A power system transient stability evaluation method and power system operation trajectory prediction method based on a koopman operator

Abstract

The application provides a power system transient stability evaluation method and a power system operation trajectory prediction method based on a Koopman operator, the power system transient stability evaluation method comprising the following steps: S1, collecting operation trajectory data of state variables of a power system; S2, using an EDMD method to increase dimensions of the collected state variables to a high-dimensional linear space to approximate an action of the Koopman operator by using a limited-dimensional linear matrix K ; S3, using spectral decomposition of the Koopman operator to locate discrete spectra of stable equilibrium points of the power system, and using characteristics of eigenvalues of the Koopman operator and inverse mapping of dictionary functions to find stable equilibrium points of the power system in an original state space; and S4, based on the obtained stable equilibrium points and analysis of a stable mechanism of a linear system, constructing a power system transient stability criterion, and using the transient stability criterion to judge whether the system is transiently stable after the power system suffers from a large disturbance and collects an arbitrary working point.

Description

Technical Field

[0001] This invention relates to the field of electrical engineering technology, and in particular to a method for evaluating the transient stability of a power system and a method for predicting the operating trajectory of a power system based on the Koopman operator. Background Technology

[0002] In the context of new power system construction, with the integration of high proportions of renewable energy and power electronic equipment, compared to traditional power systems dominated by synchronous generators, "dual-high" power systems rely on control algorithms to simulate characteristics such as inertial support and damping torque, resulting in significant differences in dynamic performance. Overall, they exhibit characteristics of low inertia and weak damping. Low inertia leads to a decrease in the system's inertial time constant, a sharp increase in the rate of frequency change after a fault, potentially triggering low-frequency load shedding protection and even causing grid disconnection. Weak damping makes it difficult for the system to quickly calm oscillations after disturbances, increasing the amplitude of power angle swing, shortening the critical cut-off time, and raising the risk of loss of synchronization. The resulting transient stability problems seriously threaten the safe and stable operation of the power system. Simultaneously, factors such as changes in load structure, complex control and interaction, and the expansion of grid interconnection lead to increasingly prominent nonlinear characteristics of the system, posing significant challenges to the system's transient stability analysis.

[0003] For the transient stability problem of power grids, including transient stability assessment and prediction of dynamic characteristics after system disturbances, existing methods are usually model-driven, requiring accurate modeling of the assessment object. However, it is difficult to construct effective and accurate models in new power systems with diverse operating modes and complex behavior of power electronic devices. Furthermore, the full-order model of the system has extremely high dimensionality. Using traditional time-domain simulation methods for transient stability analysis requires numerical integration to solve a massive system of nonlinear equations, resulting in enormous computational costs and extremely long processing times, which cannot meet the needs of online or rapid risk assessment. Moreover, predicting the dynamic characteristics of the system during disturbances requires tedious solving of nonlinear equations. In addition, classical transient stability analysis methods, such as direct methods based on energy functions, rely on the structural characteristics of the system. In highly power-electronic systems, due to the presence of numerous dissipative and controllable components, constructing a suitable energy function becomes extremely difficult. Summary of the Invention

[0004] For the current "high-voltage and high-efficiency" power systems, one objective of this invention is to provide a power system transient stability assessment method based on the Koopman operator, so as to achieve rapid and efficient identification of the transient stability of the power system. Another objective of this invention is to provide a power system operating trajectory prediction method based on the Koopman operator, which can effectively predict the dynamic characteristics of the power system during disturbances without the need for solving cumbersome nonlinear equations or constructing an accurate differential equation model of the power system.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical method: a power system transient stability assessment method based on the Koopman operator, comprising:

[0006] Step S1: Collect the state variables of the power system The running trajectory data, the state variables It refers to the inductor current, capacitor voltage, output value of integrator in power electronic equipment, or other physical quantities with energy storage properties or memory effects;

[0007] Step S2: Use the EDMD method to upgrade the collected state variables to a high-dimensional linear space, using a finite-dimensional linear matrix. To approximate the effect of the Koopman operator;

