Electric power system stable form identification method and system based on neural frequency division Kupman

Abstract

The invention discloses an electric power system stable form identification method and system based on neural frequency division Kupman, and the method comprises the steps: constructing an electric power Kupman operator based on a neural network according to a Kupman operator theory; according to the electric power Kupman operator, constructing a frequency division Kupman operator model; based on the frequency division Kupman operator model, a frequency domain attention mechanism is introduced to learn the weight of each frequency band, and a weighted feature matrix is formed; performing feature value extraction on the weighted feature matrix to obtain a feature value; judging the stability of the power system according to the characteristic value; the stability of the power system comprises transient stability, transient instability and critical stability; and when the stability of the power system is transient instability, further judging the transient instability state of the power system based on the decision tree according to the characteristic value. According to the method, the nonlinear dynamic characteristics of the complex system are considered while the calculation efficiency is kept, and the judgment accuracy is higher.

Description

Technical Field

[0001] This invention relates to the field of smart grid and power system security and stability technology, specifically to a method and system for power system stability pattern identification based on neural frequency division Koopman. Background Technology

[0002] The construction of new power systems in the field of smart grids, especially against the backdrop of large-scale integration of renewable energy, faces unprecedented challenges. Stable operation, as a fundamental requirement of the power system, is the foundation for ensuring the safe, efficient, and continuous operation of the power grid. How to ensure the stable operation of the power system in complex and volatile environments has become a key issue in the current construction and optimization of power systems. Therefore, how to effectively perceive the stability of the power grid through data has become a difficult problem in current research and practice. First, with the integration of various smart devices, sensors, and control components, the composition of the power system is becoming increasingly complex, and the models of the integrated components are becoming more refined and complex, increasing the difficulty of system calculation and analysis. Second, the massive scale and highly integrated nature of the power system itself means that numerous variables need to be processed in real-time monitoring and analysis, further exacerbating the system's complexity. Most importantly, the nonlinear dynamics of the power system are particularly significant when facing large-scale disturbances, especially in the case of large disturbances such as faults or severe load fluctuations. The dynamic behavior of the system is highly complex and dimensional, posing a huge challenge to the accurate determination of stability.

[0003] Transient stability of a power system is a crucial indicator of whether the power grid can recover to a steady state under large disturbances. Transient stability analysis is not only a core issue in power system operation but also an important aspect of ensuring grid reliability. When faced with large disturbances, the power system needs a rapid self-recovery process to ensure it returns to equilibrium within a short time after the disturbance occurs. The effectiveness of this process directly determines the system's stability and the reliability of power supply.

[0004] Currently, the main methods for transient stability assessment can be broadly categorized into two types: one based on linear eigenvalue analysis, and the other based on nonlinear simulation and energy analysis. Linear eigenvalue analysis simplifies the analysis process by linearizing the system's dynamic characteristics. Its advantages lie in its intuitiveness and ease of acquisition: the oscillation characteristics and stability of the system can be clearly assessed using specific data from the system's eigenvalues. More importantly, eigenvalue analysis can obtain system stability information in real time without a detailed system model, exhibiting certain black-box characteristics, making transient stability analysis more flexible and adaptable to dynamic environments.

[0005] However, when a system is subjected to large disturbances, the nonlinear effects of the system increase significantly with the increase of the disturbance, and the system behavior becomes more complex. Traditional linearization methods cannot capture this change, and linear eigenvalue analysis is no longer applicable. Therefore, transient stability analysis must rely on more complex nonlinear simulation or energy analysis methods. Although these methods can effectively reflect the nonlinear dynamic process of the system under large disturbances, they also face the challenge of high computational difficulty. Especially in multi-machine systems, nonlinear simulation requires a large amount of numerical calculation, increasing the computational complexity of system operation; energy analysis methods require accurate estimation of the system's energy conversion process and depend on complex system models, which poses a considerable computational burden for large-scale systems.

[0006] To better balance analytical accuracy and computational efficiency, the Koopman operator method has been proposed and widely applied in the transient stability analysis of power systems in recent years. The Koopman operator maps the nonlinear dynamics of a system to a high-dimensional linear space, transforming the behavior of a nonlinear system into a linear problem. This allows traditional linear analysis methods to be effectively applied to nonlinear systems while preserving their nonlinear characteristics. By extracting eigenvalues, this method can better analyze the dynamic response of the system under different disturbance conditions and provide a strong basis for judging system stability. Compared with traditional nonlinear simulation methods, the Koopman operator exhibits significant computational efficiency advantages when dealing with high-dimensional complex systems, greatly reducing computation time. Furthermore, combined with frequency division techniques, the Koopman operator can extract system eigenvalues ​​at different time scales, making the extraction of transient eigenvalues ​​of power systems more detailed and comprehensive, thus more effectively helping to assess system stability.

