Power system frequency prediction method based on recursive constraint of coupling state and deep koopman

Abstract

This invention discloses a power system frequency prediction method based on coupled state recursive constraints and deep Koopman modeling. The steps include: acquiring simulated frequency data and performing data preprocessing to obtain local fast-changing frequency deviation signals; constructing phase space trajectory vectors through time-delay embedding processing; building a deep Koopman model; using an encoder to elevate the phase space trajectory vectors to the observable space; performing linear state evolution of the frequency state vectors in the observable space using a linear Koopman operator matrix; and projecting the observable space states back to the original state space using a decoder to output predicted values ​​of the local fast-changing frequency deviation data; constructing the total loss; acquiring frequency trajectory data output by grid-following and grid-connected equipment; and training the deep Koopman model; and obtaining the frequency prediction results based on the trained deep Koopman model. This invention can replace full-order electromagnetic transient simulation for rapid analysis in large-scale scenarios, improving computational efficiency.

Description

Technical Field

[0001] This invention relates to the field of power system frequency prediction technology, specifically to a power system frequency prediction method based on coupled state recursive constraints and deep Koopman. Background Technology

[0002] With a high proportion of renewable energy integration, it is difficult to balance system stability, economy, and grid support performance by adopting a single grid-following (GFL) or grid-forming (GFM) control mode. Therefore, the hybrid configuration of GFM and GFL equipment / power sources has become an inevitable trend in the development of current power systems. However, when these two types of equipment operate in the same system, their dynamic interaction mechanism is extremely complex. When the system is disturbed, the fast tracking behavior of GFL equipment relying on phase-locked loops and the frequency support behavior autonomously established by GFM equipment may produce constructive synergistic effects or may cause destructive coupled oscillations.

[0003] However, current research on evaluation methods for frequency coordination in power systems supported by a mix of grid-connected and grid-connected equipment remains limited. Furthermore, existing analytical techniques suffer from high computational costs for electromagnetic transient simulation, failing to systematically explain the underlying mechanisms. While data-driven methods such as recurrent neural networks, convolutional networks, and Transformers reduce computational costs and can predict frequency trajectories, they primarily focus on minimizing point-by-point trajectory prediction errors. Well-trained models may accurately reproduce short-term trajectories but struggle to capture the physical laws required for rigorous stability assessment. Traditional Koopman deep learning methods mainly optimize short-term prediction accuracy. When dealing with hybrid systems containing GFM and GFL equipment exhibiting rigid multi-timescale characteristics, they fail to effectively preserve the energy interaction and causal transfer relationships between the slow electromechanical dynamics of GFM and the fast electromagnetic dynamics of GFL, easily generating spurious spectral eigenvalues. Summary of the Invention

[0004] To overcome the shortcomings and deficiencies of existing technologies, this invention provides a power system frequency prediction method based on coupled state recursive constraints and deep Koopman. The coupled state recursive (CSR) constraints are embedded into the deep Koopman learning framework, so that the learned Koopman operators follow the actual dynamic model response coordination of grid-connected and grid-connected equipment. While maintaining the electromagnetic transient level fidelity of system state analysis, it achieves orders of magnitude acceleration in computation, thus replacing the electromagnetic transient simulation model with high fidelity and efficiency for frequency prediction and support coordination capability analysis of grid-connected and grid-connected equipment systems.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] This invention provides a power system frequency prediction method based on coupled state recursive constraints and deep Koopman, comprising the following steps:

[0007] The simulated frequency data is acquired and preprocessed to obtain the local fast-changing frequency deviation signal;

[0008] Time-delay embedding is performed on the local fast-changing frequency deviation signal to construct the phase space trajectory vector;

[0009] A deep Koopman model is constructed, including an encoder, a linear Koopman operator matrix, and a decoder. The encoder elevates the phase space trajectory vector to the observable space. The linear Koopman operator matrix performs linear state evolution of the frequency state vector in the observable space. The decoder projects the observable space state back to the original state space and outputs the predicted value of the local fast-changing frequency deviation data.