[0008] Step S3: Use the spectral decomposition of the Koopman operator to locate the discrete spectrum of the stable equilibrium point of the power system. Simultaneously, utilize the characteristics of the Koopman operator eigenvalues ​​and the inverse mapping of the dictionary function to find the stable equilibrium point of the power system in the original state space. ;

[0009] Step S4: Based on the stable equilibrium point obtained in step S3 and the analysis of the stability mechanism of the linear system, a criterion for the transient stability of the power system is constructed, which is as follows:

[0010] (1)

[0011] In the formula, This is the approximate matrix of the Koopman operator. ; For matrix The left eigenvector, superscript Indicates transpose; This represents the initial state variable that eventually tends towards a stable equilibrium point. express The higher-dimensional vector after dimensionality increase; This represents the stable equilibrium point of the power system. express The higher-dimensional vector after dimensionality increase; It is a constant value;

[0012] After a power system experiences a large disturbance, any operating point of the system is collected, its state variables are upgraded, and substituted into equation (1). If the condition is met, it proves that the operating point is located within the attraction domain and will eventually tend to a stable equilibrium point. The system will then be in a transient state of stability.

[0013] Furthermore, step S2 includes:

[0014] S201, Select a set of nonlinear functions As a dictionary , Indicates the first in the dictionary The function elevates the original state space of the power system to a high-dimensional linear space. The state variable at time 1 The state after dimensional ascent is denoted as , ,in Much larger , The number of functions in the dictionary. The number of state variables in the original state space. express The high-dimensional vector after dimensionality increase by dictionary function;

[0015] S202, Constructing the matrix and The action of the Koopman operator is expressed as a finite-dimensional linear matrix. To approximate, As shown in the following formula:

[0016] (2)

[0017] Solving the matrix using the least squares method As shown in the following formula:

[0018] (3)

[0019] in, for , for superscript It indicates a false reversal.

[0020] Furthermore, step S3 includes:

[0021] S301, matrix Perform spectral decomposition to obtain the right eigenvector with eigenvalue 1. , , Represents the right eigenvector The Middle One element;

[0022] S302, calculate the stable equilibrium point according to the following formula. High-dimensional vector after dimensionality increase ;

[0023] (4)

[0024] (5)

[0025] In the formula, express about Functional relationships, based on the dictionary And prior knowledge;

[0026] S303, after obtaining Based on, according to and The identity mapping relationship is used to determine the stable equilibrium point of the power system in the original state space. .

[0027] Furthermore, in step S4, the process of constructing the criterion for the transient stability of the power system is as follows:

[0028] According to the stable equilibrium point after dimensional upgrading, it satisfies Meanwhile, the evolution of variables in the upgraded space satisfies a linear relationship, and the initial point at which the upgraded space eventually tends to the equilibrium point needs to satisfy the following conditions:

[0029] (8)

[0030] In the formula, This represents the initial state variable that eventually tends towards a stable equilibrium point. express The higher-dimensional vector after dimensionality increase;

[0031] According to the matrix If there exists a right eigenvector with eigenvalue 1, then obtain the left eigenvector corresponding to that eigenvalue 1. satisfy:

[0032] (9)

[0033] Multiply both sides of equation (8) on the left. The criterion for the transient stability of the power system is obtained as follows:

[0034] (1)

[0035] In the formula, after a large disturbance, for any operating point of the power system, the corresponding state variable is... Dimensional Ascension Substituting into equation (1), if This proves that the operating point is located within the attraction region and will eventually tend to a stable equilibrium point. The system will then be in a transient state of stability.

