A method and system for predicting transformer load based on long short-term memory networks

By employing a load forecasting method based on long short-term memory networks, combined with frequency domain kurtosis detection and topology parameters, the problem of capturing long-term dependencies and nonlinear characteristics in distribution area load data is solved. This enables high-precision load forecasting and power regulation strategy generation, supporting refined scheduling of the distribution network.

CN120767819BActive Publication Date: 2026-04-03JIANGSU HOMELITE TECH CO LTD
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-09-09
Publication Date
2026-04-03

AI Technical Summary

Technical Problem

Existing load forecasting methods are unable to effectively capture the long-term dependencies and nonlinear characteristics in the power load data of distribution areas, resulting in large errors in distribution area-level load forecasting and making it difficult to meet the needs of refined dispatching of distribution networks.

Method used

A load forecasting method based on Long Short-Term Memory (LSTM) networks is adopted. By acquiring real-time load data, feature extraction is performed, including frequency domain kurtosis detection, phase space reconstruction, and spatiotemporal aggregation of time-series graph convolutional networks. Combined with transformer area topology parameter data, a forecasting model is constructed to perform load forecasting, and power regulation strategies are generated using probabilistic power flow calculations.

Benefits of technology

It improves the accuracy and stability of load forecasting for distribution areas, can adapt to the physical structure characteristics of different distribution areas, and supports refined scheduling and dynamic optimization of the distribution network.

✦ Generated by Eureka AI based on patent content.

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Patent Text Reader

Abstract

This invention provides a method and system for load forecasting of distribution transformer areas based on Long Short-Term Memory (LSTM) networks, comprising: acquiring real-time load data of a target distribution transformer area; extracting features from the real-time load data to obtain load feature data; and using a pre-built prediction model to forecast the load of the target distribution transformer area based on the load feature data to obtain load demand data of the target distribution transformer area. The prediction model is constructed based on a LSTM network and the topology parameter data of the target distribution transformer area. This invention utilizes a prediction model based on LSTM networks and topology parameters to forecast the load of distribution transformer areas, effectively handling long-term dependencies and nonlinear characteristics in power load data. This allows the load forecasting process to adapt to the physical structure characteristics of different distribution transformer areas, thereby improving the accuracy and stability of distribution transformer area-level load forecasting.
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Description

Technical Field

[0001] This invention relates to the field of energy management technology, specifically to a method and system for predicting transformer load based on long short-term memory networks. Background Technology

[0002] Currently, with the increasingly diversified load characteristics of electricity users and the continuous increase in the proportion of distributed energy access, the dispatch and operation of the distribution network faces higher requirements for precision and intelligence. As the basic unit in the distribution network, the load changes of the distribution area exhibit obvious time dependence and periodicity, such as the morning and evening peak hours of residential electricity consumption and the regular differences between weekends and weekdays. At the same time, it is also affected by climate, seasons, and changes in energy consumption behavior, resulting in a strong long-term dependence and significant nonlinear characteristics in the load sequence.

[0003] Existing load forecasting methods, such as Autoregressive Moving Average (ARIMA) and linear regression, mainly rely on linear assumptions and short-term correlation modeling. They are difficult to effectively capture the complex dynamic changes and long-term dependence patterns in load data, resulting in limited forecast accuracy. In particular, the errors are more significant at the distribution area level, making it difficult to meet the needs of refined scheduling and dynamic optimization of the distribution network. Summary of the Invention

[0004] To address the issue that traditional load forecasting methods (such as ARIMA and linear regression) suffer from significant forecasting errors at the transformer substation level due to their inability to effectively model long-term dependencies and nonlinear characteristics caused by the strong temporal correlation of transformer substation power load data (e.g., morning and evening peak hours for residential electricity consumption, and weekly cycles), thus failing to support the requirements of refined dispatching of distribution networks, this invention proposes a transformer substation load forecasting method based on long short-term memory networks, comprising:

[0005] Obtain real-time load data for the target transformer area;

[0006] Feature extraction is performed based on the real-time load data to obtain load feature data;

[0007] Based on the load characteristic data, a pre-built prediction model is used to predict the load of the target transformer area, thereby obtaining the load demand data of the target transformer area.

[0008] The prediction model is constructed based on the Long Short-Term Memory (LSTM) network and the topology parameter data of the target transformer area.

