A method and apparatus for joint frequency-phase prediction of non-stationary signals in power systems

Abstract

The application relates to the technical field of power system intelligent sensing and signal processing, and relates to a power system non-stationary signal frequency-phase joint prediction method and device. The method comprises the following steps: generating training set data containing frequency offset and noise through a data expansion method based on parameter space traversal; constructing a multi-task neural network model; training the multi-task neural network model based on a physical constraint training strategy using the training set data; performing window division on a to-be-measured signal and inputting the signal into the trained multi-task neural network model to obtain predicted power signal frequency and phase; and outputting the instantaneous frequency and instantaneous phase prediction results after correcting the prediction results through Kalman filtering. The application realizes joint accurate estimation of fundamental frequency, instantaneous phase and harmonic components through a multi-task deep neural network model, and significantly improves the stability and time-frequency resolution capability in a strong harmonic environment.

Description

Technical Field

[0001] This application relates to the field of intelligent sensing and signal processing technology for power systems, and to a method and apparatus for joint frequency-phase prediction of non-stationary signals in power systems. Background Technology

[0002] Accurate estimation of non-stationary signals in power systems is crucial for ensuring stable grid operation. With the increasing proportion of renewable energy grid connection and the widespread application of power electronic equipment, the complexity of harmonic and interharmonic components in signals has increased significantly, making it difficult for traditional signal processing methods to meet the requirements of high-precision measurement.

[0003] Limitations of traditional signal processing methods

[0004] Fourier Transform and its variants: Methods based on Fourier Transform (such as STFT and FFT) can only extract global spectral features and cannot characterize time-varying frequency components; Windowed Fourier Transform (STFT), although improving resolution through time-domain segmentation, suffers from the inherent contradiction of "high time resolution but low frequency resolution with a narrow window". Wavelet Transform, although optimizing time-frequency resolution through variable window size, has high computational complexity, making it difficult to guarantee real-time performance in embedded systems.

[0005] Harmonic detection methods: Analog filter method is easily affected by device parameters, and it is difficult to separate the fundamental wave from the harmonics; Instantaneous reactive power method requires multiple coordinate transformations, and the tracking performance of low-pass filter is limited; Although neural network-based methods can improve accuracy, they rely on a large amount of labeled data and the model has insufficient generalization ability.

[0006] Challenges of Deep Learning in Power Systems

[0007] Data dependency problem: Existing deep learning models (such as CNN and RNN) require a large amount of labeled data for training, while the cost of labeling non-stationary signals in the power system is high and the data diversity is insufficient, which makes the model prone to overfitting.

[0008] Lack of physical constraints: Pure data-driven models are difficult to incorporate physical laws (such as energy conservation and harmonic characteristics), and are prone to producing non-physical estimation results under strong harmonic interference, resulting in insufficient stability.

[0009] Unresolved issues regarding the contradiction between time and frequency resolution

[0010] Traditional methods have bottlenecks in the correlation mapping of time-frequency domain characteristics, and cannot simultaneously capture high-frequency transient components and low-frequency slow-change components, resulting in limited analytical capabilities under complex working conditions.

[0011] Existing technologies either rely on fixed models that are difficult to adapt to non-stationary characteristics, or suffer from a lack of physical consistency due to data-driven approaches, or struggle to balance computational efficiency and accuracy. Therefore, there is an urgent need for a novel approach that integrates physical constraints with deep learning to address the challenges of data dependence, harmonic interference suppression, and the time-frequency resolution conflict.

[0012] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0013] To provide a basic understanding of some aspects of the disclosed embodiments, a brief summary is given below. This summary is not intended as a general commentary, nor is it intended to identify key / important components or describe the scope of protection of these embodiments, but rather as a prelude to the detailed description that follows.

[0014] This disclosure provides a method and apparatus for joint prediction of frequency and phase of non-stationary signals in power systems. It achieves joint and accurate estimation of fundamental frequency, instantaneous phase and harmonic components through a multi-task deep neural network model, which significantly improves stability and time-frequency analysis capability under strong harmonic environment; and provides a high-precision measurement basis for scenarios such as new energy grid connection control, power quality analysis, and fault detection.

[0015] In some embodiments, the method includes:

[0016] Training set data containing frequency offset and noise is generated by a data augmentation method based on parameter space traversal;

[0017] A multi-task neural network model is constructed, comprising, in sequence: a first convolutional layer, a frequency domain attention module, a second convolutional layer, a third convolutional layer, and a multi-task collaborative output module. The multi-task collaborative output module includes a frequency estimator, a phase estimator, and a harmonic estimator.

[0018] A multi-task neural network model is trained using training set data based on a physical constraint training strategy, which includes a multidimensional loss function, signal reconstruction loss, harmonic energy constraint, and adaptive gradient update strategy.

[0019] The signal to be tested is windowed and input into the trained multi-task neural network model to obtain the predicted power signal frequency and phase. The prediction results are then corrected by Kalman filtering and output as instantaneous frequency and instantaneous phase prediction results.

[0020] Preferably, the data processing method for the multi-task neural network model is as follows:

[0021] The first convolutional layer extracts basic temporal features from the preprocessed data;

[0022] Key frequency components are enhanced through the frequency domain attention mechanism of the frequency domain attention module to generate attention frequency domain features;

[0023] Through processing by the second and third convolutional layers, temporal and frequency domain features are fused in deep convolution and downsampling to form fused time-frequency features;

[0024] Based on the fused time-frequency characteristics, the frequency, phase, and harmonic estimates are synchronously output through a multi-task collaborative output module.

[0025] Preferably, the training set data is generated in the following specific way:

[0026] Non-uniform sampling is performed in the frequency range [45Hz, 55Hz], and the phase range [0, 2π] is discretized by phase angle segmentation to construct a frequency-phase parameter grid.