[0036] As another aspect of the present invention, a power system operation trajectory prediction method based on the Koopman operator includes steps S1 and S2 as described in the aforementioned power system transient stability assessment method, and further includes:

[0037] Step S3: Use the spectral decomposition of the Koopman operator to predict the future operating trajectory of the power system;

[0038] First, for the matrix Spectral decomposition is performed on the transpose of the vector, and its right eigenvector is... With dictionary The inner product serves as the characteristic function of the higher-dimensional linear space after dimensionality increase. The eigenvalues ​​of the corresponding matrix are the eigenvalues ​​of the function space. Based on the Koopman eigenfunction basis, the observation function in high-dimensional linear space is... Expand and reconstruct using dictionary functions as follows:

[0039] (6)

[0040] In the formula, Representing the original state space With the upgraded space It is an identity mapping relationship; The inverse mapping matrix is ​​composed of unit vectors, such that each row is a unit vector; It is a Koopman mode, which is a matrix. The Column vectors For matrix The matrix formed by the right eigenvectors of the transpose;

[0041] Next, based on the observation function The predicted trajectory of the power system at future moments is as follows:

[0042] (7)

[0043] In the formula, Indicates the first The eigenvalues ​​corresponding to the Koopman eigenfunctions Power of 1 For the predicted time; Indicates the first The Koopman feature functions in the initial state variables The value at that location.

[0044] As another aspect of the present invention, a power system operation trajectory prediction method based on the Koopman operator includes steps S1 and S2 as described in the aforementioned power system transient stability assessment method, and further includes: step S3, wherein step S3 is performed in the state after dimensionality enhancement. Extract the original state Then it is re-upgraded to a new state. And using linear operators Its function is to solve for the state after the dimensional upgrade at the next moment. By doing so, the future operating trajectory of the power system can eventually be predicted.

[0045] The beneficial effects of this invention are:

[0046] (1) The power system operation trajectory prediction method based on the Koopman operator proposed in this invention constructs a linear Koopman operator by using state space sampling data, transforming complex nonlinear problems into linear problems, and realizes effective prediction of the system's operation trajectory in a short time through spectral analysis of the linear operator. On this basis, the prediction-correction method is used to realize effective prediction of long-term dynamics. This method does not require solving cumbersome nonlinear equations or constructing Lyapunov functions to analyze the dynamic characteristics of the system under disturbance. At the same time, it does not require knowing the exact differential equation model of the system, is suitable for complex models, and can apply all linear system theories and perform global linearization analysis by means of linearization.

[0047] (2) The power system transient stability assessment method based on the Koopman operator proposed in this invention uses the finite-dimensional approximation of the infinite-dimensional linear Koopman operator and the spectral decomposition of the linear operator to quickly locate the discrete spectrum of the stable equilibrium point. Simultaneously, it uses the characteristics of eigenvalues ​​and the inverse mapping of the dictionary function to find the stable equilibrium point of the original system. Then, based on this equilibrium point and combined with the analysis of the stability mechanism of the linear system, a criterion for transient stability is proposed. Using this criterion, the transient stability of the system can be efficiently and quickly assessed, providing an effective basis for subsequent stability control and protection. It is worth mentioning that the equilibrium point location in this method is applicable to any new power system model, and the obtained stable equilibrium point can serve as the basis for subsequent transient stability analysis of the system. Attached Figure Description

[0048] Figure 1 This is an architecture diagram of the power system operation trajectory prediction method based on the Koopman operator proposed in this invention;

[0049] Figure 2 This is a schematic diagram of the linear evolution of the upgraded space in this invention;

[0050] Figure 3 This is a logic diagram of the prediction-correction method in this invention;

[0051] Figure 4 This is an architecture diagram of the power system transient stability assessment method based on the Koopman operator proposed in this invention;

[0052] Figure 5 This is a simplified model schematic diagram of a DC microgrid with a constant power load in an embodiment of the present invention;

[0053] Figure 6 This is a schematic diagram of spectral decomposition linear prediction in an embodiment of the present invention (where (a) is a schematic diagram of spectral decomposition linear prediction of the filter capacitor voltage; (b) is a schematic diagram of spectral decomposition linear prediction of the filter inductor current).

[0054] Figure 7 These are the effect diagrams of the prediction-correction method used in the embodiments of the present invention (where (a) is the effect diagram of the filter capacitor voltage obtained by the prediction-correction method; and (b) is the effect diagram of the filter inductor current obtained by the prediction-correction method).