[0009] Optionally, the step of extracting features from the real-time load data to obtain load feature data includes:

[0010] Frequency domain kurtosis detection is performed on the real-time load data to obtain the mode separation data corresponding to the real-time load data;

[0011] The phase space of the modal separation data is reconstructed to obtain a multimodal component matrix;

[0012] The multimodal component matrix is ​​spatiotemporally aggregated using a temporal graph convolutional network to obtain load characteristic data;

[0013] The modal separation data includes one or more of the following: fundamental mode, harmonic mode, and noise mode.

[0014] Optionally, the step of reconstructing the phase space of the modal separation data to obtain a multimodal component matrix includes:

[0015] Interpret time delay information and embedding dimension information from the modality separation data;

[0016] The trajectory tensor of the modality separation data is determined based on the time delay information and the embedding dimension information.

[0017] The trajectory tensor of the modal separation data is folded to obtain a multimodal component matrix.

[0018] Optionally, the prediction model includes the following construction process:

[0019] The topology parameter data of the target station area is graph encoded to obtain a topology embedding vector;

[0020] The historical load data of the target transformer area is used as the input data of the Long Short-Term Memory (LSTM) network, and the topology embedding vector is used as the initial state of the LSTM network.

[0021] The load demand corresponding to the historical load data is used as the output data of the LSTM network.

[0022] The LSTM network is trained based on the input data, the initial state, and the output data to obtain a prediction model.

[0023] Optionally, after acquiring the real-time load data of the target distribution area, and before performing feature extraction based on the real-time load data to obtain load feature data, the method further includes:

[0024] The real-time load data is cleaned to obtain cleaned load data;

[0025] The cleaning load data is normalized using the minimum-maximum scaling method to obtain normalized data.

[0026] Time series data is extracted from the normalized data, and the time series data is sliced ​​to obtain time slice data, which is then used as preprocessed real-time load data.

[0027] Optionally, after obtaining the load demand data of the target transformer area by performing load forecasting on the target transformer area using a pre-built prediction model based on the load characteristic data, the method further includes:

[0028] Based on the load demand data, real-time load data, and topology parameter data of the target transformer area, a dynamic constraint tensor is constructed.

[0029] Probabilistic power flow calculations are performed on the dynamic constraint tensor to obtain power flow calculation results;

[0030] Based on the power flow calculation results, a power regulation response strategy for the target transformer area is generated.

[0031] Optionally, the load characteristic data includes one or more of the following: physical characteristic data, spatiotemporal characteristic data, and correlation coupling characteristic data;

[0032] The physical characteristic data includes: fundamental mode components and nonlinear dynamic parameter data;

[0033] The spatiotemporal feature data includes: phase space trajectory tensor and multi-scale fluctuation patterns;

[0034] The associated coupling feature data includes: node correlation matrix and source-load interaction factor;

[0035] The topology parameter data includes one or more of the following: transformer capacity data, feeder impedance data, and the location of distributed photovoltaic access points.

[0036] Based on the same inventive concept, this invention also provides a transformer area load forecasting system based on a long short-term memory network, comprising:

[0037] The data acquisition module is used to acquire real-time load data for the target transformer area;

[0038] The feature extraction module is used to extract features from the real-time load data to obtain load feature data;

[0039] The load forecasting module is used to forecast the load of the target transformer area based on the load characteristic data and using a pre-built forecasting model to obtain the load demand data of the target transformer area.

[0040] The prediction model is constructed based on the Long Short-Term Memory (LSTM) network and the topology parameter data of the target transformer area.

[0041] Optionally, the feature extraction module includes:

[0042] The kurtosis detection submodule is used to perform frequency domain kurtosis detection on the real-time load data to obtain the mode separation data corresponding to the real-time load data.

[0043] The spatial reconstruction submodule is used to reconstruct the phase space of the modal separation data to obtain a multimodal component matrix;

[0044] The feature aggregation submodule is used to perform spatiotemporal aggregation of the multimodal component matrix using a temporal graph convolutional network to obtain load feature data;

[0045] The modal separation data includes one or more of the following: fundamental mode, harmonic mode, and noise mode.

[0046] Optionally, the spatial reconstruction submodule includes:

[0047] The feature parsing unit is used to parse time delay information and embedding dimension information from the modality separation data;

[0048] A trajectory output unit is used to determine the trajectory tensor of the modality separation data based on the time delay information and the embedding dimension information.

[0049] Tensor folding unit is used to fold the trajectory tensor of the modal separation data to obtain a multimodal component matrix.

[0050] Optionally, the transformer area load forecasting system further includes: a model building module, comprising:

[0051] The graph encoding submodule is used to perform graph encoding on the topology parameter data of the target station area to obtain a topology embedding vector.