[0007] However, as the Koopman operator enters the engineering application stage, its practical complexity and limitations gradually become apparent. First, in most practical engineering projects, the nonlinear operators used for dimensional scaling to achieve high-dimensional mappings are difficult to obtain, thus limiting the application of the Koopman method. Second, the Koopman operator theoretically requires the use of infinite-dimensional operators to fully describe the dynamic behavior of the system, which is impossible in engineering practice. Therefore, its operability and practicality are greatly reduced, making the traditional Koopman method difficult to apply in practical power systems.

[0008] In view of the above, this application is hereby submitted. Summary of the Invention

[0009] The technical problem this invention aims to solve is that new power systems are prone to instability loss under large disturbances, requiring them to restore power balance and operational stability within a short period. However, due to the significant nonlinear effects accompanying large disturbances, the dynamic characteristics of the system are complex and highly coupled, posing a severe challenge to transient stability assessment. Traditional linearization-based analysis methods are insufficient to accurately characterize such nonlinear dynamic behaviors and are no longer suitable for complex systems with high proportions of renewable energy integration. Furthermore, existing transient stability analysis methods are highly dependent on system models and computationally burdensome, making it difficult to quickly and accurately identify dominant instability mechanisms and characteristic modes within a limited timeframe, thus hindering stability assessment.

[0010] The purpose of this invention is to provide a method and system for identifying the stable state of power systems based on the neural frequency division Koopman operator. It proposes an efficient mapping method for nonlinear dynamics based on the Koopman operator, forming a system that, while ensuring the stable characteristics of the power system under nonlinear dynamics, also considers the nonlinear dynamic features of the system, resulting in a system-dominant stability identification strategy based on a small number of low-dimensional eigenvalues. Compared to traditional time-domain simulation methods, this invention maintains computational efficiency while taking into account the nonlinear dynamic characteristics of complex systems, achieving higher identification accuracy.

[0011] This invention is achieved through the following technical solution:

[0012] In a first aspect, the present invention provides a method for identifying the stable state of a power system based on neural frequency division Koopman, the method comprising:

[0013] Based on the Koopman operator theory, an electric Koopman operator is constructed using a neural network.

[0014] Based on the electric Koopman operator, a frequency division Koopman operator model is constructed;

[0015] Based on the frequency division Koopman operator model, a frequency domain attention mechanism is introduced to learn the weight of each frequency band, forming a weighted feature matrix;

[0016] Eigenvalues ​​are extracted from the weighted feature matrix to obtain eigenvalues; and the stability of the power system is determined based on the eigenvalues; the stability of the power system includes transient stability, transient instability, and critical stability;

[0017] When the power system stability is transiently unstable, the transient instability mode of the power system is further determined based on the eigenvalues ​​and the decision tree.

[0018] Furthermore, based on the Koopman operator theory, an electric Koopman operator is constructed using a neural network, including:

[0019] For any power system, when observed using discrete measurements, the power system can be summarized as a discrete-time nonlinear dynamic system: ,in, It is the power system state vector at time t. Let be the power system state vector at time t+1. It is a nonlinear function describing the evolution of a power system;

[0020] Based on nonlinear dynamical systems, the Koopman operator is expressed using a neural network, yielding a discrete expression: K is the Koopman operator. For observation functions;

[0021] The discrete expression is reconstructed to obtain the equivalent expression: , For finite-dimensional embedding functions.

[0022] Furthermore, based on the electric Koopman operator, a frequency division Koopman operator model is constructed, including:

[0023] The physical state at time t is based on the encoder network. Mapped to a Koopman embedding vector;

[0024] Based on the Koopman embedding vector, an embedding state sequence window of length L is constructed to form a mapping sequence;

[0025] The component signals are obtained by transforming the mapped sequence using the Discrete Fourier Transform.

[0026] Based on the component signals, the frequency range is divided into M non-overlapping frequency bands; and the inverse discrete Fourier transform is used to perform an inverse transform on each frequency band to obtain the sub-embedding sequence of that frequency band in the time domain.

[0027] Based on the sub-embedding sequence, within each frequency band subspace, a one-step linear deduction is performed on the filtered component signal based on the frequency band-specific linear dynamic matrix to obtain the predicted sub-state of the next time step for that frequency band.

