes: There are no repeated roots at this time, and the differential equation in the m domain is obtained: Then solve the m-domain analytical expression: Then find m 10 and m 20 The x-domain perturbation is (0.1,0), according to Figure 1 Find m 10 =0,m 20 =0.1. Therefore, the solution is: From the inverse transformation of the m domain to the x domain, the solution is obtained in the form of:

[0064] Therefore, the system contains a constant term, an independent frequency term, and a coupled frequency term at the non-equilibrium point. The constant term is caused by the non-zero derivatives of the state variables at the non-equilibrium point. Among the state variables, x1 includes a frequency multiplication term and a frequency coupling term. Therefore, this expression describes the multi-timescale characteristics of the system at the non-equilibrium point.

[0065] The differential equation of the x-domain state variable of plant 2 is: Expand on the non-equilibrium point (1, 0.5), and the perturbation of the system state variable x is (0.1, 0). The steps are similar to the above, so the differential equation in the z domain is directly given. In this case, the z domain contains the repeated root -1; we get

[0066]

[0067] Solve the equation for this: The matrix consisting of right eigenvectors and generalized right eigenvectors is obtained from r1 and r2, so it is converted to the m domain: Then solve the m-domain analytical expression: Then find m 10 and m 20 The x-domain perturbation is (0.1,0), according to Figure 1 Find m 10 =0.1,m 20 = 0. Therefore, the solution is: Converting to the x domain, the solution is in the form of:

[0068]

[0069] Therefore, the system contains constant terms, independent frequency terms, and coupled frequency terms at non-equilibrium points. The constant terms are caused by the non-zero derivatives of the state variables at non-equilibrium points. The state variable x1 contains frequency-multiplier terms and frequency-coupled terms. Due to the presence of repeated roots, the amplitudes of the independent and coupled frequency terms include the time constant t. Since the exponential decay is faster than the growth of the variable t, the modes still converge when the characteristic roots are less than 0. This expression describes the multi-timescale characteristics of the system at non-equilibrium points.

[0070] Example 2

[0071] This embodiment provides an analysis device for cross-scale interactions of a power system under transient disturbances, including: a construction module, a decoupling module, a transformation module, and an analysis module.

[0072] Among them, the construction module is used to construct the Taylor expansion differential equation of the x-domain state variable of the power system under transient disturbance, perform linear coordinate transformation on the differential equation of the x-domain state variable to obtain the differential equation of the y-domain state variable containing second-order nonlinear terms; perform normal form nonlinear transformation on the differential equation of the y-domain state variable to eliminate the nonlinear terms and convert it into the differential equation of the z-domain state variable.

[0073] The decoupling module is used to transfer the differential equations of the z-domain state variables to the decoupled domain m to obtain the analytical expressions of the m-domain state variables.

[0074] The transformation module is used to sequentially transform the analytical expressions of the m-domain state variables into the z-domain, y-domain, and x-domain, so as to convert the m-domain, which does not contain actual physical meaning, into the x-domain, which has actual physical meaning, and obtain the analytical expressions of the x-domain state variables of the power system under transient disturbances. The analytical expressions of the x-domain state variables are expanded to include constant terms, independent frequency terms, and coupled frequency terms.

[0075] The analysis module is used to analyze independent frequency terms and coupled frequency terms to determine the cross-scale characteristics of the power system under transient disturbances.

[0076] Example 3

[0077] This embodiment provides a control system for an electric power system, including a memory and a processor. The memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0078] Example 4

[0079] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the above method are implemented.

[0080] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for analyzing cross-scale interactions of power systems under transient disturbances, characterized in that: include: S1: Construct a nonlinear differential equation of the x-domain state variable with physical meaning for the power system under transient disturbance, perform a second-order Taylor expansion on the differential equation of the x-domain state variable at a non-equilibrium point, and then perform a linear coordinate transformation to obtain a differential equation of the y-domain state variable containing a second-order nonlinear term; perform a normal form nonlinear transformation on the differential equation of the y-domain state variable to eliminate the nonlinear term and convert it into a differential equation of the z-domain state variable; S2: Transfer the differential equation of the z-domain state variable to the decoupled domain m to obtain an analytical expression of the m-domain state variable; S3: Inversely transforming the analytical expression of the m-domain state variable into the z-domain, y-domain, and x-domain in sequence, so as to convert the m-domain, which does not contain actual physical meaning, into the x-domain, which has actual physical meaning, to obtain the analytical expression of the x-domain state variable of the power system under the transient disturbance, wherein the analytical expression of the x-domain state variable is expanded to include a constant term, an independent frequency term, and a coupled frequency term; S4: Analyze the independent frequency terms and the coupled frequency terms to determine cross-scale characteristics of the power system under transient disturbances.