[0027] Generate an electrical signal containing the 3rd, 5th, 7th, and 11th harmonics superimposed with Gaussian white noise. The formula is as follows:

[0028] ,

[0029] in, For the fundamental frequency amplitude, The fundamental frequency, The initial phase of the fundamental wave, For the first Relative amplitude coefficient of subharmonics For random phase shift, For noise level, Indicates time, Indicates Gaussian white noise;

[0030] The generated power signal is slidably segmented according to a set window length and step size, and encoded into triples, with the encoding label being... , Indicates the end phase of the window. ;

[0031] Perform on frequency tags Normalized, phase label encoding is .

[0032] Preferably, the first convolutional layer sequentially includes a one-dimensional convolution, a batch normalization layer, and a SiLU activation function;

[0033] The second convolutional layer consists of a max pooling layer, a one-dimensional convolution, a batch normalization layer, and a SiLU activation function.

[0034] The third convolutional layer includes, in sequence, a max pooling layer, a one-dimensional convolution, a batch normalization layer, a SiLU activation function, and an adaptive average pooling layer;

[0035] The frequency domain attention mechanism is implemented as follows:

[0036] Execute three sets of convolutions in parallel:

[0037] Q-branch, 1D convolution generates the query matrix;

[0038] K-branch, 1D convolution generates the key matrix;

[0039] V-branch, 1D convolution generates value matrix;

[0040] After flattening Q and K, calculate the attention weight matrix, multiply it with V, and output the weighted frequency domain features.

[0041] Preferably, the frequency estimator uses a fully connected layer to map features to a hidden layer. After batch normalization and random deactivation regularization, it outputs normalized frequency parameters through a linear layer without bias. These frequency parameters are constrained to the (0,1) interval by a sigmoid activation function and then transformed back to the actual frequency values. :

[0042] ,

[0043] in, This is the frequency weight matrix. This is a time-frequency fusion feature vector;

[0044] The phase estimator performs feature compression on the time-frequency fusion feature vector through a fully connected layer and batch normalization, and applies L2 norm normalization to the compressed features:

[0045] ,

[0046] in, The phase weight matrix is... For L2 norm normalization operation, This is a normalized two-dimensional vector;

[0047] The final instantaneous phase angle estimate is calculated using inverse trigonometric functions. :

[0048] ;

[0049] The harmonic estimator is a four-dimensional output structure. After passing through a fully connected layer, batch normalization, and mild random deactivation regularization, the original harmonic amplitude coefficients are generated by a linear layer. These coefficients are then compressed to the (0,1) interval by Sigmoid activation and multiplied by the physical constraint upper limit of 0.05 to obtain the harmonic estimate. :

[0050]

[0051] in This is the harmonic weighting matrix.

[0052] Preferably, the multidimensional loss function is as follows:

[0053] ,

[0054] in, For frequency smoothing loss function, The frequency deviation loss function is... Let cosine be the phase error loss function. To reconstruct the mean squared error loss function, The harmonic energy constraint loss function;

[0055] The frequency smoothing loss The sensitivity of the fundamental frequency estimation is balanced using the Huber loss function, as detailed below:

[0056] ,

[0057] in, To estimate the deviation, For the smoothing threshold, This represents the number of samples in the current training batch. Indicates the first Frequency prediction value for each sample Indicates the first The true frequency value of each sample;

[0058] The frequency deviation loss function is as follows:

[0059] ,

[0060] The phase cosine error loss function is as follows:

[0061] ,

[0062] in, This is the phase prediction value. This is the true value of the phase;

[0063] The signal reconstruction loss is as follows:

[0064] ,

[0065] ,

[0066] in, Represents the mathematical expectation. This represents the reconstructed time-domain signal. For the normalized fundamental amplitude, This is the actual frequency value. This is the initial phase estimate. These are harmonic estimates;

[0067] The harmonic energy constraint is as follows:

[0068] .

[0069] The adaptive gradient update uses the AdamW optimization algorithm.

[0070] Preferably, the output of dynamic frequency and instantaneous phase prediction results after Kalman filtering specifically includes:

[0071] The frequency prediction result is input into the frequency tracking filter, which is a Kalman filter based on a second-order state-space model; the phase prediction result is input into the phase smoothing filter, which is constructed based on the Kalman smoothing filtering method of the phase difference state-space model.

[0072] A joint filtering strategy is used to achieve coordinated optimization of frequency and phase, and the joint filtering strategy employs Kalman filtering.

[0073] Preferably, the linear mapping of the frequency tracking filter is as follows:

[0074] ,

[0075] ,

[0076] in, For the frequency observation matrix, For frequency observation noise variance, For frequency observation noise, This represents the instantaneous value of the fundamental frequency at time k. Characterizing the rate of change of frequency, The sampling window interval, For frequency process noise, Here is the frequency process noise covariance matrix. Here is the state transition matrix. This is the state vector of the current frequency and its rate of change. This is the state vector representing the frequency and rate of change of the previous time step;

[0077] The linear mapping of the phase smoothing filter is as follows:

[0078] ,

[0079] ,

[0080] in, For the phase observation matrix, To observe the noise variance, For phase observation noise, This indicates the phase deviation between adjacent windows. Describe the rate of phase change. The sampling window interval, For phase process noise, The phase process noise covariance matrix is... Here is the state transition matrix. This is the state vector representing the current phase difference and its rate of change. The state vector represents the phase difference and its rate of change at the previous moment.

[0081] Preferably, the joint filtering strategy is as follows:

[0082] Frequency prediction value With the previous phase Combined, the current phase prediction is calculated through integration. :

[0083] ,

[0084] Perform nonlinear correction on the current phase prediction:

[0085] ,

[0086] in, This indicates the wrapToPi operation.

[0087] In some embodiments, the apparatus includes a processor and a memory storing program instructions, the processor being configured to execute the deep attention mechanism-based non-stationary signal frequency-phase joint estimation method when the program instructions are executed.