[0010] Construct the total loss, obtain the output frequency trajectory data of network-following and network-building devices, and train the deep Koopman model;

[0011] Frequency prediction results are obtained based on the trained deep Koopman model.

[0012] As a preferred technical solution, acquiring simulation frequency data and performing data preprocessing specifically includes:

[0013] Simulated frequency data is obtained based on time-domain simulation. Local frequency deviation data is decomposed into global slow-changing and local fast-changing signals. The deviation between the instantaneous frequency and the rated frequency in the power grid is calculated. The inertia center signal is used as an analytical reference to decompose the local frequency deviation.

[0014] The deviation between the instantaneous frequency and the rated frequency in the power grid is standardized to obtain a local fast-changing frequency deviation signal.

[0015] As a preferred technical solution, the local frequency deviation data is decomposed into globally slow-changing and locally fast-changing signals, and the deviation between the instantaneous frequency and the rated frequency in the power grid is calculated, expressed as:

[0016] ;

[0017] in, This represents the inertial weighted average frequency. Reflecting the interactions caused by rapid coupling, This represents the deviation between the instantaneous frequency and the rated frequency of the power grid at node i at time t.

[0018] As a preferred technical solution, the deviation between the instantaneous frequency and the rated frequency in the power grid is standardized and expressed as follows:

[0019] make After standardization, it is represented as:

[0020] ;

[0021] in, , These are the mean and standard deviation of the local frequency deviation, respectively. This indicates a localized rapid frequency deviation signal.

[0022] As a preferred technical solution, a time-delay embedding is performed on the standardized frequency sequence to construct a phase space trajectory vector, which is represented as:

[0023] ;

[0024] Where d is the embedding dimension, Due to time lag, This indicates a localized rapid frequency deviation signal. This represents the phase space trajectory vector.

[0025] As a preferred technical solution, the total loss is constructed based on the state prediction fidelity loss and the coupling state recursive spectrum consistency loss in the observable frequency space.

[0026] As the preferred technical solution, the total loss is expressed as:

[0027] ;

[0028] ;

[0029] ;

[0030] in, Indicates the total loss. Indicates the weight value. This represents the prediction fidelity loss, where B is the number of samples and P is the prediction step size. The actual state trajectory generated for electromagnetic transient simulation. Let represent the state of the b-th batch at time t. To perform feature mapping on the state of the b-th sample at time t, a high-dimensional feature representation is obtained, where C is the decoder projection matrix and K represents the linear Koopman operator matrix. To calculate different lag steps based on joint recursive graph analysis The recursive probability of the coupling state of the selected network type and network structure device. To predict the time lag window, Let be the i-th eigenvalue of the Koopman operator matrix K, and Δt be the simulation sampling time interval. For the selected set of lag steps, Re(·) denotes taking the real part of the complex number. It is the statistical coordination attenuation rate of the frequency support effect of the selected mesh-type and mesh-type equipment observed in the electromagnetic transient simulation trajectory data. This represents the consistency loss of the recursive spectrum of coupled states.

[0031] As a preferred technical solution The attenuation is limited by the spectral gap of the Koopman operator K, expressed as:

[0032] ;

[0033] in, This represents the invariant joint recursive measure under a stationary distribution. The K matrix is ​​the dominant non-unit eigenvalue of the Koopman operator K, and M is a positive constant derived from the coefficients of the spectral decomposition.

[0034] The present invention also provides a computer-readable storage medium storing a program that, when executed by a processor, implements the power system frequency prediction method based on coupled state recursive constraints and deep Koopman as described above.

[0035] The present invention also provides a computer device, including a processor and a memory for storing a processor-executable program, wherein when the processor executes the program stored in the memory, it implements the power system frequency prediction method based on coupled state recursive constraints and deep Koopman as described above.

[0036] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0037] (1) This invention forces the Koopman operator to follow the real physical coordination of the system by constraining the recursive decay rate of the coupling state of the network-type and network-type devices. This solves the problem of the lack of physical mechanism in the pure data-driven method and significantly improves the model’s fidelity to the system’s inherent physical laws.