[0055] Figure 8 This is a schematic diagram illustrating the reliability analysis of the equilibrium point positioning in an embodiment of the present invention;

[0056] Figure 9 This is an evaluation effect diagram of the transient stability criterion in the embodiments of the present invention. Detailed Implementation

[0057] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0058] In view of the problems mentioned in the background, this invention aims to transform complex nonlinear problems into high-dimensional linear problems through a data-driven approach. It effectively characterizes the future dynamics of the system using spectral decomposition of linear operators and prediction-correction methods. Simultaneously, it proposes a method for locating the system's stable equilibrium point and a transient stability assessment criterion, enabling rapid and efficient determination of system transient stability. This provides a basis for stability control design and protection actions, ensuring the safe and stable operation of the system. In short, this invention provides a power system transient stability assessment method based on the Koopman operator and a power system operating trajectory prediction method based on the Koopman operator.

[0059] like Figure 1 As shown, the power system operation trajectory prediction method based on the Koopman operator provided by this invention includes:

[0060] Step S1: Collect system operation trajectory data.

[0061] For a given novel power system (usually a nonlinear system), the Koopman operator theory requires system operating data as the basis for analysis; this data consists of the power system's state variables. (State variables in a power system essentially refer to physical quantities with energy storage properties or memory effects; they cannot change instantaneously, their changes are continuous, and they are governed by the system's differential equations (state-space equations)). In new power systems with a high proportion of integrated power electronic devices, the observed values ​​of variables such as inductor current, capacitor voltage, and integrator output can dynamically reflect the system's operating status. Within a reasonable range, an initial state is randomly selected, and a sampling period is chosen. Collect multiple different running trajectories to obtain a series of paired data. ,in, Indicates the first The state variables at each moment.

[0062] Step S2: Construct a linear Koopman operator using the system state space sampling data.

[0063] After data acquisition is complete, select a set of nonlinear functions. As a dictionary , Indicates the first in the dictionary The function elevates the original state space of the power system to a high-dimensional linear space. The state variable at time 1 The state after dimensional ascent is denoted as , ,in Much larger , The number of functions in the dictionary. The number of state variables in the original state space. express The resulting high-dimensional vector after dimensionality increase using a dictionary function.

[0064] Constructing a matrix and The action of the Koopman operator is expressed as a finite-dimensional linear matrix. To approximate, As shown in the following formula:

[0065] (2)

[0066] The purpose of constructing the above formula (2) is to find a matrix. This makes the above approximation as accurate as possible across all data points. This transforms into a least squares problem, the solution of which is:

[0067] (3)

[0068] in, for U is superscript It indicates a false reversal.

[0069] Step S3: Predict the system's operating trajectory.

[0070] Get matrix Then, the global dynamic information of the original nonlinear system can be obtained by analyzing this linear system. For the matrix... Spectral decomposition is performed on the transpose of the vector, and its right eigenvector is... With dictionary The inner product serves as the characteristic function of the higher-dimensional linear space after dimensionality increase. The eigenvalues ​​of the corresponding matrix are the eigenvalues ​​of the function space. .

[0071] For a given power system, this invention focuses on the observation function in a high-dimensional linear space. (Under normal circumstances, attention should be paid to the state variables in the original state space) , and For identity mappings in different spaces, satisfying ), the observation function Expanding on the basis of the Koopman feature function, it is reconstructed using a dictionary function as follows:

[0072] (6)

[0073] In the formula, Let the inverse mapping matrix be composed of unit vectors, such that each row is a unit vector (dictionary). Typically includes (items); It is a Koopman mode, which is a matrix. The Column vectors For matrix The matrix formed by the right eigenvectors of the transpose.

[0074] Because the observation function in a high-dimensional linear space Under the action of the Koopman operator, it evolves linearly (see...). Figure 2 ,Note: Figure 2 In this context, M represents the original state space, and C represents the high-dimensional linear space. For any initial state, its predicted future trajectory is:

[0075] (7)

[0076] In the formula, Indicates the first The eigenvalues ​​corresponding to the Koopman eigenfunctions Power of 1 For the predicted time; Indicates the first The Koopman feature functions in the initial state variables The value at that location.

