A method for identifying low-frequency oscillation modes in power systems based on MAK-Net
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-17
- Publication Date
- 2026-08-14
AI Technical Summary
这些方法通常依赖于较长的振荡信号序列，并且对噪声较为敏感，在复杂电网环境下难以满足实时辨识的需求
[0014]（1）、本发明针对电力系统低频振荡模态快速识别问题，构建了一种融合MinGRU、自注意力机制和KAN网络的MAK-Net深度学习模型，实现了对电力系统相对功角振荡序列特征的高效提取，提高了低频振荡频率和阻尼比的识别精度。
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Figure CN122577045A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of power technology, and more specifically, relates to a method for identifying low-frequency oscillation modes in power systems based on MAK-Net. Background Technology
[0002] With the development of modern power systems, the structure and operation of power grids have become more complex, making them more susceptible to low-frequency oscillations after disturbances. Low-frequency oscillations typically refer to electromechanical oscillations with frequencies between 0.1Hz and 2.5Hz, primarily manifested as periodic fluctuations in the generator power angle. Insufficient oscillation damping or excessively long oscillation duration can severely impact the safe and stable operation of the power system, potentially leading to large-scale power outages. Therefore, rapidly and accurately identifying the oscillation modes of low-frequency oscillations in power systems is crucial for ensuring stable grid operation. Currently, low-frequency oscillation mode identification methods mainly include those based on time-domain signal processing, frequency-domain analysis, and physical models, such as the Prony method, ESPRIT method, and ARMA model. These methods typically rely on long oscillation signal sequences and are sensitive to noise, making them unsuitable for real-time identification in complex power grid environments.
[0003] In recent years, with the development of deep learning technology, researchers have begun to try to use neural network models to learn feature patterns from a large amount of historical oscillation data, thereby achieving intelligent identification of low-frequency oscillation mode parameters. For example, the paper "Muhammed, AO, Isbeih, YJ, Moursi, MSE, & Hosani, KHA (2024). Deep Learning-Based Models for Predicting Poorly Damped Low-Frequency Modes of Oscillations. IEEE Transactions on Power Systems, 39(2), 3257–3270" uses and compares three different model architectures: stacking LSTM, CNN-LSTM, and Conv-LSTM to achieve online identification of oscillation modes. The paper "Zhang, C., Xu, Z., Zhang, K., Wu, Y., Liu, Q., Wei, J., & Ye, S.(2021). Long short-term memory-based robust and qualitative modal feature identification of non-stationary low-frequency oscillation signals in power systems. IET Renewable Power Generation, 16(7), 1368–1379" proposes a low-frequency oscillation mode identification method based on LSTM. It adopts a classification approach, dividing continuous values into small intervals and obtaining the intervals of modal parameters through classification. This method has good online identification capabilities.
[0004] Low-frequency oscillations are often a contributing factor to stability problems in large power grids. Accurate and rapid identification of the dominant oscillation modes is beneficial for staff to perceive and make decisions regarding the stability of the power grid in real time. Therefore, in the current era of rapid development of artificial intelligence, there is a need for a low-frequency oscillation mode identification method with higher computational efficiency and stronger feature representation capabilities to achieve rapid identification and accurate analysis of low-frequency oscillation modes in power systems. Summary of the Invention
[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for identifying low-frequency oscillation modes in power systems based on MAK-Net. By constructing and fusing a deep learning model with MinGRU, self-attention mechanism and KAN layer, a high-precision online identification of the low-frequency oscillation frequency and damping ratio of power systems can be achieved.
[0006] To achieve the above-mentioned objectives, this invention provides a method for identifying low-frequency oscillation modes in power systems based on MAK-Net, characterized by comprising the following steps:
[0007] (1) Acquisition and preprocessing of low-frequency oscillation data in power systems;
[0008] (2) Construct the MAK-Net model;
[0009] (3) Train the MAK-Net model using the preprocessed low-frequency oscillation data;
[0010] (4) Use the trained MAK-Net model to predict the generator’s frequency and damping ratio at the current moment to complete the identification of low-frequency oscillation modes of the power system.