[0088] This disclosure provides a method and apparatus for joint frequency-phase prediction of non-stationary signals in a power system, which can achieve the following technical effects:

[0089] This invention achieves multi-dimensional technological breakthroughs in the field of dynamic signal processing in power systems. By integrating a frequency domain feature focusing mechanism with a deep learning architecture constrained by physical laws, it constructs an intelligent analysis system for non-stationary signals. Compared to traditional methods, its innovative advantages are mainly reflected in the following aspects:

[0090] At the dynamic signal feature extraction level, the frequency domain feature focusing mechanism introduced in this scheme can effectively capture key frequency components in the signal through an adaptive weight allocation strategy. This mechanism, combined with sliding window processing technology, achieves fine-grained tracking of rapidly fluctuating signals, resolving the inherent contradiction in time-frequency resolution of traditional global transform methods. Through multi-level feature interaction and nonlinear transformation, the system can autonomously establish a correlation mapping between the time-domain and frequency-domain characteristics of the signal, significantly improving its analytical capabilities for complex operating conditions.

[0091] To address the unique harmonic interference problem in power systems, this technical solution innovatively designs a harmonic energy constraint module. Based on the physical laws of electromagnetic transient processes, this module effectively suppresses non-physical harmonic interference on fundamental frequency estimation by dynamically adjusting the energy distribution ratio of harmonic components. This constraint mechanism not only enhances the system's stability under strong harmonic environments but also ensures that the output results conform to the inherent laws of the power system's dynamic response, providing a physically interpretable decision-making basis for subsequent control strategy formulation.

[0092] Regarding data-driven capabilities, this solution proposes an intelligent sampling strategy based on parameter space traversal. Through a combination of phase discretization and non-uniform frequency sampling, it achieves the physical law-guided construction of the training dataset. This method significantly improves the rationality of data sample distribution while ensuring data diversity, enabling the model to maintain excellent generalization performance even with limited training data, effectively solving the problem of traditional methods' dependence on massive labeled data.

[0093] In terms of system interpretability, this technology deeply embeds the core elements of transient equations into the learning process through joint optimization of the signal reconstruction loss function and harmonic energy constraints. This physics-guided machine learning paradigm not only ensures that the output results conform to the basic laws of power system dynamic equations, but also realizes an explicit correlation between the feature space and the physical parameter space. This provides a transparent decision-making basis for subsequent applications such as fault diagnosis and protection setting, effectively breaking through the engineering application bottleneck of traditional black-box models.

[0094] In terms of engineering deployability, this solution designs an output correction module based on Kalman filtering. By establishing a state-space model for frequency tracking and phase compensation, dynamic smooth optimization of the network output is achieved. This module employs a nonlinear constraint prediction-correction mechanism, effectively suppressing phase jump errors caused by window truncation and controlling the steady-state error of the frequency estimation results within the allowable range for engineering applications, thus providing reliable technical support for real-time monitoring systems.

[0095] The above general description and the description below are exemplary and illustrative only and are not intended to limit this application. Attached Figure Description

[0096] One or more embodiments are illustrated by way of example with reference to the accompanying drawings. These illustrations and drawings do not constitute a limitation on the embodiments. Elements having the same reference numerals in the drawings are shown as similar elements. The drawings are not to be scaled. And wherein:

[0097] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0098] Figure 2 A flowchart illustrating the overall architecture and data generation process of a joint frequency-phase estimation system for non-stationary power signals;

[0099] Figure 3 The graph shows the test results for the 50-45Hz frequency jump.

[0100] Figure 4 The graph shows the frequency error results of a 1-second long sequence signal test.

[0101] Figure 5 The graph shows the phase error results of a 1-second long sequence signal test.

[0102] Figure 6 Graph showing time consumption for single-window inference;

[0103] Figure 7 This is a schematic diagram of the device structure according to an embodiment of the present disclosure. Detailed Implementation

[0104] To provide a more detailed understanding of the features and technical content of the embodiments of this disclosure, the implementation of the embodiments of this disclosure will be described in detail below with reference to the accompanying drawings. The accompanying drawings are for illustrative purposes only and are not intended to limit the embodiments of this disclosure. In the following technical description, for ease of explanation, several details are used to provide a full understanding of the disclosed embodiments. However, one or more embodiments may still be implemented without these details. In other cases, well-known structures and devices may be simplified in their depiction to simplify the drawings.

[0105] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this disclosure are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this disclosure described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion.

[0106] Unless otherwise stated, the term "multiple" means two or more.

[0107] In this embodiment of the disclosure, the character " / " indicates that the objects before and after it are in an "or" relationship. For example, A / B means: A or B.

[0108] The term "and / or" describes an association between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or A and B.

[0109] The term "correspondence" can refer to an association or binding relationship. The correspondence between A and B means that there is an association or binding relationship between A and B.

[0110] Example 1

[0111] like Figures 1-2 As shown, a joint frequency-phase prediction method for non-stationary signals in power systems is proposed. This method generates a training dataset containing frequency offset and noise by augmenting the physical characteristics of the power signal. A multi-task neural network architecture with a frequency domain attention mechanism is designed to achieve joint decoupled estimation of the fundamental frequency, phase, and harmonics. An energy-constrained loss function is provided to ensure that the harmonic components analyzed by the model conform to actual physical laws. A dynamic noise injection and learning rate correction strategy is designed to enhance the robustness of the method under various complex noise environments.

[0112] Specifically, including:

[0113] S1: Generate training set data containing frequency offset and noise by using a data augmentation method based on parameter space traversal.

[0114] S2: Construct a multi-task neural network model, which includes, in sequence: a first convolutional layer, a frequency domain attention module, a second convolutional layer, a third convolutional layer, and a multi-task collaborative output module. The multi-task collaborative output module includes a frequency estimator, a phase estimator, and a harmonic estimator.