[0028] All derived sub-states will be mapped back to the linear time domain through inverse Fourier transform, and then the system state in the original nonlinear space will be obtained through inverse Koopman observation transform, i.e., the frequency-division Koopman operator model.

[0029] Furthermore, the expression for the frequency division Koopman operator model is:

[0030] ;

[0031] In the formula, Let be the power system state vector at time t+1. Let be the inverse transform function of the Koopman observation. For frequency band, For the frequency band sub-embedded sequence in the time domain, It corresponds to the digital frequency;

[0032] In the frequency division Koppman operator model, each frequency band Configure a linear dynamics matrix The dynamic matrix It is consistent with the linear matrix in the original neural Koopman network.

[0033] Furthermore, the expression for the weighted characteristic matrix is:

[0034] ;

[0035] In the formula, For the weighted characteristic matrix, For time t, the frequency band Attention score For each frequency band The configured linear dynamics matrix, where M is the number of frequency bands.

[0036] Furthermore, based on eigenvalues, the stability of the power system is determined, including:

[0037] If the magnitude of the eigenvalue is less than 1, then the stability of the power system under large disturbances is transient stability.

[0038] If the magnitude of the eigenvalue is greater than 1, then the stability of the power system under large disturbances is transient instability.

[0039] If the magnitude of the eigenvalue is equal to 1, then the stability of the power system under large disturbances is critically stable.

[0040] Furthermore, based on the eigenvalues, the transient instability mode of the power system is further determined using a decision tree, including:

[0041] Based on the characteristic values ​​of multiple frequency bands, characteristic indices are constructed. The characteristic indices include the most negative damping ratio, the frequency corresponding to the most negative damping, the maximum real part, the average damping, and the damping distribution dispersion for each frequency band.

[0042] The characteristic values ​​of the characteristic indicators are input into a pre-constructed decision tree, and the transient instability mode of the power system is output. The transient instability modes include power angle instability, voltage instability, frequency instability, broadband oscillation and coupling instability.

[0043] Secondly, the present invention provides a power system stability pattern recognition system based on neural frequency division Koopman, the system comprising:

[0044] The first building unit is used to construct the electric Koopman operator based on the Koopman operator theory and a neural network.

[0045] The second building unit is used to build a frequency division Koopman operator model based on the electric Koopman operator;

[0046] The weighted feature matrix forming unit is used to learn the weights of each frequency band based on the frequency division Koopman operator model and introduce a frequency domain attention mechanism to form a weighted feature matrix.

[0047] The first discrimination unit is used to extract eigenvalues ​​from the weighted feature matrix to obtain eigenvalues; and to determine the stability of the power system based on the eigenvalues; the stability of the power system includes transient stability, transient instability and critical stability;

[0048] The second discrimination unit is used to further discriminate the transient instability mode of the power system based on the feature value and the decision tree when the power system stability is transient instability.

[0049] Thirdly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-mentioned method for identifying the stable mode of a power system based on neural frequency division Koopman.

[0050] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for identifying the stable state of a power system based on neural frequency division Koopman.

[0051] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0052] 1. This invention relates to a power system stability pattern identification method and system based on neural frequency division Koopman, and an efficient mapping method for nonlinear dynamics based on the Koopman operator. This method ensures the stable characteristics of the system under nonlinear dynamics while considering the nonlinear dynamic features of the system, resulting in a system-dominant stability identification strategy based on a small number of low-dimensional eigenvalues. Compared to traditional time-domain simulation methods, this method maintains computational efficiency while taking into account the nonlinear dynamic characteristics of complex systems, achieving higher identification accuracy.

[0053] 2. This invention relates to a power system stability pattern identification method and system based on neural frequency division Koopman. It achieves interpretable modeling of complex nonlinear dynamic processes with a simple algorithm, without relying on complex black-box models or manually set thresholds. Instead, it guides the algorithm to automatically learn instability mechanisms through physical characteristics. Therefore, it not only outputs instability pattern conclusions with engineering physical significance but also possesses clear and traceable decision-making logic, providing a technical approach for identifying the dominant stable behavior of a system that combines theoretical rigor with engineering feasibility. Attached Figure Description

[0054] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0055] Figure 1 This is a flowchart of the power system stability pattern identification method based on neural frequency division Koopman in this invention;

[0056] Figure 2 This is a detailed flowchart of the power system stability pattern identification method based on neural frequency division Koopman of the present invention;

[0057] Figure 3 This is a structural block diagram of the power system stability pattern identification system based on neural frequency division Koopman based on the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0059] When subjected to large disturbances, new power systems are prone to instability loss, requiring them to restore power balance and operational stability within a short period. However, due to the significant nonlinear effects accompanying large disturbances, the dynamic characteristics of the system are complex and highly coupled, posing a severe challenge to transient stability assessment. Traditional linearization-based analysis methods are insufficient to accurately characterize such nonlinear dynamic behaviors and are no longer suitable for complex systems with high proportions of renewable energy integration. Furthermore, existing transient stability analysis methods are highly dependent on system models and computationally burdensome, making it difficult to quickly and accurately identify dominant instability mechanisms and characteristic modes within a limited timeframe, thus hindering stability assessment.