[0038] (2) The present invention adopts adaptive spectrum control, without applying rigid constraints on the spectral radius, allowing spectral characteristics that conform to physical reality to appear in pseudo-coordinated scenarios to accurately capture real oscillations, avoiding the distortion of dynamic characteristics caused by incorrect damping constraints in traditional methods, and achieving high fidelity of spectral characteristics.

[0039] (3) This invention combines the spectrum calculation method with deep Koopman. Online inference only involves linear matrix operations, with low computational complexity. It achieves several orders of magnitude speedup compared to full-order electromagnetic transient simulation, and can replace full-order electromagnetic transient simulation for rapid analysis in large-scale scenarios, thus improving computational efficiency. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the power system frequency prediction method based on coupled state recursive constraints and deep Koopman sampling of the present invention.

[0041] Figure 2 This is a schematic diagram illustrating the implementation framework of the power system frequency prediction method based on coupled state recursive constraints and deep Koopman in this invention.

[0042] Figure 3 This is a schematic diagram of the deep Koopman neural network architecture of the present invention;

[0043] Figure 4 This is a schematic diagram of the improved IEEE 14-node system architecture of the present invention;

[0044] Figure 5 These are schematic diagrams of the training loss curves for Case 1 to Case 4 using the CSR-Koopman method in this invention;

[0045] Figure 6 This is a schematic diagram of the frequency trajectory under load step disturbance according to the present invention;

[0046] Figure 7 This is a schematic diagram comparing the COI frequency response of the present invention in Case 4;

[0047] Figure 8 This is a schematic diagram comparing the frequency prediction of different DMD methods in Case 4 of the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be 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 illustrative and not intended to limit the invention.

[0049] Example 1

[0050] like Figure 1 , Figure 2 As shown, this embodiment provides a power system frequency prediction method based on coupled state recursive constraints and deep Koopman, including the following steps:

[0051] S1: Acquire simulation frequency data and perform data preprocessing, specifically including:

[0052] In this embodiment, time-domain simulation is performed using electromagnetic transient simulation software to obtain simulation frequency data. The local frequency deviation data is decomposed into globally slow-changing and locally fast-changing signals. To decouple multi-timescale dynamics, the center of inertia (COI) signal is used as an analytical reference to decompose the local frequency deviation, specifically as follows:

[0053] ;

[0054] in, The effective inertia of the GFL element is set to the inertial weighted average frequency, according to analysis convention. This decomposition reflects that the overall inertial response of the system is mainly dominated by the GFM source. This decomposition is only used to distinguish between global inertial drift and relative synchronization dynamics. It reflects the interactions caused by rapid coupling (such as tracking deviation caused by PLL). It refers to the deviation between the measured instantaneous frequency at node i at time t in the power grid and the rated frequency of the system;

[0055] make Standardization is performed to eliminate the influence of dimensions:

[0056] ;

[0057] in, , These are the mean and standard deviation of the local frequency deviation, respectively. The data used in subsequent steps are the standardized local fast-changing frequency deviation signals. ;

[0058] For each unit u, the normalized frequency sequence is time-delayed embedded to construct a phase space trajectory vector, represented as:

[0059] ;

[0060] Where d is the embedding dimension, Due to time lag, This data serves as the training data for the deep Koopman network in this embodiment.

[0061] S2: Constructing a deep Koopman encoding-decoding architecture;

[0062] like Figure 3 As shown, a neural network architecture is constructed that includes an encoder, a linear Koopman operator matrix, and a decoder. The input data of the encoder is the phase space trajectory vector of the local fast-changing frequency deviation data of all nodes in the power system after time-delay embedding. The encoder elevates the state vector formed by the input data to the observable space. The Koopman operator matrix performs linear state evolution of the frequency state vector in the observable space. The decoder projects the observable space state back to the original state space and outputs the predicted value of the local fast-changing frequency deviation data.