[0052] An initialization submodule is used to take the historical load data of the target transformer area as the input data of the Long Short-Term Memory (LSTM) network and take the topology embedding vector as the initial state of the LSTM network.

[0053] The output setting submodule is used to use the load demand corresponding to the historical load data as the output data of the LSTM network.

[0054] The model training submodule is used to train the LSTM network based on the input data, the initial state, and the output data to obtain a prediction model.

[0055] Optionally, the transformer area load forecasting system further includes: a data preprocessing module, comprising:

[0056] The data cleaning submodule is used to clean the real-time load data to obtain cleaned load data.

[0057] The normalization submodule is used to normalize the cleaning load data using the minimum-maximum scaling method to obtain normalized data.

[0058] The time slicing submodule is used to extract time series data from the normalized processed data, slice the time series data to obtain time slice data, and use the time slice data as preprocessed real-time load data.

[0059] Optionally, the distribution area load forecasting system further includes: a dispatch response module, comprising:

[0060] The constraint construction submodule is used to construct a dynamic constraint tensor based on the load demand data, real-time load data and topology parameter data of the target transformer area;

[0061] The power flow calculation submodule is used to perform probabilistic power flow calculation on the dynamic constraint tensor to obtain the power flow calculation results.

[0062] The strategy generation submodule is used to generate the power regulation response strategy for the target transformer area based on the power flow calculation results.

[0063] Optionally, the load characteristic data includes one or more of the following: physical characteristic data, spatiotemporal characteristic data, and correlation coupling characteristic data;

[0064] The physical characteristic data includes: fundamental mode components and nonlinear dynamic parameter data;

[0065] The spatiotemporal feature data includes: phase space trajectory tensor and multi-scale fluctuation patterns;

[0066] The associated coupling feature data includes: node correlation matrix and source-load interaction factor;

[0067] The topology parameter data includes one or more of the following: transformer capacity data, feeder impedance data, and the location of distributed photovoltaic access points.

[0068] In another aspect, the present invention also provides an electronic device, comprising: at least one processor and a memory; the memory and the processor are connected via a bus;

[0069] The memory is used to store one or more programs;

[0070] When the one or more programs are executed by the at least one processor, a method for predicting transformer load based on a long short-term memory network as described above is implemented.

[0071] In another aspect, the present invention also provides a computer device readable storage medium having an executable program stored thereon, wherein when the executable program is executed, it implements the aforementioned method for predicting transformer load based on a long short-term memory network.

[0072] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0073] This invention provides a method and system for substation load forecasting based on a Long Short-Term Memory (LSTM) network, comprising: acquiring real-time load data of a target substation; extracting features from the real-time load data to obtain load feature data; and using a pre-built prediction model to forecast the load of the target substation based on the load feature data to obtain load demand data for the target substation. The prediction model is constructed based on a LSTM network and the topology parameter data of the target substation. This invention constructs a prediction model based on LSTM networks and topology parameters. The model effectively handles long-term dependencies and nonlinear characteristics in power load data, enabling the load forecasting process to adapt to the physical structure characteristics of different substations, thereby improving the accuracy and stability of substation-level load forecasting. Attached Figure Description

[0074] Figure 1 A flowchart illustrating a transformer area load prediction method based on long short-term memory networks provided by this invention;

[0075] Figure 2 This is a schematic diagram of the network structure of the prediction model in the transformer area load prediction method based on long short-term memory network provided by the present invention.

[0076] Figure 3 A schematic diagram of the overall architecture of a transformer area load prediction method based on a long short-term memory network provided by the present invention;

[0077] Figure 4 A schematic diagram showing the comparison between the predicted load value and the actual load value output by the prediction model in a transformer area load prediction method based on a long short-term memory network, provided as a specific embodiment of the present invention.