[0060] To address the above issues, this invention introduces a deep learning-based neural network method into the application of the Koopman operator, forming the Neural-Koopman method. This method approximates nonlinear operators through a deep learning network and obtains the mapping operator for dimensionality increase and its inverse solution for dimensionality reduction through network learning, thereby achieving dimensionality increase linearization of complex high-dimensional power systems. Neural-Koopman not only overcomes the difficulty of obtaining nonlinear operators in the traditional Koopman method but also leverages the powerful approximation capabilities of deep learning, enabling its effective application in practical engineering. Utilizing the automation characteristics of deep learning, Neural-Koopman can efficiently perform nonlinear dynamic modeling in large-scale power systems and significantly improve computational efficiency, making the analysis of high-dimensional systems more feasible.

[0061] This invention is based on the Koopman operator theory, uses the Neural-Koopman method to account for the nonlinear dynamic characteristics of the system, extracts the high-dimensional characterization of the system, and performs transient stability analysis through the obtained eigenvalues.

[0062] Example 1

[0063] like Figure 1 and Figure 2 As shown, the present invention provides a power system stability pattern identification method based on neural frequency division Koopman, which includes:

[0064] Step 1: Based on the Koopman operator theory, construct the electric Koopman operator using a neural network;

[0065] Considering that after a transient disturbance occurs in a power system, large-scale equipment in the power system will experience a severe disturbance process with a high degree of nonlinearity, making it difficult to judge using the stability analysis methods of dynamic systems in classical linear control theory. Therefore, this invention considers constructing a Koopman operator suitable for dynamic modeling of power systems. Step 1 specifically includes:

[0066] For any power system, if discrete measurements are used for observation, the power system can be summarized as a discrete-time nonlinear dynamic system:

[0067] (1.1)

[0068] in, It is the power system state vector at time t (in the power system, it can be represented by response measurements such as generator power angle, speed, and bus voltage). Let be the power system state vector at time t+1; It is a nonlinear function that describes the evolution of a power system.

[0069] Koopman theory provides a linear perspective for the stability analysis of such strongly nonlinear dynamical systems, and this linearization does not lose any nonlinear characteristics of the system. The core of the Koopman operator lies in transforming the state space... The nonlinear evolution is elevated to an infinite-dimensional observation function space. Linear evolution over [a certain period]. For any observation function (or observable)... There exists a linear operator K (i.e., the Koopman operator) that satisfies:

[0070] (1.2)

[0071] The discrete expression (1.2) represents the current state. Arbitrary observation function Applying the Koopman operator K is equivalent to applying the state of the observation function at the next time step. The computation is performed on top of this. The goal of the Neural Koopman Network is to find a finite-dimensional embedding function. , the original state A vector mapped to a Koopman space And learn a finite-dimensional linear operator in this space. , so that:

[0072] (1.3)

[0073] In addition, a decoding function is also needed. This allows the state of the Koopman space to be mapped back to the original nonlinear space, and it needs to satisfy the following conditions: Therefore, after the Koopman mapping, the strongly nonlinear dynamic behavior of the power system after transient disturbances can be described in a linear space, and the stability determination method for linear systems can be directly applied to the stability determination of this power system. However, the Koopman observation function itself is a nonlinear function, and the theory requires it to have infinite dimensions, making it difficult to directly apply Koopman theory. Therefore, this invention uses a deep learning model to parameterize the Koopman observation function, enabling the system to be conveniently linearized while preserving nonlinearity.

[0074] Step 2: Construct a frequency division Koopman operator model based on the electric Koopman operator;

[0075] To parameterize the Koopman observation function using a neural network, the network needs two key functions: dimensionality increase and nonlinear mapping. Autoencoders can flexibly change the representational dimension of data and possess nonlinear mapping capabilities through the activation functions of neurons. Therefore, an encoder using an autoencoder... With decoder Implement the Koopman observation function and the inverse Koopman observation transform function, respectively.