[0115] S3: Train a multi-task neural network model using training set data based on a physical constraint training strategy. The physical constraint training strategy includes a multidimensional loss function, signal reconstruction loss, harmonic energy constraint, and adaptive gradient update strategy.

[0116] S4: The signal to be tested is windowed and input into the trained multi-task neural network model to obtain the predicted power signal frequency and phase. The prediction results are then corrected by Kalman filtering and output as instantaneous frequency and instantaneous phase prediction results.

[0117] As a refinement of the above embodiments, the specific method for generating the training set data is as follows:

[0118] S101: Construct a frequency-phase parameter grid by non-uniform sampling within the frequency range [45Hz, 55Hz] and by phase angle segmentation within the phase range [0, 2π].

[0119] S102: Generate higher harmonics (3rd, 5th, 7th, and 11th orders) for each set of parameters (amplitude according to...). The power signal is attenuated and superimposed with Gaussian white noise (σ=0.01);

[0120] Specifically, the power signal training set data is a crucial foundation for the accuracy of signal sensing in this method. To simulate the complex operating conditions of actual power grid signals, a data augmentation method based on parameter space traversal is designed, the mathematical description of which is as follows:

[0121] Generate a voltage signal containing harmonics:

[0122] ,

[0123] In the formula: For the fundamental frequency amplitude, The fundamental frequency, The initial phase of the fundamental wave, For the first Relative amplitude coefficient of subharmonics For random phase shift, noise level .

[0124] The fundamental frequency is set within the frequency range of [45Hz, 55Hz].

[0125] ,

[0126] The fundamental initial phase is set as follows:

[0127] ,

[0128] in, , The segmentation accuracy is divided into frequency and phase parameters, respectively.

[0129] S103: Divide the generated long-time domain signal into a sliding window with a window length of 64 and a step size of 1, extract the signal segment of each window, and calculate the end phase of the window. And encode the tags as triples: ,in .

[0130] S104: Write all window data and corresponding labels to data.memmap and labels.memmap respectively via memory mapping, and perform frequency label processing. Normalized, phase label encoding is This yields the preprocessed training dataset.

[0131] As a refinement of the above embodiments, the network structure of the multi-task neural network model is as follows: Figure 2 As shown, the core components include a frequency domain attention module and a multi-task collaborative output module, and the specific principles are as follows:

[0132] S201: Extract basic temporal features from the preprocessed data through the first convolutional layer;

[0133] S202: Enhance key frequency components through the frequency domain attention mechanism of the frequency domain attention module to generate attention frequency domain features;

[0134] S203: Through the processing of the second and third convolutional layers, temporal and frequency domain features are fused in deep convolution and downsampling to form fused time-frequency features;

[0135] S204: Based on the fused time-frequency characteristics, the frequency, phase and harmonic estimates are synchronously output through the multi-task collaborative output module.

[0136] The first convolutional layer sequentially comprises a one-dimensional convolution, a batch normalization layer, and a SiLU activation function. The convolutional kernel has a width of 9 and the number of channels is mapped from 1 to 128 to extract the original temporal features, while the SiLU activation function enhances the nonlinear representation capability.

[0137] The second convolutional layer consists of a max pooling layer, a one-dimensional convolution, a batch normalization layer, and a SiLU activation function. The processing procedure is as follows:

[0138] The temporal attention features are input into MaxPool1d (kernel=2) for downsampling, halving the temporal length; a deeper level of frequency domain response is extracted through a second layer of one-dimensional convolution (in=128, out=256, kernel=5, pad=2), and BatchNorm1d and SiLU activation are performed in sequence.

[0139] The third convolutional layer sequentially includes a max pooling layer, a one-dimensional convolution, a batch normalization layer, a SiLU activation function, and an adaptive average pooling layer. The processing procedure is as follows:

[0140] The features are downsampled by MaxPool1d (kernel=2) to further reduce the temporal dimension; through the third layer of one-dimensional convolution (in=256, out=512, kernel=3, pad=1) and BatchNorm1d, the temporal dimension is finally fixed to 8 using AdaptiveAvgPool1d (output_size=8) to obtain a time-frequency feature vector of length 512×8.

[0141] Specifically, the frequency domain attention module is as follows:

[0142] To effectively suppress the impact of noise and harmonic interference on fundamental frequency and phase estimation, this module uses a frequency domain attention mechanism to dynamically reweight the input features in the frequency domain dimension. This enables the network to autonomously focus on the frequency components that contribute the most to the fundamental frequency and phase estimation tasks, while suppressing non-critical frequency band responses dominated by higher harmonics or noise.

[0143] The module takes as input the basic temporal feature tensor processed by one-dimensional convolution, batch normalization (BatchNorm1d), and SiLU activation function. (dimension is) Where B is the batch size. (where L is the number of input channels and L is the time sequence length). The core operation of this module is based on the query-key-value attention mechanism, implemented through three independent parallel convolutional paths:

[0144] ,

[0145] in, For query vector, For key vectors, For value vectors, Input the number of channels. Number of output channels It is the basic time-domain feature tensor.

[0146] In this embodiment, the three convolutions are as follows:

[0147] Q-branch: 1D convolution (in=128, out=16, kernel=3, pad=1) generates the query matrix;

[0148] K-branch: 1D convolution (in=128, out=16, kernel=3, pad=1) generates the key matrix;

[0149] V branch: 1D convolution (in=128, out=128, kernel=1) generates a value matrix.

[0150] The attention weight matrix is ​​obtained by multiplying the transpose of Q by the matrix product of K and then normalizing it using the Softmax function on the last dimension. This weight matrix accurately characterizes the relative importance of each frequency component at different time steps. Finally, the module output Attention is obtained by multiplying the calculated attention weight matrix by the value vector V.