[0078] Figure 5 A topology diagram of a transformer area load prediction method based on a long short-term memory network provided in a specific embodiment of the present invention;

[0079] Figure 6 A schematic diagram of the power flow at both ends of line L1 in a transformer area load prediction method based on a long short-term memory network, provided as a specific embodiment of the present invention;

[0080] Figure 7A schematic diagram of the power flow at both ends of line L2 in a transformer area load prediction method based on long short-term memory network provided for a specific embodiment of the present invention;

[0081] Figure 8 A schematic diagram illustrating the power flow of load LP1 in a transformer area load prediction method based on a long short-term memory network, provided as a specific embodiment of the present invention;

[0082] Figure 9 A schematic diagram illustrating the power flow of load LP2 in a transformer area load prediction method based on a long short-term memory network, provided as a specific embodiment of the present invention;

[0083] Figure 10 A schematic diagram of the structural composition of a transformer area load prediction system based on a long short-term memory network provided by the present invention;

[0084] Figure 11 This is a schematic diagram of the structure of an electronic device provided by the present invention. Detailed Implementation

[0085] This invention proposes a method, system, device, and medium for predicting transformer area load based on long short-term memory networks. The specific embodiments of this invention will be further described in detail below with reference to the accompanying drawings.

[0086] Example 1:

[0087] This invention provides a method for predicting transformer load based on long short-term memory networks, the flowchart of which is shown below. Figure 1 As shown, it includes:

[0088] Step 1: Obtain real-time load data for the target transformer area;

[0089] Step 2: Extract features from the real-time load data to obtain load feature data;

[0090] Step 3: Based on the load characteristic data, use a pre-built prediction model to perform load forecasting on the target transformer area to obtain the load demand data of the target transformer area;

[0091] The prediction model is constructed based on the Long Short-Term Memory (LSTM) network and the topology parameter data of the target transformer area.

[0092] Generally, most methods for load forecasting in transformer substations only utilize the time-series characteristics of historical load data, typically employing simple linear models or neural networks based on single features. These methods overlook the multimodal characteristics hidden within the load data and the complex coupling relationship between load and transformer substation topology, making it difficult to fully capture long-term dependencies and nonlinear dynamic features. This results in insufficient accuracy and stability of the forecast results, failing to meet the needs of refined load forecasting at the transformer substation level. To address these issues, this invention proposes introducing a feature extraction step into the load forecasting process. By deeply analyzing real-time load data, key physical, spatiotemporal, and coupling features are extracted, thereby improving the model's ability to perceive transformer substation characteristics and its forecasting accuracy. Specifically:

[0093] In one implementation, the process of extracting features from the real-time load data to obtain load feature data in step 2 above may include:

[0094] Frequency domain kurtosis detection is performed on the real-time load data to obtain the mode separation data corresponding to the real-time load data;

[0095] The phase space of the modal separation data is reconstructed to obtain a multimodal component matrix;

[0096] The multimodal component matrix is ​​spatiotemporally aggregated using a temporal graph convolutional network to obtain load characteristic data;

[0097] The modal separation data may include one or more of the following: fundamental mode, harmonic mode, and noise mode;

[0098] In this implementation, after obtaining the modal separation data corresponding to the real-time load data, before performing phase space reconstruction on the modal separation data to obtain the multimodal component matrix, a sliding window adaptive modal tracking can be introduced to adjust the weights of each modality in real time, solving the problem that traditional fixed modal separation cannot track load abrupt changes. Specifically, this can include:

[0099] Monitor the energy distribution and kurtosis index of load data in real time using a fixed window (such as 15 minutes or a dynamic window);

[0100] Based on the changes in modal energy ratios and kurtosis values ​​within the window, the weights of the modal components are redistributed to form a dynamic mode matrix;

[0101] By employing Bayesian updates or exponentially weighted moving average (EWMA) strategies, modal components can respond rapidly to abrupt changes, forming a dynamically updated multimodal matrix. The phase space can then be reconstructed from the multimodal matrix. This approach can improve the robustness of short-term forecasts when wind and solar power output fluctuates or when holiday patterns change. Furthermore, it can not only predict intraday trends but also be used for real-time scheduling and early warning.

[0102] In this implementation, the process of reconstructing the phase space of the modal separation data to obtain the multimodal component matrix may include:

[0103] Interpret time delay information and embedding dimension information from the modality separation data;

[0104] The trajectory tensor of the modality separation data is determined based on the time delay information and the embedding dimension information.