[0063] In this embodiment, the encoder is designed as a three-layer fully connected network, with input layer neurons and... The encoder and decoder have the same dimension, n=d. The input data is the local fast-changing frequency deviation data of each node. There are 128 neurons in the hidden layer and 64 neurons in the output layer. The output data is an observable spatial vector. Both the encoder and decoder use the tanh activation function. The Koopman matrix K is a learnable parameter matrix with a dimension of 64×64 and is initialized uniformly by Xavier. The decoder has 64 neurons in the input layer, 128 neurons in the hidden layer, and 10 neurons in the output layer. The output is the frequency prediction result at 10 time steps.

[0064] S3: Constructing a loss function oriented towards physical mechanisms ;

[0065] Loss function oriented towards physical mechanisms It consists of two parts: one part is the state prediction fidelity loss in the observable frequency space. The first part is mainly used to fit electromagnetic transient simulation data of actual systems to ensure prediction accuracy. The second part is the consistency loss of the coupling state (frequency) recursive spectrum. It is mainly used to retain dynamic coupling and coordination information between devices, through non-negative weights. balance and , represented as:

[0066] ;

[0067] A mandatory requirement is placed on achieving multi-step prediction accuracy within the time range P to ensure that the learned linear evolution matches the EMT trajectory, thus reducing prediction fidelity loss. The expression is:

[0068] ;

[0069] Where B is the batch size and P is the prediction step size. The actual state trajectory generated for electromagnetic transient simulation. Let represent the state of the b-th batch at time t. To perform feature mapping on the state of the b-th sample at time t, a high-dimensional feature representation is obtained, where C is the decoder projection matrix. The balancing weight coefficient β is determined through a hyperparameter grid search, and its optimal value is obtained by considering the root mean square error (RMSE) and CSR retention bias on the validation set. Determined through joint assessment;

[0070] The coupling state recursive spectrum consistency loss function is expressed as:

[0071] ;

[0072] in, To calculate different lag steps based on joint recursive graph analysis The recursive probability of the coupling state of the selected network type and network structure device. To predict the time lag window, Let be the i-th eigenvalue of the Koopman operator matrix K, and Δt be the sampling time interval of the EMT simulation. For the selected set of lag steps, Re(·) denotes taking the real part of the complex number. The statistical coordination attenuation rate of the frequency support effect of the selected mesh-type and mesh-structured equipment was observed in the electromagnetic transient simulation trajectory data. This was discovered through statistical data. ,so Structurally related to the spectral properties of the Koopman operator The attenuation rate, It is the dominant decay rate extracted from the eigenvalues ​​of the Koopman matrix. The difference between the decay rate of the dominant eigenvalue of the Koopman operator and the recursive empirical decay rate of the coupling state of the selected network-type and network-type devices is measured. The model training objective is to make the dominant decay rate extracted from the eigenvalue of the Koopman matrix consistent with the coordinated decay rate of the frequency support effect of the selected network-type and network-type devices as determined by the actual system statistics.

[0073] In this embodiment, based on the hybrid ergodic theory, a statistical coordination attenuation rate for the frequency support function of network-type and network-structured devices is established. The theoretical boundary associated with the spectral gap of the Koopman operator, The attenuation is limited by the spectral gap of the Koopman operator K, expressed as:

[0074] ;

[0075] in, This represents the invariant joint recursive measure under a stationary distribution. These are the dominant non-unit eigenvalues ​​of the K-matrix in the Koopman operator. Dominant non-unit eigenvalues ​​refer to the modes that decay the slowest and survive the longest in transient processes; mathematically, they are defined as: [the modes that are eliminated]. Then, the eigenvalue with the largest modulus among the remaining eigenvalues ​​is usually denoted as... In practical applications, this stationarity measure is empirically approximated by long-term EMT trajectories, where M is a positive constant (M>0) derived from the coefficients of spectral decomposition.