[0076] In this embodiment, step 2 specifically includes:

[0077] First, based on the encoder network, the physical state at time t is... Mapped to Koopman embedding vector To analyze its dynamic temporal characteristics, this invention constructs an embedded state sequence window of length L:

[0078] (1.4)

[0079] The system dynamics of the mapped sequence (1.4) are linearized, and a linear dynamic matrix can be constructed using Koopman theory. The parameters of this linear dynamics matrix are constructed from trainable parameters and tuned during the training of the neural Koopman network, specifically designed to deduce the dynamic evolution of the system.

[0080] However, transient signals in power systems are typically non-stationary signals, with their frequency components varying over time. Using a single linear dynamic matrix... It is difficult to fully express the different frequency characteristics of power system transient processes. Therefore, this invention introduces Fourier decomposition into the neural Koopman network to refine the state deduction of signals in each frequency band.

[0081] The mapped sequence is transformed by the Discrete Fourier Transform (DFT) to obtain the result for... component signals , is represented as:

[0082] (1.5)

[0083] in, This corresponds to the digital frequency. To ensure the number of frequency divisions and the degree of difference between each frequency band, this invention divides the frequency range into M non-overlapping frequency bands according to a logarithmic scale. For each frequency band The inverse discrete Fourier transform (IDFT) can be used to obtain the sub-embedded sequence of this frequency band in the time domain:

[0084] (1.6)

[0085] Then, for each frequency band A dedicated linear dynamics matrix can be configured. This linear dynamics matrix is ​​consistent with the linear matrix in the original neural Koopman network, both consisting of trainable parameters, and is used only to extrapolate the dynamic evolution within this frequency band. Within each frequency band subspace, its own dedicated linear dynamics matrix is ​​used. Filtered component signals By performing a linear extrapolation, the predicted sub-state of this frequency band at the next time step is obtained:

[0086] (1.7)

[0087] All derived sub-states will be mapped back to the linear time domain through inverse Fourier transform, and then the system state in the original nonlinear space will be obtained through Koopman observation inverse transform. That is, the frequency-division Koopman operator model, can be expressed as:

[0088] (1.8)

[0089] In the formula, Let be the power system state vector at time t+1. Let be the inverse transform function of the Koopman observation. For frequency band, For the frequency band sub-embedded sequence in the time domain, It corresponds to the digital frequency.

[0090] Step 3: Based on the frequency division Koopman operator model, a frequency domain attention mechanism is introduced to learn the weights of each frequency band, forming a weighted feature matrix;

[0091] Considering that the transient processes triggered by different disturbances in a power system vary, the importance of the dynamic information contained in each frequency band differs. Therefore, this invention introduces a frequency-domain attention mechanism to adaptively learn the weights of each frequency band.

[0092] Specifically, this attention mechanism uses the linearized vector after the Koopman mapping. As input, each frequency band is computed through an attention network. Attention score :

[0093] (1.9)

[0094] (1.10)

[0095] in, These are learnable parameters. Attention weights. satisfy This reflects the importance of the dynamics of each frequency band at time t for predicting the next state. This attention mechanism is applied to the linear dynamic matrix of the weighted frequency band state derivation. The stability characteristics of the final system can be characterized by the weighted dynamic matrix of each frequency band. The expression for the weighted characteristic matrix is:

[0096] (1.11)

[0097] In the formula, For the weighted characteristic matrix, For time t, the frequency band Attention score For each frequency band The configured linear dynamics matrix, where M is the number of frequency bands.

[0098] Step 4: Extract eigenvalues ​​from the weighted feature matrix to obtain eigenvalues; and determine the stability of the power system based on the eigenvalues; power system stability includes transient stability, transient instability, and critical stability;

[0099] The frequency-division Koopman operator model provides a powerful tool for stability analysis. For any time window, the state derivation matrix... This method can effectively characterize the dynamic characteristics of a system. To further simplify the analysis, eigenvalue analysis, a method from the field of linear control, can be used. By observing the region where the eigenvalues ​​are located, the stability of the system can be easily determined. The eigenvalue extraction process can be formalized:

[0100] (1.12)

[0101] in, It is an eigenvalue matrix. It is the eigenvector matrix.

[0102] Therefore, the stability criterion of a power system can be determined based on the magnitude of its eigenvalues, and the criteria can be summarized as follows:

[0103] (1) If the modulus of the eigenvalue is less than 1, i.e. Then the stability of the power system under large disturbances is transient stability;

[0104] (2) If the magnitude of the eigenvalue is greater than 1, that is If so, the stability of the power system under a large disturbance is transient instability;

[0105] (3) If the modulus of the eigenvalue is equal to 1, that is If the stability of the power system under large disturbances is critically stable, then the stability of the power system is critically stable.