[0077] Given the initial conditions, the first can be predicted using equation (7). The system state at any given time. Considering that numerical errors accumulate exponentially with the number of iterations, the aforementioned prediction method can only effectively predict the system's trajectory in the short term, but the prediction results tend to deviate rapidly from the actual trajectory in later stages. Therefore, preferably, this invention proposes the following prediction-correction-based optimization method:

[0078] Since dictionary functions typically contain identity mappings, this invention can be applied to states after dimensionality increase. Extract the original state directly from the middle Then it is re-upgraded to a new state. And using linear operators Its function is to solve for the state after the dimensional upgrade at the next moment. By analogy, the future operating trajectory of the power system can be predicted. For specific logic, please refer to [reference needed]. Figure 3 In this prediction-correction method, prediction is performed linearly in a high-dimensional linear space, and then nonlinear correction is performed by returning to the original state space, similar to the "multi-step method" of numerical integration, but this method is achieved by reapplying nonlinear transformation.

[0079] like Figure 4 As shown, the power system transient stability assessment method based on the Koopman operator provided by this invention, in addition to steps S1 and S2 of the aforementioned power system operation trajectory prediction method based on the Koopman operator, also requires equilibrium point location and stability judgment, as detailed below.

[0080] (1) Equilibrium point location

[0081] Dictionary functions typically include That is, it includes the original state variables. Then, when the original system is in steady state (referring to the stable equilibrium point) It is constant, corresponding to a high-dimensional linear space. The values ​​are also stable, and the dictionary is constructed based on the original state variables, i.e. yes If the function is such that the system remains stable after dimensionality increase, then the evolution of the function variable satisfies the following conditions: That is, satisfying the following form:

[0082] (10)

[0083] In the formula, eigenvalues The value equals 1, meaning that when the original system is stable, the matrix in the corresponding high-dimensional linear space is equal to 1. Theoretically, there must exist an eigenvalue equal to 1, and the right eigenvector corresponding to this eigenvalue must be... With the stable state after dimensional ascension There exists a Proportional relationship:

[0084] (4)

[0085] In the formula, , Represents the right eigenvector The Middle Each element.

[0086] Since dictionary functions are user-defined, their structure is known, such as polynomial basis functions or Fourier basis functions, and their coefficients can be obtained based on prior knowledge. Value:

[0087] (5)

[0088] in, express about The functional relationship.

[0089] The stable equilibrium point of the original system From the higher-dimensional vector identity mapping "Sure.

[0090] Based on the above analysis, this invention first transforms the matrix... Perform spectral decomposition to obtain the right eigenvector with eigenvalue 1. Then, calculate the stable equilibrium point according to equations (4) and (5). High-dimensional vector after dimensionality increase Finally, after obtaining Based on, according to and By establishing the identity mapping relationship, the stable equilibrium point of the power system in the original state space can be determined. .

[0091] It is worth noting that the matrix The spectral decomposition may have repeated roots with eigenvalues ​​of 1, and each corresponding right eigenvector satisfies the relationship of the aforementioned formula (4). Through subsequent... The calculation of parameters and the identity mapping both correspond to an equilibrium point of the nonlinear system, which is consistent with the situation that a nonlinear system may have multiple equilibrium points (the limit cycle may be related to the dynamics of the eigenvalue with a magnitude of 1, but this invention only considers it as a stable equilibrium point and will not discuss it).

[0092] (2) Stability judgment

[0093] The aforementioned stable equilibrium point obtained after dimensional elevation satisfies Meanwhile, the evolution of variables in a high-dimensional linear space satisfies a linear relationship. Therefore, the initial point at which the high-dimensional linear space eventually tends to the equilibrium point must satisfy the following condition:

[0094] (8)

[0095] In the formula, , This represents the initial state variable that eventually tends towards a stable equilibrium point. express The identity transformations corresponding to all initial points satisfying the conditions of the upgraded high-dimensional vector. The set of points that correspond to the original system converging to a stable equilibrium point. The attraction domain.