[0076] Conventional deep Koopman standard regularization methods typically impose strict stability constraints, such as... This approach enables deep Koopman models to... The model always assumes the system is stable, which does not match reality. This embodiment uses an adaptive approach to ensure that the eigenvalues ​​of the Koopman matrix K are consistent with the observed attenuation characteristics of the actual coordinated and continuous operation of the two types of equipment in the mixed power system with grid-connected and grid-connected devices. When the system exhibits frequency instability, the eigenvalues ​​of the Koopman matrix K obtained by the model will... The situation matches the actual circumstances, and the loss is permissible. The characteristic values ​​are used to accurately capture the continuous oscillations caused by the interaction between mesh-type and mesh-type equipment, thus avoiding the application of incorrect damping constraints.

[0077] S4: End-to-end training based on electromagnetic transient simulation data;

[0078] This embodiment utilizes the output frequency trajectory data of the tracking and meshing devices generated by electromagnetic transient simulation to jointly optimize the encoder, linear Koopman operator matrix, and decoder in an end-to-end manner, thereby obtaining a deep Koopman model that satisfies the dynamic coordination and consistency constraints of the tracking and meshing coupling.

[0079] S5: Deep Koopman model inference;

[0080] During the inference phase, the pre-trained deep Koopman model parameters are first loaded. Then, the local rapid frequency deviation data of the system is fed into the network in the form of [n_features, d], where n_features is the number of nodes in the system, and each feature corresponds to the frequency deviation sequence of a node over the past d time steps. During prediction, the network extracts the time series for each feature, inputs the d-step historical data of each node into the encoder, maps it to a 64-dimensional latent space, and then performs state advancement through a shared Koopman linear operator to obtain the latent state at the next time step. Subsequently, the decoder restores the latent state to the predicted values ​​for the next 10 time steps, and finally concatenates the prediction results of all nodes to obtain the output of [n_features, 10].

[0081] Example 2

[0082] This embodiment is based on the power system frequency prediction method based on coupled state recursive constraints and deep Koopman analysis from Embodiment 1 above. An improved IEEE 14-bus system is used as a verification platform to simulate the complete implementation process, such as... Figure 4 As shown, the improved IEEE 14-node system includes 5 GFM device units (located on buses 1, 2, 3, 6, and 8) and 3 GFL device units (located on buses 11, 12, and 13). Frequency trajectory datasets under power disturbance scenarios are generated using electromagnetic transient simulation software.

[0083] The disturbance scenario is set as follows: a 10% load step increase occurs in the GFL unit at bus 11, with a sampling step size of 40μs. The dataset is divided into a training set (70%), a validation set (15%), and a test set (15%), as shown in Table 1 below. These are the equipment parameters for the improved IEEE 14-bus system.

[0084] Table 1. Equipment Parameters of IEEE 14-Node System

[0085]

[0086] In this embodiment, the encoder is designed as a three-layer fully connected network, and the number of neurons in the input layer is taken from the local fast-changing frequency deviation data of the system nodes. The encoder has a dimension n=50, 128 hidden neurons, and 64 output neurons. Both the encoder and decoder use the tanh activation function. The Koopman matrix K is a learnable parameter matrix with a dimension of 64×64, initialized uniformly by Xavier. The decoder has an input layer of 64 neurons, a hidden layer of 128 neurons, and a 10-dimensional output, which represents the predicted local rapid frequency deviation data of the system nodes after 10 steps.

[0087] In this embodiment, the true value of the recursive decay rate of the coupled state is obtained: based on the electromagnetic transient simulation trajectory, the set of lag steps H = {5, 10, 15, 20, 25, 30} (corresponding to a time of 5-30ms) is set, the joint recursive matrix is ​​calculated using a 10% density invariant threshold, and the empirical logarithmic decay rate is fitted. ;

[0088] The spectral consistency loss function is constructed as follows:

[0089] ;

[0090] in , Let K be the eigenvalue of the Koopman matrix.