[0106] Large disturbances typically refer to disturbances that cause the power system's operating point to deviate significantly from its original steady state, triggering strongly nonlinear transient processes. Their amplitudes far exceed the applicability of the small disturbance assumption, often leading to significant shifts in system frequency, voltage, or power angle, and even causing changes in network topology. Typical large disturbances include three-phase short-circuit faults, line or main transformer tripping, large-scale load surges, concentrated disconnection of new energy sources from the grid, and converter blocking or DC pole faults in flexible DC projects.

[0107] The eigenvalue with the largest magnitude among the above eigenvalues ​​is the dominant eigenvalue, and its corresponding eigenvector is... This can indicate the mode of system instability. Therefore, the present invention continues with step 5 based on step 4 to determine the specific transient instability mode.

[0108] Step 5: When the power system stability is transient instability, the transient instability mode of the power system is further determined based on the eigenvalues ​​and the decision tree.

[0109] While eigenvalues ​​can effectively analyze whether a power system is experiencing transient instability, they are insufficient to further analyze the dominant instability patterns. Therefore, this invention uses decision trees to further discriminate transient instability patterns, establishing a refined mapping relationship from frequency-specific eigenvalues ​​to instability patterns. The basic idea is to leverage the interpretability of decision tree algorithms to transform the dynamic characteristics of the power system at different frequency bands into a series of physically meaningful real-valued features, thereby enabling automatic identification and classification of system stability patterns through a standard Classification and Regression Tree (CART) model.

[0110] In this embodiment, step 5 specifically includes:

[0111] Step 51: Construct feature indicators based on the feature values ​​of multiple frequency bands;

[0112] Specifically, based on multi-band eigenvalues ​​and considering their physical meaning, multiple characteristic indices are defined to enhance the accuracy of identifying dominant transient instability patterns. These characteristic indices include the most negative damping ratio for each frequency band. The frequency corresponding to the most negative damping Maximum real part Average damping With damping distribution dispersion To characterize the divergence risk within the frequency band, the nature of the oscillation mode, the damping level of the mode within the frequency band, the modal compatibility, and the interaction between dynamics at different time scales, respectively.

[0113] Step 52: Input the feature values ​​of the feature indicators into the pre-constructed decision tree and output the transient instability mode of the power system; the transient instability mode includes power angle instability, voltage instability, frequency instability, broadband oscillation and coupling instability.

[0114] Specifically, the characteristic value information of the power system under multiple frequency bands is quantized into a unified feature vector, which is then input into the decision tree CART algorithm for training along with the corresponding instability mode labels (power angle instability, voltage instability, frequency instability, broadband oscillation, coupling instability).

[0115] The training process of the decision tree uses recursive partitioning optimization. Let the training sample set be:

[0116] (1.13)

[0117] in, For the first The feature vector of a sample, whose components are derived from the physical statistical indices of the feature values:

[0118] (1.14)

[0119] These components reflect the stability characteristics of the power system at different time scales: Describe the overall damping distribution. Reflects the overall stability margin, and Characterizing broadband mode energy diffusion characteristics, This measures the degree of oscillatory aggregation. Each sample's label... The corresponding stability type of the system, such as stable, power angle instability, voltage instability, frequency instability, etc.

[0120] The CART decision tree algorithm starts from the root node and selects the optimal feature. and splitting threshold The sample set is divided into two parts:

[0121] (1.15)

[0122] The optimal partition is obtained by minimizing the weighted impurity:

[0123] (1.16)

[0124] in, The Gini coefficient can be used. A commonly used definition of the Gini coefficient is:

[0125] (1.17)

[0126] This partitioning process is performed recursively in the spectral feature space, meaning the model continuously searches for feature indicators and thresholds that can most effectively distinguish instability patterns. For example, when partitioning features... At that time, the decision tree model is actually comparing the modulus distribution of the dominant modes of the system, thereby capturing the divergence trend of the power angle; when the segmentation features are or When this occurs, it corresponds to identifying the dynamic characteristics of wideband oscillation or mode coupling.

[0127] The splitting stops when the impurity or sample size of all leaf nodes falls below a set threshold, and the tree model construction is complete. Each leaf node outputs the class probability:

[0128] (1.18)

[0129] Its highest probability corresponds to the current stable state category of the system, that is, the determined transient instability state.