[0105] The trajectory tensor of the modal separation data is folded to obtain a multimodal component matrix;

[0106] For example, the load characteristic data mentioned above may include one or more of the following: physical characteristic data, spatiotemporal characteristic data, and correlation and coupling characteristic data;

[0107] The physical characteristic data may include: fundamental mode components and nonlinear dynamic parameter data;

[0108] The spatiotemporal feature data may include: phase space trajectory tensor and multi-scale fluctuation patterns;

[0109] The associated coupling feature data may include: node correlation matrix and source-load interaction factor;

[0110] In the above implementation, during the feature extraction stage, frequency domain kurtosis detection is performed on the real-time load data. The load time-series signal can then be Fourier transformed to obtain its spectrum. The kurtosis value of the frequency domain signal is then calculated to measure the degree of deviation of the signal from Gaussian white noise, thereby distinguishing different modes such as fundamental, harmonics, and noise, and forming mode-separated data. Furthermore, by reconstructing the phase space of the obtained mode-separated data, its potential dynamic features are extracted. For example, the optimal time delay parameter and embedding dimension parameter can be analytically determined using the delay coordinate embedding method to construct the trajectory matrix of the mode-separated data. Then, the trajectory matrix is ​​folded and dimensionality reduced to obtain a multi-modal component matrix reflecting the system's state evolution. Finally, a time-series graph convolutional network is used to process the multi-modal component matrix. By performing spatiotemporal aggregation, this network combines the local feature extraction capability of convolutional neural networks with the topology perception capability of graph neural networks. By encoding the correlation matrix between nodes in the transformer area, it captures long-term dependencies in the temporal dimension and characterizes node coupling relationships in the spatial dimension, generating load feature data. Ultimately, the extracted feature data includes fundamental mode components, nonlinear dynamic parameters, phase space trajectory tensors, multi-scale fluctuation modes, node correlation matrices, source-load interaction factors, etc., which can comprehensively reflect the physical, spatiotemporal, and coupling characteristics of the load. Therefore, this feature extraction method can overcome the shortcomings of traditional methods that ignore multimodal, nonlinear, and spatiotemporal coupling characteristics, and is conducive to improving the prediction model's perception and generalization ability of load change patterns.

[0111] In one implementation, the prediction model in step 3 above may include the following construction process:

[0112] The topology parameter data of the target station area is graph encoded to obtain a topology embedding vector;

[0113] The historical load data of the target transformer area is used as the input data of the Long Short-Term Memory (LSTM) network, and the topology embedding vector is used as the initial state of the LSTM network.

[0114] The load demand corresponding to the historical load data is used as the output data of the LSTM network.

[0115] The LSTM network is trained based on the input data, the initial state, and the output data to obtain a prediction model.

[0116] For example, the topology parameter data may include one or more of the following: transformer capacity data, feeder impedance data, and the location of distributed photovoltaic access points;

[0117] For example, the network structure of the prediction model in this implementation can be as follows: Figure 2 As shown, where:

[0118] Input Layer (lstm_1_input): This layer represents the input layer of the model. Input means input and output means output. This layer can receive data of shape (None, 96, 1). Here, None means that the batch size can be arbitrary, 96 may represent the number of time steps for each sample, and 1 is the number of features for each time step.

[0119] LSTM (lstm_1): This indicates that the first LSTM layer receives data of the same shape as the input layer and outputs data of shape (None, 96, 100). This means that the layer has 100 units and can capture more complex temporal dependencies.

[0120] Dropout (dropout_1): This indicates that there is a Dropout layer after the first LSTM layer. Its function is to randomly drop a portion of neurons to prevent overfitting, and the shape of the input and output remains unchanged, which is (None, 96, 100).

[0121] LSTM (lstm_2): This indicates that the second LSTM layer continues to process the data from the Dropout layer. It also has 100 units, and the output shape is still (None, 96, 100).

[0122] LSTM (lstm_3): This indicates a third LSTM layer that further processes the data, but this time its output shape becomes (None, 100), which means it only retains the output of the last time step;

[0123] Dropout (dropout_2): Represents another Dropout layer applied to the output of the third LSTM layer, with a shape of (None, 100);

[0124] Dense (dense_1): This indicates that the last layer is a fully connected layer (Dense layer), which can map the output of the Dropout layer to a single output value with shape (None, 1). This means that the final output of the model is a scalar value, such as predicting a numerical value in a regression problem.