[0151] ,

[0152] This module allows the fundamental frequency time-domain characteristics to be highlighted, while harmonic and noise interference can be suppressed. The module output will be passed to subsequent pooling layers and deeper convolutional structures for further time-frequency feature fusion.

[0153] Specifically, the multi-task collaborative output module is as follows:

[0154] This module constructs a parallelized task-specific estimator based on time-frequency fusion feature vectors. It synchronously generates accurate estimates of the fundamental frequency, instantaneous phase, and harmonic energy distribution through a heterogeneous mathematical transformation strategy. First, the high-dimensional feature tensor output by global average pooling is flattened into a 512×8-dimensional time-frequency fusion feature vector. Then, it is input into three independently designed estimators for decoupled computation: a frequency estimator, a phase estimator, and a harmonic estimator.

[0155] The following section details each estimator.

[0156] (1) Frequency estimator

[0157] The frequency estimator uses a fully connected layer to map features to hidden layers. After batch normalization (BatchNorm1d) and dropout regularization, a linear layer with no bias outputs a normalized frequency parameter. This value is constrained to the (0,1) interval by a sigmoid activation function and finally transformed back to the actual frequency value (45-55Hz).

[0158] ,

[0159] in The frequency weight matrix has random initial values ​​and is updated during training. This is the time-frequency fusion feature vector.

[0160] (2) Phase estimator

[0161] The phase estimator performs feature compression on the time-frequency fusion feature vector through a fully connected layer and batch normalization, outputting a two-dimensional vector. To satisfy the periodicity constraint of the phase parameter, L2 norm normalization is applied to the output:

[0162] ,

[0163] in, The phase weight matrix has random initial values ​​and is updated during training. L2 norm normalization operation: .

[0164] The two-dimensional vector after the above normalization process Based on this, the system calculates the final instantaneous phase angle estimate using inverse trigonometric functions. The vector has been constrained to the unit circle by L2 norm normalization, and its elements represent the sine and cosine components of the phase angle, satisfying the following conditions: The periodicity condition. To solve for the actual phase angle, the four-quadrant arctangent function atan2 is used for mapping, and its mathematical definition is:

[0165] ,

[0166] This function dynamically determines the quadrant of the phase angle based on the sign information of the sine and cosine components, thereby avoiding the numerical jump problem caused by the discontinuity of the angle.

[0167] (3) Harmonic estimator

[0168] The harmonic estimator is designed as a four-dimensional output structure (corresponding to the 3rd, 5th, 7th, and 11th harmonics). After passing through a fully connected layer, batch normalization, and mild dropout regularization, the original harmonic amplitude coefficients are generated by a linear layer. These coefficients are compressed to the (0,1) interval by sigmoid activation and then multiplied by the physical constraint upper limit of 0.05.

[0169] ,

[0170] in This is the harmonic weighting matrix.

[0171] In this embodiment, the estimator is designed as follows:

[0172] The frequency estimator consists of a fully connected layer of 512×8→512, BatchNorm1d, Dropout(0.3), and then fully connected to a 1D regression output.

[0173] The phase estimator consists of a fully connected layer of 512×8→256, BatchNorm1d, and then fully connected to a 2D output, with the output vector normalized to α2.

[0174] The harmonic estimator consists of a fully connected layer of 512×8→128, BatchNorm1d, Dropout(0.1), then fully connected to 4-dimensional arrays, and multiplied by 0.05 after passing through the Sigmoid output to obtain the energy ratio of each harmonic.

[0175] The three outputs are combined into the final output of the model, which can be used for subsequent loss calculation and online inference.

[0176] Specifically, the output correction module is as follows:

[0177] This module addresses the phase jump and frequency fluctuation issues caused by neural network windowing processing by designing a collaborative filtering optimization system. It achieves dynamic smoothing of the output and ensures physical plausibility through a state-space model. Its core structure includes a frequency tracking filter, a phase smoothing filter, and a joint filtering strategy, aiming to eliminate discrete truncation errors and improve real-time monitoring accuracy.

[0178] (1) Frequency tracking filter

[0179] This system designs a Kalman filter based on a second-order state-space model to dynamically track the instantaneous change process of the power signal's fundamental frequency.

[0180] Its core lies in constructing a joint state vector of frequency and its rate of change:

[0181] ,

[0182] in, This represents the instantaneous value of the fundamental frequency at time k. The frequency change rate is represented by T, which represents the transpose of the matrix. This meaning will be used throughout the following text.

[0183] This state model describes the dynamic evolution characteristics of the system through discrete-time state transition equations:

[0184] ,

[0185] in, The sampling window interval, For frequency process noise, Let be the frequency process noise covariance matrix.

[0186] The observation process employs a linear relationship:

[0187] ,

[0188] in, For the frequency observation matrix, This represents the variance of frequency observation noise.

[0189] (2) Phase smoothing filter

[0190] The phase smoothing filter is constructed based on the Kalman smoothing filtering method of the phase difference state-space model. This filter uses the phase difference and its rate of change as the core state vector.

[0191] ,

[0192] in, This indicates the phase deviation between adjacent windows. Describe the rate of phase change.

[0193] Establish the discrete-time state transition equation:

[0194] ,

[0195] in, The sampling window interval, For phase process noise, Let be the phase process noise covariance matrix.

[0196] The observation model uses a linear mapping:

[0197] ,

[0198] in, For the phase observation matrix, To observe the noise variance.

[0199] (3) Joint filtering strategy

[0200] This strategy constructs a collaborative optimization structure based on a dual-channel state-space model, achieving joint correction of the network output through parallel independent frequency tracking filters and phase smoothing filters. This strategy achieves dynamic smoothing optimization of the network output through the state-space model, effectively suppressing phase jump errors and frequency fluctuations caused by window truncation. The process integrates the frequency tracking filter and the phase smoothing filter, constructs a second-order state-space model based on Kalman filtering theory, and ensures the rationality of the output results through nonlinear constraints, ultimately outputting optimized instantaneous frequency and phase values.