[0011] The objective of this invention is achieved as follows:
[0012] This invention presents a low-frequency oscillation mode identification method for power systems based on MAK-Net. Based on the characteristics of relative power angle oscillation data in power systems, oscillation mode parameter extraction methods, and deep learning model structures, an oscillation mode identification model is constructed with the goal of accurately identifying the dominant low-frequency oscillation mode parameters. A MinGRU-Attention-KAN (MAK-Net) deep learning network is used to achieve parallel extraction and nonlinear mapping of oscillation characteristics from power angle time-series data, thereby enabling rapid prediction of oscillation frequency and damping ratio parameters. This identification model is then integrated into the online monitoring framework of power systems, resulting in an intelligent identification method suitable for real-time identification of low-frequency oscillation modes in power systems.
[0013] Meanwhile, the MAK-Net-based low-frequency oscillation mode identification method for power systems of this invention also has the following beneficial effects:
[0014] (1) This invention addresses the problem of rapid identification of low-frequency oscillation modes in power systems by constructing a MAK-Net deep learning model that integrates MinGRU, self-attention mechanism and KAN network. This model achieves efficient extraction of the characteristics of the relative power angle oscillation sequence of power systems and improves the identification accuracy of low-frequency oscillation frequency and damping ratio.
[0015] (2) By introducing the MinGRU structure, this invention realizes parallel computation of time series features, avoiding the problem of low computational efficiency caused by the reliance on backpropagation of time in traditional recurrent neural networks, thereby significantly improving the computational speed and real-time performance of oscillation mode recognition.
[0016] (3) The present invention can effectively identify oscillation mode parameters under relatively short oscillation time series conditions, and can complete mode identification without waiting for the oscillation process to completely end, thereby improving the real-time performance of power system oscillation monitoring and control. Attached Figure Description
[0017] Figure 1 This is a schematic diagram of the IEEE-39 node system architecture used in the simulation;
[0018] Figure 2 This is a flowchart of the low-frequency oscillation mode identification method for power systems based on MAK-Net according to the present invention;
[0019] Figure 3 This is a schematic diagram of the MAK-Net model structure;
[0020] Figure 4 This is a thermal comparison diagram of the errors of the present invention and other methods;
[0021] Figure 5 This is a comparison chart of the convergence speed and stability of the loss function curves of the present invention and other methods; Detailed Implementation
[0022] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.
[0023] Example
[0024] For ease of description, the relevant technical terms appearing in the specific implementation method will be explained first:
[0025] ARMA (Auto-Regressive Moving Average): An autoregressive moving average model;
[0026] ESPIRIT (Estimation of Signal Parameters via Rotational Invariance Techniques): A signal parameter estimation method based on rotational invariance.
[0027] LSTM (Long Short-Term Memory): Long Short-Term Memory network;
[0028] CNN-LSTM (Convolutional Neural Network - Long Short-Term Memory): A convolutional neural network with long short-term memory.
[0029] Conv-LSTM (Convolutional Long Short-Term Memory): A convolutional long short-term memory network;
[0030] KAN (Kolmogorov-Arnold Networks): Kolmogorov-Arnold Networks;
[0031] MAK-Net (minGRU-Attention-KAN Network): Minimum Gated Recurrent Unit-Kolmogorov-Arnold Network based on attention mechanism;
[0032] In this embodiment, Figure 1 This is a schematic diagram of the IEEE-39 node system architecture used in the simulation. (For example...) Figure 1 As shown, the IEEE 39-node power system mainly includes: 10 generators, 39 nodes, transmission lines, and system load nodes.
[0033] Each generator delivers electrical energy to the system load nodes through the transmission network, collectively maintaining the power balance of the power system. When the system is disturbed (such as by a three-phase short-circuit fault or line disconnection), electromechanical oscillations occur between the generators, causing the relative power angle of the generators to change periodically over time. By collecting relative power angle oscillation data at each generator node, time-series signals of low-frequency oscillations in the power system can be obtained. This oscillation data can then be used to construct a low-frequency oscillation mode identification dataset, providing fundamental data support for the subsequent training of the MAK-Net model and the identification of oscillation mode parameters.
[0034] Below we combine Figure 1 This invention provides a detailed description of a low-frequency oscillation mode identification method for power systems based on MAK-Net, such as... Figure 2 As shown, it includes the following steps:
[0035] (1) Acquisition and preprocessing of low-frequency oscillation data in power systems;
[0036] (1.1) Collect the relative power angle data of each generator at different times, and record the result. A generator in The relative work angle data collected at each moment is , , Where m is the number of generators, This is the time when sampling ends;
[0037] In this embodiment, a specific scenario is constructed in the PSASP power system simulation platform using an IEEE 39-bus system, with the following conditions: a short-circuit fault occurs between the 3rd and 4th nodes of phases A and B, with a fault duration of 0.2 seconds. The power angle curve during the oscillation process is extracted within a 15-second time window, with a sampling frequency of 10 Hz. Subsequently, load parameters are adjusted, and a 10% fluctuation threshold is applied to simulate various operating conditions under different loads, generating samples for deep learning methods.