[0125] In the above implementation, during the construction of the prediction model, the topological parameter data of the target transformer area (such as transformer capacity, feeder impedance, and location of distributed photovoltaic access points) is graph-encoded. This graph encoding process involves constructing a node-edge topology graph of the transformer area to represent each node and its connection relationships. A graph convolutional network (GCN) or a node embedding algorithm based on random walks (such as Node2Vec or DeepWalk) is used to encode the structural features and global correlations of each node in the topology graph, resulting in a low-dimensional topology embedding vector. This preserves the similarity and coupling relationships between nodes while avoiding the computational burden of high dimensionality. Based on this, the historical load data of the target transformer area is used as the input sequence of a Long Short-Term Memory (LSTM) network, and the obtained topology embedding vector is used as the initial state vector of the LSTM network. This initialization method explicitly injects the physical structural features of the transformer area, enabling the model to not only capture long-term dependencies in the time dimension but also perceive the spatial coupling characteristics within the transformer area. In terms of network structure, the above implementation can use a multi-layer stacked LSTM network to extract and aggregate deep features of the time series layer by layer. By inserting dropout layers between LSTM layers, overfitting can be effectively prevented. High-dimensional features are mapped to predicted output through fully connected (dense) layers. The first LSTM layer retains the complete time step sequence feature output, the second LSTM layer further refines the sequence pattern based on the first layer, and the third LSTM layer extracts the global representation of the final time step. This setup ensures that the model can capture useful feature patterns at different levels.

[0126] In actual transformer load data collection, due to factors such as measurement equipment errors, communication delays, and external interference, the obtained raw data often contains problems such as missing values, outliers, noise interference, and inconsistent units. Furthermore, load data, as time-series data, often spans a long period and has high dimensionality; directly inputting it into a model can easily lead to training difficulties, slow convergence, and even affect prediction accuracy. Therefore, before using real-time load data for feature extraction, it is necessary to preprocess the collected raw data to improve data quality, enhance data interpretability, and make it meet the requirements of model training. Specifically:

[0127] In one implementation, after obtaining the real-time load data of the target distribution area in step 1 above, and before performing feature extraction based on the real-time load data to obtain load feature data in step 2, the following may be included:

[0128] The real-time load data is cleaned to obtain cleaned load data (for example, samples with missing values ​​can be deleted, missing values ​​can be filled using interpolation methods, or outlier detection algorithms can be used to handle outliers).

[0129] The cleaning load data is normalized using the min-max scaling method (by scaling the data to a smaller range, the differences between features are avoided from causing difficulties in model training), resulting in normalized data.

[0130] Time series data is extracted from the normalized data, and the time series data is sliced ​​(the data is converted into a sample sequence and target value pair, for example, the load data of the transformer area is a sampling point every 15 minutes, that is, 96 points are sampled per day, so three time series lengths of 96, 96*7, and 96*14 can be selected for slicing), to obtain time slice data;

[0131] In this implementation, data cleaning effectively removes invalid data with missing or outlier values, or uses interpolation and outlier detection to correct the data, reducing noise and anomalies from interfering with the prediction model and ensuring the reliability and stability of the input data. The min-max scaling method is used to normalize the data, scaling features with different dimensions and numerical ranges to a uniform interval, avoiding gradient explosion or convergence difficulties caused by excessive feature scale differences, making the model easier to train and accelerating convergence. Time series slicing divides the original long-sequence data into standardized sample-target pairs, fully utilizing the periodicity and long-term regularity of the load data. Different time lengths (e.g., one day, seven days, fourteen days) are flexibly selected based on the sampling frequency of the transformer area load, enabling the model to better capture long-term dependencies and periodic changes. Furthermore, in addition to load data, auxiliary features such as date, time, weather, and holidays can be introduced. By calculating feature correlation, the most relevant historical load data is ultimately selected as input features, further improving the accuracy and stability of the prediction.

[0132] In one implementation, after step 3 above, which uses a pre-built prediction model to predict the load demand data of the target transformer area based on the load characteristic data, the method may further include:

[0133] Based on the load demand data, real-time load data, and topology parameter data of the target transformer area, a dynamic constraint tensor is constructed.

[0134] Probabilistic power flow calculations are performed on the dynamic constraint tensor to obtain power flow calculation results;

[0135] Based on the power flow calculation results, a power regulation response strategy for the target transformer area is generated;

[0136] In this implementation, the process of constructing the dynamic constraint tensor may specifically include:

[0137] Based on the predicted load demand data and real-time load data, a predicted-actual load demand difference matrix is ​​formed over time to reflect the load change trend.

[0138] Based on the topology parameters of the distribution area (such as transformer capacity, feeder impedance, location of distributed photovoltaic access points, etc.), a node-edge topology graph of the distribution area network is constructed, and the load data is mapped to the nodes.