[0201] include:

[0202] Frequency prediction value With the previous phase Combined, the current phase prediction is calculated through integration. :

[0203] ,

[0204] This step simulates the continuous evolution of the signal phase, effectively bridging the phase discontinuities between discrete windows.

[0205] Perform nonlinear correction on the current phase prediction:

[0206] ,

[0207] in, This indicates the wrapToPi operation; the wrapToPi operation will take the input angle (in radians) beyond the specified range. Adjust the values ​​within the range to this interval to avoid distortion caused by boundary jumps.

[0208] As a refinement of the above embodiments, the physical constraint training strategy integrates fundamental knowledge of power system physical signals into the neural network training framework. It guides the model output to conform to the dynamic characteristics of actual circuits by constructing a multi-dimensional constraint mechanism.

[0209] The specific design includes four core strategies: multidimensional loss function, signal reconstruction loss, harmonic energy constraint, and adaptive gradient update.

[0210] (1) Multidimensional loss function

[0211] This strategy designs a composite loss function that integrates multi-dimensional constraints, coordinating core objectives such as frequency estimation accuracy, phase continuity, and the rationality of harmonic energy distribution through weighted adjustments. Its mathematical expression is:

[0212] ,

[0213] in, For frequency smoothing loss function, This is the frequency deviation loss function. Let cosine be the phase error loss function. To reconstruct the mean squared error loss function, This is the harmonic energy constraint loss function. The weights were determined through training experiments.

[0214] Specifically:

[0215] (101) Frequency smoothing loss The sensitivity of the fundamental frequency estimation balanced using the Huber loss function is defined as follows:

[0216] ,

[0217] in, To estimate the deviation, For the smoothing threshold, This represents the number of samples in the current training batch. This design employs a quadratic penalty to improve accuracy within the ±0.1Hz error range, and a linear penalty outside this range to enhance robustness against outliers.

[0218] (102) Frequency deviation penalty to suppress systematic measurement bias Statistical properties of constrained batch prediction frequencies:

[0219] ,

[0220] This loss effectively suppresses the overall measurement bias of the model across different frequency ranges, ensuring that the estimation results are unbiased.

[0221] (103) For the periodic characteristics of the phase parameter, phase cosine loss Solving the angle discontinuity problem using vector space similarity:

[0222] ,

[0223] in, and These are the predicted and actual phase values, respectively. This formula calculates the predicted phase vector. The negative value of the dot product with the real vector is physically equivalent to the complement of the cosine similarity, effectively avoiding the 2π periodic jump problem in angle calculation.

[0224] (2) Signal reconstruction loss

[0225] The core mechanism of this strategy is to reconstruct the loss function from the signal. The network output must conform to the physical fluctuation characteristics of power system signals. Specifically, the network needs to simultaneously generate the baseband frequency. Instantaneous phase and harmonic energy ratio The predicted values ​​are obtained, and the time-domain signal is reconstructed based on the basic components of the signal. The reconstruction process strictly follows the following physical model:

[0226] ,

[0227] in, This represents the reconstructed time-domain signal. This represents the normalized fundamental amplitude.

[0228] Reconstruction loss is defined as the predicted signal With input signal Mean square error:

[0229]

[0230] in, Represents the mathematical expectation. To reconstruct the mean squared error loss function.

[0231] (3) Harmonic energy constraint

[0232] To suppress anomalous amplitudes that may be generated by neural networks and violate harmonic attenuation laws, this strategy integrates two types of physical priors to construct an energy-constrained loss mechanism. :

[0233] Amplitude attenuation constraint: The energy of higher harmonics attenuates as the frequency increases, and their theoretical ratio satisfies the 1 / h relationship (that is, the ideal amplitude ratio of the 3rd, 5th, 7th and 11th harmonics is 1 / 3:1 / 5:1 / 7:1 / 11).

[0234] Total Harmonic Distortion (THD) Limitation: In practical systems, THD is typically below 5%, hence the constraint. .

[0235] The mathematical definition of the loss function is:

[0236] ,

[0237] The first term in the formula forces the harmonic amplitude distribution to conform to the 1 / h attenuation law, and the second term penalizes the excessive THD value through the ReLU function.

[0238] (4) Adaptive gradient update

[0239] The iterative update process of the model parameters employs the AdamW optimization algorithm, which reconstructs the weight decay mechanism based on Adaptive Moment Estimation (Adam): decoupling the regularization term from gradient calculation and directly applying it to the parameter update term, thereby improving the model's generalization ability. This optimization algorithm calculates the loss function... gradient with respect to network parameter θ And dynamically update the first moment of the gradient. and second moment The exponential moving average is used to adaptively adjust the update step size for different parameters. Its core iterative formula is as follows:

[0240] ,

[0241] in, and The decay rates of the first and second moments are controlled separately. This represents the current iteration step. For learning rate, This is a numerical stability constant used to avoid division by zero errors. (The last term in the formula...) Weight decay is achieved by decoupling the decay term from the learning rate and applying it directly to the parameters themselves rather than the gradient, which effectively reduces model complexity and improves the model's robustness to noise interference.

[0242] It should be noted that: the experimental results are as follows Figures 3-6 As shown, this method innovatively integrates deep learning with physical constraints, achieving a triple breakthrough in the field of non-stationary signal analysis in power systems through a frequency domain attention mechanism in conjunction with a harmonic energy constraint mechanism: First, it significantly improves measurement accuracy, achieving a frequency error ≤0.1Hz and a phase error ≤0.05rad within a dynamic range of 45-55Hz; second, it effectively enhances anti-interference capabilities, maintaining measurement accuracy even in noisy environments such as high-order harmonics; and finally, it compresses the single-window inference time to 0.1ms through a real-time correction module, providing millisecond-level measurement support for high-proportion renewable energy grid-connected control.