[0091] The total loss function is: ;

[0092] Prediction step size P = 50 (corresponding to a 50ms prediction time domain), batch size B = 64. β is initially set to... It was finally determined through grid search to be End-to-end training was performed, as shown in Table 2 below, which lists the training platform and parameters:

[0093] Table 2. Training Platform and Parameter Details

[0094]

[0095] like Figure 5 As shown, the training convergence of the proposed dual-loss objective in different scenarios was obtained;

[0096] The real trajectory was generated through EMT simulation (40 μs step size). The proposed CSR-Koopman method was benchmarked against TransferFunction, DMD, EDMD (third-order polynomial), Hankel-DMD, and DeepKoopman. The model performance was evaluated using root mean square error (RMSE), mean absolute error (MAE), and CSR hold-up bias. Conduct performance evaluation;

[0097] like Figure 6 As shown, under different operating conditions, the power generation loss in the low inertia region (Case 1), the load change in the high inertia region (Case 2), and the load shedding of the high voltage DC transmission (Case 3) are obtained. The center of inertia (COI) frequency curve of the proposed method is highly consistent with the EMT simulation in these scenarios, which verifies the accuracy of the improved IEEE 14-node system modeling.

[0098] In Case 4, when the PLL bandwidth of the network-connected device decreased from 2Hz to 0.25Hz, the system exhibited complex dynamic characteristics that challenged traditional methods. For example... Figure 7 and Figure 8 As shown, the transfer function, DMD, and EDMD methods all failed to capture the COI oscillations caused by PLL bandwidth reduction, while Hankel-DMD could only achieve partial tracking. The method of this invention can completely track the EMT simulation curve.

[0099] As shown in Table 3 below, although both Deep Koopman and the proposed method can predict trajectories, CSR-Koopman exhibits superior fidelity. The model of this invention not only achieves the highest accuracy (RMSE = 0.0094Hz) but also reduces the CSR holding bias ΔCSR by 79.1%, and the accuracy of the model of this invention is 24.3% higher than that of the transfer function model.

[0100] Table 3. Performance Comparison of the Invention Method with Other Methods

[0101]

[0102] This invention quantifies the computational efficiency of the proposed CSR–Koopman framework to evaluate its feasibility in large-scale and multi-scenario frequency dynamics and the collaborative effects of different supporting devices. Although the offline training process takes approximately 6.2 hours, the online inference stage involves only linear matrix operations, with a complexity of O(n log n). As shown in Table 4 below, the method of this invention achieves a speedup of 4817 times compared with full-order EMT simulation, supporting rapid emergency screening and planning-oriented analysis.

[0103] Table 4. Schematic diagram of calculation time comparison method within a 5-second simulation time range.

[0104]

[0105] Example 3

[0106] This embodiment provides a storage medium, which may be a ROM, RAM, disk, optical disk, or other storage medium. The storage medium stores one or more programs. When the program is executed by the processor, it implements the power system frequency prediction method based on coupled state recursive constraints and deep Koopman in Embodiment 1.

[0107] Example 4

[0108] This embodiment provides a computing device, which may be a desktop computer, laptop computer, smartphone, PDA handheld terminal, tablet computer or other terminal device with display function. The computing device includes a processor and a memory. The memory stores one or more programs. When the processor executes the program stored in the memory, it implements the power system frequency prediction method based on coupled state recursive constraints and deep Koopman based on embodiment 1.

[0109] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A power system frequency prediction method based on recursive constraints on coupling states and deep Koopman, characterized in that, Includes the following steps: The simulated frequency data is acquired and preprocessed to obtain the local fast-changing frequency deviation signal; Time-delay embedding is performed on the local fast-changing frequency deviation signal to construct the phase space trajectory vector; A deep Koopman model is constructed, including an encoder, a linear Koopman operator matrix, and a decoder. The encoder elevates the phase space trajectory vector to the observable space. The linear Koopman operator matrix performs linear state evolution of the frequency state vector in the observable space. The decoder projects the observable space state back to the original state space and outputs the predicted value of the local fast-changing frequency deviation data. Construct the total loss, obtain the output frequency trajectory data of network-following and network-building devices, and train the deep Koopman model; Frequency prediction results are obtained based on the trained deep Koopman model.