[0139] By encoding node capacity constraints, line carrying capacity, and inter-node interactions, these constraints are comprehensively expressed as a multidimensional tensor in both spatial and temporal dimensions. This tensor comprehensively describes the dynamic relationships between transformer load, network topology, and operational constraints, and probabilistic power flow calculations are performed on the constructed dynamic constraint tensor. Compared to traditional deterministic power flow calculations, this approach utilizes probabilistic power flow calculation methods (such as Monte Carlo methods, Latin hypercube-based sampling, and point estimation methods) to account for uncertainties arising from load forecasting errors and distributed generation fluctuations. Through extensive random sampling and iterative solving of the dynamic constraint tensor, probabilistic characteristic values ​​of voltage, current, and power flow distribution at each node in the transformer area are obtained, such as mean, variance, and confidence interval. Finally, based on the power flow calculation results and combined with the real-time operating status and constraints of the transformer area, optimized power regulation response strategies are generated, such as adjusting load, regulating distributed photovoltaic output, and optimizing feeder power flow direction, to ensure the safe, stable, and efficient operation of the transformer area. Therefore, this implementation method not only allows for real-time perception and prediction of potential operational risks in distribution areas based on load forecasts, but also enables proactive development of reasonable power regulation strategies to effectively alleviate problems such as distribution area overload and node voltage exceeding limits.

[0140] In summary, this invention addresses the problem that traditional load forecasting methods (such as ARIMA and linear regression) suffer from large prediction errors at the distribution network level due to the inability of traditional methods to effectively model long-term dependencies and nonlinear characteristics in distribution area power load data (e.g., morning and evening peak hours for residential electricity consumption, and weekly cycles), making it difficult to support the needs of refined dispatching of distribution networks. Therefore, this invention proposes a distribution area load forecasting method based on Long Short-Term Memory (LSTM) networks. The overall architecture is illustrated in the diagram below. Figure 3As shown, load data of the transformer area is first collected in real time through terminal devices such as smart meters. After data cleaning, normalization and other preprocessing operations, the preprocessed data is divided into training set and test set. Feature extraction is performed using mode decomposition and phase space reconstruction techniques. Spatiotemporal feature aggregation is achieved through feature correlation analysis, and a prediction model based on long short-term memory network is constructed. The load demand data generated by the model prediction can not only be directly used for power planning, but will also be input into the OpenDSS simulation system for probabilistic power flow calculation. By analyzing safety constraints such as voltage over-limit and line overload, a list of power regulation strategies including source-grid-load collaborative optimization is automatically generated, ultimately realizing full-chain intelligence from data perception to regulation decision-making.

[0141] Example 2:

[0142] A specific embodiment of the present invention provides a method for predicting transformer load based on a long short-term memory network. Specifically, the method uses a pre-trained prediction model to predict power consumption on a future day (e.g., July 18, 2024). First, power load data is imported from a file (e.g., totPower.csv). The pre-trained prediction model is loaded, and the input data for prediction (e.g., actual power load data for July 17, 2024) is selected. The input data is preprocessed to conform to the data distribution characteristics during model training. The model is then used to perform load prediction, and the prediction results are restored to the actual power load value through inverse normalization. The executed code can be as follows:

[0143] #Import the processed data totPower.csv

[0144] input_file='totPower.csv'

[0145] data = pd.read_csv(input_file, header=0, encoding='GBK')

[0146] #Import Model

[0147] model = load_model("LSTM_model2.h5")

[0148] #Filter data for forecasting

[0149] end_date = pd.to_datetime('2024-07-17').date()

[0150] data_for_prediction = data[(data['time'].dt.date == end_date)]

[0151] x_test = data_for_prediction['power']

[0152] #Data Normalization

[0153] scaler = MinMaxScaler()

[0154] x_test_nor = scaler.fit_transform(x_test.values.reshape(-1, 1))

[0155] #Perform data prediction

[0156] y_pred_nor = model.predict(x_test_nor)

[0157] #Inverse normalization of prediction results

[0158] y_pred = scaler.inverse_transform(y_pred_nor)

[0159] #Filter actual values

[0160] true_data = data[(data['time'].dt.date == pd.to_datetime('2024-07-18').date())]

[0161] The above code can also filter out the actual power load data for July 18, 2023. A comparison diagram of the predicted daily load for the corresponding transformer area output by the forecast model and the actual load value is shown below. Figure 4 As shown (the horizontal axis represents time points, and the vertical axis represents output load power), based on the comparison of the curves of the predicted and actual load values, and using the absolute percentage error (MAPE) as the evaluation standard, the algorithm error rate of this invention is found to be 0.254%.