[0038] (1.2) To eliminate the interference of the initial power angle offset on subsequent analysis, we use the power angle of each generator at the initial moment as the benchmark to obtain the power angle deviation relative to the initial state, unify the initial benchmark of different units, and highlight the dynamic change process of the power angle. We perform benchmarking processing on the relative power angle data of each generator:
[0039] ;
[0040] By subtracting the initial power angle value at the moment of fault onset, the initial deviation of different generators is eliminated, the oscillation characteristics of the power angle sequence are highlighted, the difference in initial value is avoided from masking the oscillation law, and the foundation is laid for subsequent normalization processing.
[0041] (1.3) For benchmarked data Normalization is performed:
[0042] ;
[0043] In this embodiment, the data is mapped to the [0,1] interval through normalization to avoid model training imbalance caused by numerical differences and improve the model convergence speed.
[0044] (1.4) The normalized power angle data is decomposed using the Prony method. Then, calculate the frequency and damping ratio of each oscillation mode;
[0045] ;
[0046] in, For the first The amplitude of the order, The attenuation rate, Angular frequency, Let n be the phase and n be the oscillation mode order. Prony decomposition breaks down the complex power angle sequence into multi-order exponentially decaying sine curves. Based on this, the commonly used oscillation frequency and damping ratio in engineering are calculated respectively. The two together constitute the supervised learning label of the model, ensuring that the model learns the prediction law of the two core oscillation parameters.
[0047] (2) Construct the MAK-Net model;
[0048] The MAK-Net model includes a temporal feature extraction module, a multi-head self-attention module, and a KAN output module;
[0049] The time-series feature extraction module MinGRU consists of an initial hidden layer and three cascaded gating units. The initial hidden layer is constructed using an all-zero matrix. The three gating units have the same structure, each consisting of two linear transformation layers, used to generate gating parameters and candidate states, respectively. Each gating unit completes state recursion through a parallel scanning algorithm and combines a custom activation function to complete the step-by-step extraction of time-series features. MinGRU adopts a three-layer stacked structure to improve parallel computing capabilities, adapt to the real-time requirements of online identification, and efficiently extract local features of the power angle sequence.
[0050] Each gating unit contains two branches: gating calculation and state update. The gating calculation branch generates gating parameters through linear transformation, while the state update branch generates candidate states through linear transformation and a custom activation function. The outputs of the two branches are then scanned and recursively processed in parallel to obtain the temporal features of the current level and passed to the next level gating unit.
[0051] The multi-head self-attention module is located after the temporal feature extraction module. It consists of a multi-head self-attention layer, which performs global correlation modeling on the extracted temporal features and fuses the attention output with the original temporal features through residual connections to enhance the representation of key features.
[0052] The KAN output module consists of a KAN linear layer, which takes the features of the last time step after temporal feature extraction and attention fusion as input, and outputs the target prediction value through the nonlinear mapping of the KAN network to complete the temporal sequence regression prediction.
[0053] (3) Train the MAK-Net model;
[0054] (3.1) Place the generator in Normalized power angle data at time As the input to the MAK-Net model, denoted as ;
[0055] (3.2) will Input is fed into the time series feature extraction module for calculation. Hidden state of time :
[0056] ;
[0057] in, , These are the weight matrix and bias term of the update gate, respectively. The sigmoid activation function is used. , These are the weight matrix and bias term of the candidate hidden state, respectively. It is the hyperbolic tangent activation function;
[0058] (3.3) Normalize the power angle data sequence of any generator at different times. These are sequentially used as inputs to the MAK-Net model to obtain the hidden state sequence. ;
[0059] (3.4) Hidden state sequence As input to the multi-head self-attention module, the attention feature sequence is obtained through attention calculation. , This represents the attentional features after weighted fusion using the attention mechanism at time t;
[0060] (3.5) Attention characteristics at each time step With the original hidden state h t Perform residual connections to obtain fused features. :
[0061] ;
[0062] in, This represents the residual connection operation; it connects the attention output with the MinGRU hidden state residual to avoid gradient vanishing, normalizes the feature distribution of the layer, improves the model convergence speed, and provides high-quality feature input for subsequent nonlinear mapping.