[0243] Example 2

[0244] Combination Figure 7 As shown, this disclosure provides a power system non-stationary signal frequency-phase joint prediction device 300, including a processor 304 and a memory 301. Optionally, the device may further include a communication interface 302 and a bus 303. The processor 304, communication interface 302, and memory 301 can communicate with each other via the bus 303. The communication interface 302 can be used for information transmission. The processor 304 can call logical instructions in the memory 301 to execute the power system non-stationary signal frequency-phase joint prediction method of the above embodiment.

[0245] Furthermore, the logic instructions in the aforementioned memory 301 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium.

[0246] The memory 301, as a computer-readable storage medium, can be used to store software programs and computer-executable programs, such as the program instructions / modules corresponding to the methods in the embodiments of this disclosure. The processor 304 executes functional applications and data processing by running the program instructions / modules stored in the memory 301, thereby realizing the power system non-stationary signal frequency-phase joint prediction method in the above embodiments.

[0247] The memory 301 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the terminal device. Furthermore, the memory 301 may include high-speed random access memory and may also include non-volatile memory.

[0248] The technical solutions of this disclosure can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes one or more instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in this disclosure. The aforementioned storage medium can be a non-transitory storage medium, including: a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, and other media capable of storing program code. It can also be a transient storage medium.

[0249] The foregoing description and accompanying drawings fully illustrate embodiments of this disclosure to enable those skilled in the art to practice them. Other embodiments may include structural, logical, electrical, procedural, and other changes. The embodiments represent only possible variations. Individual components and functions are optional unless explicitly required, and the order of operation may vary. Parts and features of some embodiments may be included in or replace parts and features of other embodiments. Moreover, the terminology used in this application is for describing embodiments only and is not intended to limit the claims. As used in the description of embodiments and claims, the singular forms “a,” “an,” and “the” are intended to equally include the plural forms unless the context clearly indicates otherwise. Similarly, the term “and / or” as used in this application means including one or more of the associated listed items and all possible combinations thereof. Additionally, when used in this application, the term "comprise" and its variations "comprises" and / or "comprising" refer to the presence of stated features, integrals, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or groups thereof. Without further limitations, an element defined by the phrase "comprises a..." does not exclude the presence of other identical elements in the process, method, or apparatus that includes said element. In this document, each embodiment may focus on the differences from other embodiments, and similar or identical parts between embodiments can be referred to mutually. For methods, products, etc., disclosed in the embodiments, if they correspond to the method section disclosed in the embodiments, the relevant parts can be referred to the description of the method section.

[0250] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the embodiments of this disclosure. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0251] The methods and products (including but not limited to devices and equipment) disclosed in the embodiments herein can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For instance, the division of units may be merely a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. In addition, the coupling or direct coupling or communication connection shown or discussed between each other may be through some interfaces, and the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the units may be selected to implement this embodiment according to actual needs. In addition, the functional units in the embodiments of this disclosure may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0252] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than that shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. In the descriptions corresponding to the flowcharts and block diagrams in the accompanying drawings, the operations or steps corresponding to different blocks may also occur in a different order than disclosed in the description, and sometimes there is no specific order between different operations or steps. For example, two consecutive operations or steps may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. Each block in a block diagram and / or flowchart, and combinations of blocks in a block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

Claims

1. A method for non-stationary signal frequency-phase joint prediction of power system, characterized in that, The method comprises the following steps: generating training set data containing frequency offset and noise through a data augmentation method based on parameter space traversal; constructing a multi-task neural network model, which comprises, in sequence, a first convolutional layer, a frequency domain attention module, a second convolutional layer, a third convolutional layer, and a multi-task collaborative output module, the multi-task collaborative output module comprising a frequency estimator, a phase estimator, and a harmonic estimator; training the multi-task neural network model based on a physical constraint training strategy using the training set data, the physical constraint training strategy comprising a multi-dimensional loss function, a signal reconstruction loss, a harmonic energy constraint, and an adaptive gradient update strategy; performing window segmentation on a to-be-tested signal and inputting the signal into the trained multi-task neural network model to obtain predicted power signal frequency and phase, and outputting dynamic frequency and instantaneous phase prediction results after the prediction results are corrected through Kalman filtering; the first convolutional layer comprises, in sequence, a one-dimensional convolution, a batch normalization layer, and a SiLU activation function; the second convolutional layer comprises, in sequence, a max-pooling layer, a one-dimensional convolution, a batch normalization layer, and a SiLU activation function; the third convolutional layer comprises, in sequence, a max-pooling layer, a one-dimensional convolution, a batch normalization layer, a SiLU activation function, and an adaptive average pooling layer; the frequency domain attention mechanism is implemented as follows: three groups of convolutions are executed in parallel: a Q branch, a 1D convolution generates a query matrix; a K branch, a 1D convolution generates a key matrix; a V branch, a 1D convolution generates a value matrix; the Q and K are flattened to calculate an attention weight matrix, which is multiplied by V to output weighted frequency domain features; The frequency estimator adopts a full connection layer to map features to a hidden layer, and after batch normalization and random deactivation regularization, outputs a normalized frequency parameter through a linear layer without a bias term; the frequency parameter is constrained to the interval (0, 1) through a Sigmoid activation function, and is then restored to an actual frequency value through transformation ; The phase estimator performs feature compression on the time-frequency fusion feature vector through a full connection layer and batch normalization, and performs L2 norm normalization on the compressed features; and calculates the final instantaneous phase angle estimation value through an inverse trigonometric function ; The harmonic estimator is a four-dimensional output structure, and the original harmonic amplitude coefficient is generated by a linear layer after full connection, batch normalization and light random inactivation regularization, the coefficient is compressed to the interval (0, 1) through Sigmoid activation, and then multiplied by the upper limit 0.05 of the physical constraint to obtain the harmonic estimation value .