[0096] The proof matrix in the aforementioned equilibrium point location If there exists a right eigenvector with eigenvalue 1, then the left eigenvector corresponding to eigenvalue 1 satisfies:

[0097] (9)

[0098] In the formula, For matrix The left eigenvector, superscript This indicates transpose.

[0099] Multiply both sides of equation (8) on the left. ,but:

[0100] (1)

[0101] In the formula, This represents the initial state variable that eventually tends towards a stable equilibrium point. express The higher-dimensional vector after dimensionality increase; This represents the stable equilibrium point of the power system. express The higher-dimensional vector after dimensionality increase; This is a constant value. For any operating point of the system, its corresponding state variable is... Dimensional Ascension Substituting into equation (1), if This proves that the operating point is located within the attraction region and will eventually tend to a stable equilibrium point. The system will then be in a transient state of stability.

[0102] Considering that in practical applications, due to errors in numerical calculations, it is difficult to exactly satisfy the condition of equation (1), therefore, based on equation (1), the present invention constructs the following error calculation formula:

[0103] (11)

[0104] In the formula, To account for tolerances, the errors vary across different power systems. The value can be set according to the actual situation. The smaller the value, the more accurate the judgment of stability, and the stronger the conservatism; after a power system suffers a large disturbance, for any operating point of the system, its corresponding state variable... Dimensional Ascension Substituting into equation (11), if This proves that the operating point is located within the attraction region and will eventually tend to a stable equilibrium point. The system will then be in a transient state of stability.

[0105] Since the aforementioned stability judgment method only involves one nonlinear transformation (dimensional increase) and one algebraic operation, the method can determine the stability of the system almost instantaneously. Under large disturbances, it can immediately determine whether the system is unstable by collecting data of the state variables at a certain moment after the disturbance, providing a basis for subsequent stability control and protection.

[0106] Next, this implementation method uses a simplified model of a DC microgrid with a constant power load as an example, such as... Figure 5 As shown, where, and The line resistance from the source to the constant power load and The inductance of the filter, The input capacitor of the constant power load (the filter capacitor) is represented by CPL, which is also a constant power load and serves as the nonlinear term of the system. In the experiment, polynomials of degree no more than 15 are used as basis functions, and the matrix is ​​obtained using the EDMD (Extended Dynamic Mode Decomposition) method. .

[0107] Figure 6 This is a schematic diagram of spectral decomposition prediction, from... Figure 6 (a) and Figure 6 (b) It can be seen that the spectral decomposition prediction has an accurate prediction effect at 100 time steps.

[0108] Figure 7 This diagram illustrates the effect of using the prediction-correction method. Figure 7 (a) and Figure 7 (b) It can be seen that the prediction-correction method can ensure efficient prediction for 1000 time steps and can be used as an effective tool for long-term dynamic analysis of power systems.

[0109] Figure 8 This diagram illustrates the reliability analysis of the equilibrium point location. Figure 8 It can be seen that the estimated equilibrium point falls within the region plotted with the standard deviation of the error as the radius, and the absolute error is 0.0156, indicating that the estimated and measured results are very close, verifying the rationality of the proposed method.

[0110] Regarding the aforementioned equilibrium point, Figure 9 The effect diagram of the transient stability criterion is shown. Figure 9 The tolerance shown is controlled below 0.5%, and the misclassification rate is approximately 0 in 100 test samples. The box plot shows excellent discrimination and maintains a separation ratio of 5.05. This fully demonstrates the correctness and efficiency of the proposed transient stability criterion, and provides a theoretical basis for the safe and stable operation of the power system.

[0111] The above embodiments are preferred implementations of the present invention. In addition, the present invention can be implemented in other ways. Any obvious substitutions without departing from the concept of the present technical solution are within the protection scope of the present invention.

[0112] To facilitate understanding by those skilled in the art of the improvements of this invention over the prior art, some of the accompanying drawings and descriptions have been simplified, and for clarity, some other elements have been omitted from this application. Those skilled in the art should realize that these omitted elements may also constitute the content of this invention.