[0130] Therefore, the resulting decision tree can be viewed as a nonlinear function that statistically maps eigenvalues ​​to a stable form:

[0131] (1.19)

[0132] The path from the root node to the leaf node constitutes a complete discrimination rule, which is a combination of several logical judgments:

[0133] (1.20)

[0134] The splitting stops when the impurity or sample size of all leaf nodes falls below a set threshold, and the tree model construction is complete. The output class probability of each leaf node is shown in formula (1.18).

[0135] This form means that the model can express the instability mechanism in a "condition-conclusion" manner: when specific characteristics of the power system satisfy certain numerical relationships, it can be classified into the corresponding instability category. In other words, each leaf node represents a typical instability mode, and the path leading to it reveals the triggering conditions of that mode. For example, if the minimum damping ratio in the low-frequency band... And the maximum real part in the mid-frequency band The system can be identified as having power angle instability dominated by mid-frequency dynamics.

[0136] The advantage of this invention lies in its ability to interpretably model complex nonlinear dynamic processes using a concise algorithm. It does not rely on complex black-box models or manually set thresholds, but rather guides the algorithm to automatically learn instability mechanisms through physical characteristics. Therefore, it not only outputs instability morphology conclusions with engineering physical significance but also possesses a clear and traceable decision tree logic, providing a technical approach that combines theoretical rigor with engineering feasibility for identifying the dominant stable behavior of a system.

[0137] In specific implementation, the example of this invention uses a DC feed-in system with a high proportion of new energy output built by the China Electric Power Research Institute, as shown in Tables 1 and 2. The stability of the system is judged under two scenarios: an ideal situation with no noise and a scenario with 40% noise added. Six results are obtained: stable / frequency unstable / power angle unstable / coupling unstable / large disturbance oscillation state. The accuracy of judgment is compared with that of four methods: DNN (deep neural network), MMOE (multi-expert hybrid model), PINN (physical information neural network), and Neural-Koopman (this invention). The Neural-Koopman method proposed in this invention has the highest accuracy.

[0138] Table 1. Accuracy of different algorithms under noise-free / ideal conditions

[0139]

[0140] Table 2. Accuracy of different algorithms under 40% noise conditions

[0141]

[0142] Example 2

[0143] like Figure 3 As shown, the difference between this embodiment and Embodiment 1 is that this embodiment provides a power system stability pattern identification system based on neural frequency division Koopman, which corresponds one-to-one with the power system stability pattern identification method based on neural frequency division Koopman in Embodiment 1; the system includes:

[0144] The first building unit is used to construct the electric Koopman operator based on the Koopman operator theory and a neural network.

[0145] The second building unit is used to build a frequency division Koopman operator model based on the electric Koopman operator;

[0146] The weighted feature matrix forming unit is used to learn the weights of each frequency band based on the frequency division Koopman operator model and introduce a frequency domain attention mechanism to form a weighted feature matrix.

[0147] The first discrimination unit is used to extract eigenvalues ​​from the weighted feature matrix to obtain eigenvalues; and to determine the stability of the power system based on the eigenvalues; the stability of the power system includes transient stability, transient instability and critical stability;

[0148] The second discrimination unit is used to further discriminate the transient instability mode of the power system based on the feature value and the decision tree when the power system stability is transient instability.

[0149] The execution process of each unit can be carried out according to the steps of the power system stable mode identification method based on neural frequency division Koopman in Example 1, and will not be described in detail in this example.

[0150] Meanwhile, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-mentioned method for identifying the stable mode of a power system based on neural frequency division Koopman.

[0151] Meanwhile, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described method for identifying the stable state of a power system based on neural frequency division Koopman.

[0152] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0153] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0154] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0155] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0156] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for identifying the stable state of a power system based on neural frequency division Koopman, characterized in that, The method includes: Based on the Koopman operator theory, an electric Koopman operator is constructed using a neural network. Based on the described electric Koopman operator, a frequency division Koopman operator model is constructed; Based on the frequency division Koupman operator model, a frequency domain attention mechanism is introduced to learn the weights of each frequency band, forming a weighted feature matrix; The weighted feature matrix is ​​subjected to eigenvalue extraction to obtain eigenvalues; and the stability of the power system is determined based on the eigenvalues; the power system stability includes transient stability, transient instability and critical stability; When the power system stability is transiently unstable, the transient instability mode of the power system is further determined based on the aforementioned feature values ​​and a decision tree.