2. The method of claim 1, wherein the method is based on recursive constraints on the coupling state and deep Koopman for power system frequency prediction. Acquire simulation frequency data and perform data preprocessing, specifically including: Simulated frequency data is obtained based on time-domain simulation. Local frequency deviation data is decomposed into global slow-changing and local fast-changing signals. The deviation between the instantaneous frequency and the rated frequency in the power grid is calculated. The inertia center signal is used as an analytical reference to decompose the local frequency deviation. The deviation between the instantaneous frequency and the rated frequency in the power grid is standardized to obtain a local fast-changing frequency deviation signal.

3. The method of claim 2, wherein the method is based on recursive constraints on the coupling state and deep Koopman for power system frequency prediction. The local frequency deviation data is decomposed into globally slow-changing and locally fast-changing signals. The deviation between the instantaneous frequency and the rated frequency in the power grid is calculated and expressed as: ； wherein represents the inertial weighted average frequency, reflects the interaction caused by fast coupling, represents the deviation of the instantaneous frequency in the power grid at the i-node at time t from the rated frequency.

4. The method of claim 3, wherein the method is based on recursive constraints on the coupling state and deep Koopman for power system frequency prediction. The deviation between the instantaneous frequency and the rated frequency in the power grid is standardized and expressed as follows: Let Standardization is performed and expressed as: ； wherein , are the mean and standard deviation of the local frequency deviation, respectively, denotes the local fast varying frequency deviation signal.

5. The method of claim 1, wherein the method is based on recursive constraints on the coupling state and deep Koopman for power system frequency prediction. By performing time-delay embedding on the standardized frequency sequence, a phase space trajectory vector is constructed, which is represented as: ； where d is the embedding dimension, is the time delay, denotes the local fast frequency deviation signal, denotes the phase space trajectory vector.

6. The method of claim 1, wherein the method is based on recursive constraints on the coupling state and deep Koopman for power system frequency prediction. The total loss is constructed based on the state prediction fidelity loss in the observable frequency space and the consistency loss of the coupled state recursive spectrum.

7. The method of claim 1, wherein the method is based on recursive constraints on the coupling state and deep Koopman for power system frequency prediction. The total loss is expressed as: ； ； ； in, Indicates the total loss. Indicates the weight value. This represents the prediction fidelity loss, where B is the batch size and P is the prediction step size. The actual state trajectory generated for electromagnetic transient simulation. Let's consider the state of batch b at time t. To perform feature mapping on the state of the b-th sample at time t, a high-dimensional feature representation is obtained, where C is the decoder projection matrix and K represents the linear Koopman operator matrix. To calculate different lag steps based on joint recursive graph analysis The recursive probability of the coupling state of the selected network type and network structure device. To predict the time lag window, Let be the i-th eigenvalue of the Koopman operator matrix K, and Δt be the simulation sampling time interval. For the selected set of lag steps, Re(·) denotes taking the real part of the complex number. It is the statistical coordination attenuation rate of the frequency support effect of the selected mesh-type and mesh-type equipment observed in the electromagnetic transient simulation trajectory data. This represents the consistency loss of the recursive spectrum of coupled states.

8. The power system frequency prediction method based on coupled state recursive constraints and deep Koopman as described in claim 7, characterized in that, The attenuation is limited by the spectral gap of the Koopman operator K, expressed as: ； in, This represents the invariant joint recursive measure under a stationary distribution. The K matrix is ​​the dominant non-unit eigenvalue of the Koopman operator K, and M is a positive constant derived from the coefficients of the spectral decomposition.

9. A computer-readable storage medium storing a program, characterized in that, When the program is executed by the processor, it implements the power system frequency prediction method based on coupled state recursive constraints and deep Koopman as described in any one of claims 1-8.

10. A computer device comprising a processor and a memory for storing a processor-executable program, characterized in that, When the processor executes the program stored in the memory, it implements the power system frequency prediction method based on coupled state recursive constraints and deep Koopman as described in any one of claims 1-8.

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