2. The method for analyzing cross-scale interactions of power systems under transient disturbances according to claim 1, characterized in that: Said S1 comprises: Construct the power system model under transient disturbance The differential equation of x-domain state variables with Taylor second-order expansion at non-equilibrium points Substitute x=Uy into get Set y = z + G(z), and take the derivative of y = z + G(z) to get Bring it in get Set (I+DG(z)) -1 =I-DG(z) get Where P = U -1 B, O(3) is the third-order and higher-order term, D is the Jacobian matrix operator, U is the right eigenvector matrix of x, H j is the Hessian matrix of the jth state variable, Λ is the characteristic root of matrix A λ1,λ2,···,λ n The diagonal matrix formed; Let F(z)=(DG(z))Λz-ΛG(z) and calculate and the differential equations for the z-domain state variables It is the coefficient matrix of z after merging -DG(z)P+Λz.

3. The method for analyzing cross-scale interactions of power systems under transient disturbances according to claim 2, characterized in that: The S2 includes: By transforming z=Rm, the differential equation of the state variable in the z domain is converted to the m domain, and the differential equation of the state variable in the m domain is obtained: R is The right eigenvector matrix composed of the right eigenvector and the generalized right eigenvector; The analytical expression of the m-domain state variable is obtained according to the solution formula of the linear non-homogeneous differential equation.

4. The method for analyzing cross-scale interactions of power systems under transient disturbances according to claim 3, characterized in that: In the S3: When the matrix When there are no repeated roots, The jth analytical expression of the x-domain state variable of the power system under transient disturbance is Among them, the j-th state variable x j Contains the constant term C j0 , independent frequency terms and the coupling frequency term η1, η2…η n yes Characteristic root.

5. The method for analyzing cross-scale interactions of power systems under transient disturbances according to claim 3, characterized in that: In the S3: For the matrix The i-th repeated characteristic root η si The multiplicity is e si , then the corresponding analytical solution is: For the matrix Non-repeated characteristic roots, the corresponding analytical solution is: m i (t) = C i0 +C i1 e ηit ; When the matrix When there are i repeated roots, the jth analytical expression of the x-domain state variable of the power system under transient disturbance is: Among them, the j-th state variable x j Contains the constant term C ji0 , independent frequency terms and the coupling frequency term yes Characteristic root, dmax is the maximum multiplicity of all repeated roots.

6. The method for analyzing cross-scale interactions of power systems under transient disturbances according to any one of claims 1 to 5, characterized in that: The S4 includes: The characteristic roots in the independent frequency terms and the characteristic roots corresponding to the coupled frequency terms are analyzed to obtain cross-scale characteristics of the power system under transient disturbances.

7. An analysis device for cross-scale interaction of power systems under transient disturbances, characterized in that: include: A construction module is used to construct a Taylor-expanded differential equation of the x-domain state variable of the power system under transient disturbances, perform a linear coordinate transformation on the differential equation of the x-domain state variable to obtain a differential equation of the y-domain state variable containing a second-order nonlinear term; perform a normal form nonlinear transformation on the differential equation of the y-domain state variable to eliminate the nonlinear term, and convert it into a differential equation of the z-domain state variable; a decoupling module, configured to transfer the differential equation of the z-domain state variable to the decoupled domain m to obtain an analytical expression of the m-domain state variable; a transformation module, configured to sequentially transform the analytical expressions of the m-domain state variables into the z-domain, y-domain, and x-domain, so as to convert the m-domain, which does not contain actual physical meaning, into the x-domain, which has actual physical meaning, to obtain analytical expressions of the x-domain state variables of the power system under transient disturbances, wherein the analytical expressions of the x-domain state variables are expanded to include a constant term, an independent frequency term, and a coupled frequency term; An analysis module is used to analyze the independent frequency terms and the coupled frequency terms to determine the cross-scale characteristics of the power system under transient disturbances.

8. A control system for an electric power system, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: 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.

Images