[0063] (3.6) The last one Fusion characteristics at each moment As a global feature, it is denoted as Then, global features Input to the KAN output module for nonlinear mapping:
[0064] ;
[0065] Where p is the index of the B-spline basis function inside the KAN. The maximum possible value for the sequence number. and For learnable B-spline coefficients, For d-order B-spline basis functions, and These are learnable node vectors; and , and These are the learnable linear projection matrix and bias term during two-layer spline transformation, respectively, which perform linear mapping on the features after the two-layer spline transformation to enhance the feature representation capability.
[0066] KAN uses learnable B-spline basis functions as activation functions, has strong nonlinear mapping capabilities, and can accurately fit the complex relationship between features and oscillation parameters.
[0067] (3.7) Y is processed by the KAN linear layer in the KAN output module. KAN By applying different linear mappings, the k-th modal frequency and damping ratio of the i-th generator are obtained.
[0068] ;
[0069] in, and The output branch weights for each mode prediction of the generator are given. and For bias;
[0070] (3.8) Calculate the loss function value after this round of training. :
[0071] ;
[0072] Where m is the total number of generators in the dataset, and n is the total number of dominant oscillation modes extracted from each generator; and These are the true frequency and true damping ratio of the k-th dominant mode of the i-th generator calculated using the Prony method; and These are the predicted frequency and predicted damping ratio of the k-th dominant mode of the i-th generator by the MAK-Net model, respectively. and These are the weighting coefficients for the total frequency loss term and the damping ratio loss term, respectively, used to balance the training priorities of the two tasks; The L2 regularization coefficient is... The L2 norm squared is used to suppress overfitting and improve the generalization ability of the model for all learnable parameters W.
[0073] (3.9) Based on the loss function value The model parameters are updated using the backpropagation algorithm to minimize the loss function, and the next round of model training is performed until the MAK-Net model converges, resulting in the trained MAK-Net model.
[0074] (4) Collect the first A generator in The relative work angle data at time is Preprocessing is performed according to steps (1.2) to (1.3), and then the result is input into the trained MAK-Net model to predict the first... A generator in By determining the frequency and damping ratio at each moment, the mode identification of low-frequency oscillations in the power system driven by data was completed.
[0075] The results of low-frequency oscillation mode identification in power systems using the proposed method are presented below:
[0076] First, nine sets of original relative power angle curves of the IEEE 39-bus system under the perturbation described in (1.1) extracted using PSASP simulation were used as input, and the dominant mode of the system was used as the overall training label. An error heatmap was used to compare the performance of the proposed method with other methods when learning the same oscillatory feature set. The color of each square represents the error between the identification result of the sampled data and the true mode. For example... Figure 4 As shown, cool colors indicate smaller errors, while warm colors indicate larger errors.
[0077] from Figure 4 As can be seen, the proposed method achieves the standard of the original time-propagating LSTM, and even surpasses it in accuracy, outperforming the simplified gated GRU algorithm. The Transformer method also exhibits significant errors because its attention mechanism focuses more on global information of oscillatory features, lacking the extraction of local features. BPNN performs the worst because its simple linear layers combined with activation functions struggle to effectively learn complex oscillatory features. Furthermore, the proposed method is slightly more accurate than the method using minLSTM.
[0078] Using mean squared error (MSE) as the loss function, the loss function curves of the proposed method and the comparison method on the test set are plotted, and the convergence speed and stability are compared.
[0079] from Figure 5As can be seen, when using other methods to learn noisy signals, the loss curves of these methods all exhibit instability, which is well addressed in the proposed method. When dealing with more complex time series, the Transformer method converges faster in the early stages of training due to its global information extraction characteristics, but it exhibits instability in the subsequent training process; while the LSTM and GRU methods, due to their time processing characteristics, although the loss decreases more slowly in the early stages, can ultimately achieve lower loss values than the Transformer. The proposed method, due to its parallel computing advantages and the use of RNN as its foundation, has both the advantages of fast convergence and low loss, exhibiting the best performance in both accuracy and real-time performance.
[0080] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.