Claims

1. A method for power system transient stability assessment based on Koopman operator, characterized in that, Comprising: Step S1, collecting state variable of power system running track data of the state variable inductor current, capacitor voltage, output value of integrator in power electronic device, or other physical quantity with energy storage property or memory effect Step S2, the collected state variables are upgraded to high-dimensional linear space by EDMD method, and a finite-dimensional linear matrix is used to approximate the action of Koopman operator ; Step S3, the discrete spectrum of the power system stable equilibrium point is located by using the spectral decomposition of the Koopman operator, and the stable equilibrium point of the power system in the original state space is found by using the characteristics of the Koopman operator eigenvalue and the inverse mapping of the dictionary function ; Step S4, based on the stable equilibrium point obtained in step S3 and the analysis of the stability mechanism of the linear system, constructing a criterion for power system transient stability, which is as follows: （1） In the formula, is an approximate matrix of the Koopman operator, is a left eigenvector of the matrix , and the superscript represents transposition; represents an initial state variable of the final stable equilibrium point, represents a high-dimensional vector after dimensionality increase; represents a stable equilibrium point of the power system, represents a high-dimensional vector after dimensionality increase; is a constant value;​ After the power system suffers from a large disturbance, any working point of the system is collected, the state variable is upgraded, and the equation (1) is brought in. If the condition is met, it is proved that the working point is in the attraction domain, and it will eventually tend to the stable equilibrium point , and the system will be transiently stable.

2. The Koopman operator-based power system transient stability assessment method of claim 1, wherein: The step S2 comprises: S201, Select a set of nonlinear functions As a dictionary , Indicates the first in the dictionary The function elevates the original state space of the power system to a high-dimensional linear space. The state variable at time 1 The state after dimensional upgrade is denoted as , ,in Much larger , The number of functions in the dictionary. The number of state variables in the original state space. express The high-dimensional vector after dimensionality increase using dictionary functions; S202, construct a matrix and approximate the action of the Koopman operator with a finite-dimensional linear matrix as follows:​ （2） Solving the matrix using the least squares method as follows: （3） wherein is , is the superscript denotes the pseudo-inverse.

3. The Koopman operator-based power system transient stability assessment method of claim 2, wherein: The step S3 comprises: S301, matrix Spectrally decompose to obtain a right eigenvector with eigenvalue 1 , , denotes the element in the right eigenvector th th S302, calculate the stable equilibrium point according to the following formula high-dimensional vector after dimensionality increase ; （4） （5） wherein represents with respect to the functional relationship of the function and prior knowledge; S303, on the basis of , according to and the identity mapping relationship, determine the stable equilibrium point of the power system in the original state space .

4. A power system operation trajectory prediction method based on a Koopman operator, characterized by, The power system transient stability evaluation method comprising the steps S1 and S2 as claimed in any one of claims 1-2, further comprising: Step S3, predicting the future operation trajectory of the power system by spectral decomposition of the Koopman operator; First, the transpose of the matrix is spectrally decomposed, and its right eigenvectors are taken as the inner product with the dictionary as the eigenfunctions of the high-dimensional linear space after dimensionality increase , and the corresponding matrix eigenvalues are the eigenvalues of the function space . The observed function of the high-dimensional linear space is expanded under the basis of the Koopman eigenfunctions and reconstructed by the dictionary functions as （6） In the formula, represents the original state space and the space after dimensionality increasing is an identity mapping relationship; is the inverse mapping matrix composed of unit vectors, and each row is a unit vector; is the Koopman mode, and the matrix is the first column vector of the matrix is the matrix composed of the right eigenvectors of the transpose of the matrix ; Next, the observation function is defined as The future trajectory of the power system is predicted as follows: （7） wherein represents the eigenvalue corresponding to the th Koopman eigenfunction raised to the th power, is the prediction time; represents the value of the th Koopman eigenfunction at the initial state variable x0.

5. The Koopman operator-based power system operating trajectory prediction method of claim 4, wherein: Step S3, in the state after dimensionality upgrade Extract the original state Then it is re-upgraded to a new state. And using linear operators Its function is to solve for the state after the dimensional upgrade at the next moment. By doing so, the future operating trajectory of the power system can eventually be predicted.

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