2. The power system non-stationary signal frequency-phase joint prediction method according to claim 1, characterized in that, the multi-task neural network model processes data as follows: basic time domain features are extracted from preprocessed data through the first convolutional layer; key frequency components are enhanced through the frequency domain attention mechanism of the frequency domain attention module to generate attention frequency domain features; fusion time-frequency features are formed by fusing time sequence features and frequency domain features in deep convolution and down-sampling through the second convolutional layer and the third convolutional layer; frequency, phase, and harmonic estimation values are synchronously output based on the fusion time-frequency features through the multi-task collaborative output module.

3. The power system non-stationary signal frequency-phase joint prediction method according to claim 2, characterized in that, the training set data is generated in the following specific manner: non-uniform sampling is performed in a frequency interval [45Hz, 55Hz], and phase angle segmentation is performed in a phase interval [0, 2π] to construct a frequency-phase parameter grid; Generating power signals containing 3, 5, 7, 11 harmonics superimposed with gaussian white noise The formula is as follows: ， wherein, is the fundamental amplitude, is the fundamental frequency, is the fundamental initial phase, is the mth harmonic relative amplitude coefficient, is the random phase offset, is the noise level, denotes time, denotes a Gaussian white noise; The generated power signal is slidingly cut according to a set window length and step, and encoded into triplets, and the encoding label is , indicates the end of the window phase, ; performing on the frequency tag normalization, phase tag encoding as .

4. The power system non-stationary signal frequency-phase joint prediction method according to claim 1, characterized in that, The frequency estimator adopts a full connection layer to map features to a hidden layer, and after batch normalization and random deactivation regularization, outputs a normalized frequency parameter through a linear layer without a bias term; the frequency parameter is constrained to the interval (0, 1) through a Sigmoid activation function, and is then restored to an actual frequency value through transformation : ， wherein, is a frequency weight matrix, is a time-frequency fusion feature vector; the phase estimator performs feature compression on a time-frequency fusion feature vector through a fully connected layer and batch normalization, and applies L2 norm normalization to the compressed features: ， wherein, is a phase weight matrix, is an L2 norm normalization operation, is a normalized two-dimensional vector; calculating the final instantaneous phase angle estimate by an inverse trigonometric function : ； The harmonic estimator is a four-dimensional output structure, and the original harmonic amplitude coefficient is generated by a linear layer after full connection, batch normalization and light random inactivation regularization. The coefficient is compressed to the interval (0, 1) through Sigmoid activation, and then multiplied by the upper limit 0.05 of the physical constraint to obtain the harmonic estimation value : wherein is a harmonic weight matrix.

5. The power system non-stationary signal frequency-phase joint prediction method according to claim 4, characterized in that, the multi-dimensional loss function is as follows: ， wherein, is a frequency smoothing loss function, is a frequency deviation loss function, is a phase cosine error loss function, is a reconstruction mean square error loss function, is a harmonic energy constraint loss function; the frequency smoothing loss The sensitivity of the fundamental frequency estimation is balanced with Huber loss function, in particular as follows: ， wherein, is the estimated bias, is the smoothing threshold, is the number of samples in the current training batch, denotes the frequency prediction value of the th sample, denotes the frequency true value of the th sample; the frequency offset loss function is as follows: ， the phase cosine error loss function is as follows: ， wherein is a phase prediction value, is a phase true value; the signal reconstruction loss is as follows: ， ， wherein denotes the mathematical expectation, denotes the reconstructed time domain signal, is the normalized fundamental amplitude, is the actual frequency value, is the initial phase estimate, is the harmonic estimate; the harmonic energy constraint is as follows: ， the adaptive gradient update adopts an AdamW optimization algorithm.

6. The power system non-stationary signal frequency-phase joint prediction method according to claim 4, characterized in that, the dynamic frequency and instantaneous phase prediction results output after Kalman filtering of the prediction results specifically comprise: the frequency prediction results are input into a frequency tracking filter, which is a Kalman filter based on a second-order state space model; and the phase prediction results are input into a phase smoothing filter, which is constructed based on a Kalman smoothing filtering method of a phase difference state space model; The frequency and phase are cooperatively optimized by a joint filtering strategy, which employs Kalman filtering.

7. The power system non-stationary signal frequency-phase joint prediction method according to claim 6, characterized in that, The linear mapping of the frequency tracking filter is as follows: ， ， wherein, is a frequency observation matrix, is a frequency observation noise variance, is a frequency observation noise, denotes the kth base frequency instantaneous value, characterizes the frequency rate of change, is a sampling window interval, is a frequency process noise, is a frequency process noise covariance matrix, is a state transition matrix, is a state vector of the current frequency and its rate of change, is a state vector of the previous frequency and its rate of change; The linear mapping of the phase smoothing filter is as follows: ， ， wherein, is a phase observation matrix, is an observation noise variance, is a phase observation noise, is a sampling window interval, denotes a phase deviation amount of adjacent windows, describes a phase change rate, is a phase process noise, is a phase process noise covariance matrix, is a state transition matrix, is a state vector of a current phase difference and its change rate, is a state vector of a previous time phase difference and its change rate.

8. The power system non-stationary signal frequency-phase joint prediction method according to claim 7, characterized in that, The joint filtering strategy is as follows: combining the frequency prediction value with the previous phase to calculate the current phase prediction by integration ， The current phase prediction is nonlinearly corrected: ， wherein, represents the wrapToPi operation.

9. An apparatus for non-stationary signal frequency-phase joint prediction of power system, comprising a processor and a memory having program instructions stored therein, characterized in that, The processor is configured to execute, when running the program instructions, the power system non-stationary signal frequency-phase joint prediction method according to any one of claims 1-8.

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