Claims
1. A method for identifying low-frequency oscillation modes in power systems based on MAK-Net, characterized in that, Includes the following steps: (1) Acquisition and preprocessing of low-frequency oscillation data in power systems; (1.1) Collect the relative power angle data of each generator at different times, and record the result. A generator in The relative work angle data collected at each moment is , , Where m is the number of generators, This is the time when sampling ends; (1.2) The relative power angle data of each generator is standardized: ； (1.3) For benchmarked data Normalization is performed: ； (1.4) The normalized power angle data is decomposed using the Prony method. Then, calculate the frequency and damping ratio of each oscillation mode; ； in, For the first The amplitude of the order, The attenuation rate, Angular frequency, Let n be the phase and n be the order of the oscillation mode; (2) Construct the MAK-Net model; The MAK-Net model includes a temporal feature extraction module, a multi-head self-attention module, and a KAN output module; The temporal feature extraction module consists of an initial hidden layer and three cascaded gating units. The initial hidden layer is constructed using an all-zero matrix. The three gating units have the same structure, each consisting of two linear transformation layers, which are used to generate gating parameters and candidate states, respectively. Each gating unit completes state recursion through a parallel scanning algorithm and combines a custom activation function to complete the stepwise extraction of temporal features. Each gating unit contains two branches: gating calculation and state update. The gating calculation branch generates gating parameters through linear transformation, while the state update branch generates candidate states through linear transformation and a custom activation function. The outputs of the two branches are then scanned and recursively processed in parallel to obtain the temporal features of the current level and passed to the next level gating unit. The multi-head self-attention module is located after the temporal feature extraction module. It consists of a multi-head self-attention layer, which performs global correlation modeling on the extracted temporal features and fuses the attention output with the original temporal features through residual connections to enhance the representation of key features. The KAN output module consists of a KAN linear layer, which takes the features of the last time step after temporal feature extraction and attention fusion as input, and outputs the target prediction value through the nonlinear mapping of the KAN network to complete the temporal sequence regression prediction. (3) Train the MAK-Net model; (3.1) Place the generator in Normalized power angle data at time As the input to the MAK-Net model, denoted as ; (3.2) will Input is fed into the time series feature extraction module for calculation. Hidden state of time : ； in, , These are the weight matrix and bias term of the update gate, respectively. The sigmoid activation function is used. , These are the weight matrix and bias term of the candidate hidden state, respectively. It is the hyperbolic tangent activation function; (3.3) Normalize the power angle data sequence of any generator at different times. These are sequentially used as inputs to the MAK-Net model to obtain the hidden state sequence. ; (3.4) Hidden state sequence As input to the multi-head self-attention module, the attention feature sequence is obtained through attention calculation. , This represents the attentional features after weighted fusion using the attention mechanism at time t; (3.5) Attention characteristics at each time step With the original hidden state h t Perform residual connections to obtain fused features. : ； in, Indicates a residual join operation; (3.6) The last one Fusion characteristics at each moment As a global feature, it is denoted as Then, global features Input to the KAN output module for nonlinear mapping: ； Where p is the index of the B-spline basis function inside KAN. The maximum possible value for the sequence number. and For learnable B-spline coefficients, For d-order B-spline basis functions, and These are learnable node vectors; and , and These are the learnable linear projection matrix and bias term during two-layer spline transformation, respectively. (3.7) Y is processed by the KAN linear layer in the KAN output module. KAN By applying different linear mappings, the k-th modal frequency and damping ratio of the i-th generator are obtained. ； in, and The output branch weights for each mode prediction of the generator are given. and For bias; (3.8) Calculate the loss function value after this round of training. : ； Where m is the total number of generators in the dataset, and n is the total number of dominant oscillation modes extracted from each generator; and These are the true frequency and true damping ratio of the k-th dominant mode of the i-th generator calculated using the Prony method; and These are the predicted frequency and predicted damping ratio of the k-th dominant mode of the i-th generator by the MAK-Net model, respectively. and These are the weighting coefficients for the total frequency loss term and the damping ratio loss term, respectively, used to balance the training priorities of the two tasks; The L2 regularization coefficient is... The L2 norm squared is used to suppress overfitting and improve the generalization ability of the model for all learnable parameters W. (3.9) Based on the loss function value The model parameters are updated using the backpropagation algorithm to minimize the loss function, and the next round of model training is performed until the MAK-Net model converges, resulting in the trained MAK-Net model. (4) Collect the first A generator in The relative work angle data at time is Preprocessing is performed according to steps (1.2) to (1.3), and then the result is input into the trained MAK-Net model to predict the first... A generator in The frequency and damping ratio at any given moment.