2. The power system stability pattern identification method based on neural frequency division Koopman as described in claim 1, characterized in that, Based on the Koopman operator theory, an electric Koopman operator is constructed using neural networks, including: For any power system, when observed using discrete measurements, the power system can be summarized as a discrete-time nonlinear dynamic system: ,in, It is the power system state vector at time t. Let be the power system state vector at time t+1. It is a nonlinear function describing the evolution of a power system; Based on the aforementioned nonlinear dynamic system, the Koopman operator is expressed using a neural network to obtain a discrete expression: K is the Koopman operator. For observation functions; The discrete expression is reconstructed to obtain the reconstructed equivalent expression: , For finite-dimensional embedding functions.

3. The power system stability pattern identification method based on neural frequency division Koopman as described in claim 1, characterized in that, Based on the described electric Koopman operator, a frequency division Koopman operator model is constructed, including: The physical state at time t is based on the encoder network. Mapped to a Koopman embedding vector; Based on the Koopman embedding vector, an embedding state sequence window of length L is constructed to form a mapping sequence; The mapped sequence is transformed by discrete Fourier transform to obtain component signals; Based on the component signals, the frequency range is divided into M non-overlapping frequency bands; and the inverse discrete Fourier transform is used to perform an inverse transform on each frequency band to obtain the sub-embedding sequence of the frequency band in the time domain. Based on the sub-embedding sequence, within each frequency band subspace, a one-step linear deduction is performed on the filtered component signal based on the frequency band-specific linear dynamics matrix to obtain the predicted sub-state of the next time step for that frequency band. All derived sub-states will be mapped back to the linear time domain through inverse Fourier transform, and then the system state in the original nonlinear space will be obtained through inverse Koopman observation transform, i.e., the frequency-division Koopman operator model.

4. The power system stability pattern identification method based on neural frequency division Koopman as described in claim 3, characterized in that, The expression for the frequency division Koupman operator model is: ； In the formula, Let be the power system state vector at time t+1. Let be the inverse transform function of the Koopman observation. For frequency band, For the frequency band sub-embedded sequence in the time domain, It corresponds to the digital frequency; In the frequency division Koupman operator model, each frequency band Configure a linear dynamics matrix The dynamic matrix It is consistent with the linear matrix in the original neural Koopman network.

5. The power system stability pattern identification method based on neural frequency division Koopman as described in claim 1, characterized in that, The expression for the weighted feature matrix is: ； In the formula, For the weighted characteristic matrix, For time t, the frequency band Attention score For each frequency band The configured linear dynamics matrix, where M is the number of frequency bands.

6. The power system stability pattern identification method based on neural frequency division Koopman as described in claim 1, characterized in that, Based on the aforementioned characteristic values, the stability of the power system is determined, including: If the magnitude of the eigenvalue is less than 1, then the stability of the power system under large disturbances is transiently stable. If the magnitude of the eigenvalue is greater than 1, then the stability of the power system under large disturbances is transient instability; If the modulus of the eigenvalue is equal to 1, then the stability of the power system under large disturbances is critically stable.

7. The power system stability pattern identification method based on neural frequency division Koopman as described in claim 1, characterized in that, Based on the aforementioned eigenvalues, the transient instability mode of the power system is further determined using a decision tree, including: Based on the characteristic values ​​of multiple frequency bands, characteristic indices are constructed; the characteristic indices include the most negative damping ratio, the frequency corresponding to the most negative damping, the maximum real part, the average damping, and the damping distribution dispersion for each frequency band. The feature values ​​of the aforementioned feature indicators are input into a pre-constructed decision tree, and the transient instability modes of the power system are output. The transient instability modes include power angle instability, voltage instability, frequency instability, broadband oscillation, and coupling instability.

8. A power system stability pattern identification system based on neural frequency division Koopman, characterized in that, The system includes: The first building unit is used to construct the electric Koopman operator based on the Koopman operator theory and a neural network. The second construction unit is used to construct a frequency division Koopman operator model based on the electric Koopman operator; The weighted feature matrix forming unit is used to learn the weights of each frequency band based on the frequency division Koopman operator model by introducing a frequency domain attention mechanism, and to form a weighted feature matrix. The first discrimination unit is used to extract eigenvalues ​​from the weighted feature matrix to obtain eigenvalues; and to discriminate the stability of the power system based on the eigenvalues; the power system stability includes transient stability, transient instability and critical stability; The second discrimination unit is used to further discriminate the transient instability mode of the power system based on the feature value and a decision tree when the power system stability is transient instability.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the power system stability pattern identification method based on neural frequency division Koopman as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the power system stability pattern identification method based on neural frequency division Koopman as described in any one of claims 1 to 7.

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