[0162] This embodiment demonstrates that by introducing an LSTM model, topological features, and data preprocessing, the present invention can fully extract the time dependence, nonlinear characteristics, and periodic patterns of load data, achieving high-precision prediction of future loads. Furthermore, the entire process is highly automated, computationally efficient, and produces stable and reliable prediction results. Compared to traditional linear prediction methods, this embodiment demonstrates the ability to capture long-term dependency characteristics, adapt to data anomalies, and accurately perceive dynamic load changes, effectively supporting refined scheduling and energy efficiency optimization at the distribution network substation level.

[0163] Example 3:

[0164] The present invention provides a method for predicting transformer load based on long short-term memory networks, which generates a power regulation response strategy for the target transformer area by introducing probabilistic power flow calculation. Specifically, as shown in the example: Figure 5 Taking the illustrated transformer substation topology as an example, a Python adapter or interface is used to interact with OpenDSS (a power system simulation tool), and a low-voltage distribution model is established based on a 230V transformer. In the figure, the source bus represents the main power supply point or substation output port of the power system, providing power to the entire transformer substation; the circular cross symbol next to the source bus indicates the phase connection point in the three-phase power system; the numerical markers (2, 3, 4) represent line numbers or node numbers, used to distinguish different lines or connection points. In practical applications, they are used to identify and manage different paths and devices in the power network; the transformer substation load points downwards, indicating that the location is a power load point within the substation, i.e., where power is consumed, and the direction of the arrow indicates that power flows from the source to the load; PV represents a photovoltaic (PV) power generation system, a distributed energy resource that can be installed within the transformer substation; the transformer substation line information in this embodiment is shown in Table 1, and the transformer substation load information is shown in Table 2.

[0165] Table 1. Information on Transit Lines in the Transit Area

[0166] Line number starting point end Length (km) L1 2 3 1.180 L2 3 4 0.075

[0167] In Table 1, the line number represents the unique identifier of each line: the start and end points are used to indicate the two nodes connected by each line (for example, L1 starts from node 2 and ends at node 3; L2 starts from node 3 and ends at node 4); the length represents the actual physical length of each line, in kilometers.

[0168] Table 2 Load Information for Transformer Areas

[0169] Load number node Load size (kW) provided by the back end LP1 3 A1+jB1 (example 50+j5) LP2 4 A² + jB² (Example 10 + j0.2)

[0170] In Table 2, the load number represents a unique identifier for each load point (e.g., LP1 and LP2); the node indicates the node location of each load point (e.g., LP1 is located at node 3, and LP2 is located at node 4); the load size (kW) backend provides the complex power requirement for each load point, in kilowatts (kW). Complex power can consist of active power (A) and reactive power (B), typically expressed as A+jB. For example, the load size of LP1 is 50+j5 kW, meaning it requires 50 kW of active power and 5 kvar of reactive power; the load size of LP2 is 10+j0.2 kW, meaning it requires 10 kW of active power and 0.2 kvar of reactive power.

[0171] These two tables, together with the topology diagram, describe the details of a small power distribution network, including the connection relationships and lengths of the lines, as well as the load demands at each node. The final distribution results of active and reactive power after power flow calculation are shown in Table 3.

[0172] Table 3 Power Distribution

[0173] Component Terminal Active power P (kW) Reactive power Q (kW) Transformer 1 1 29.1 9.3 Transformer 1 2 -29.1 -9.2 L1 1 29.1 9.2 L1 2 -16 -1.6 L2 1 13.2 1.6 L2 2 -12.6 -1.3 LP1 1 12.6 1.3 LP2 1 2.8 0.1

[0174] According to Table 3:

[0175] For transformer 1, node 1 receives 29.1 kW of active power and 9.3 kvar of reactive power from the grid; node 2 transmits 29.1 kW of active power to the downstream network and absorbs 9.2 kvar of reactive power.

[0176] For line L1, node 1 receives 29.1 kW of active power and 9.2 kvar of reactive power from upstream; node 2 transmits 16 kW of active power downstream and absorbs 1.6 kvar of reactive power. This indicates that during line transmission, some active and reactive power is consumed or allocated to other components. The power flow at both ends of line L1 is as follows: Figure 6 As shown (taking one set of data as an example, the power value marked on the left arrow is "9.69058 + j 3.06906 kVA", indicating that in each set of power data, 9.69058 kW of active power and 3.06906 kvar of reactive power flow to line L1; the power value marked on the right arrow is "-5.32284 + j -0.548266 kVA", indicating that in each set of power data, -5.32284 kW of active power and -0.548266 kvar of reactive power flow out of line L1, and the negative sign indicates that the power direction is opposite to the set reference direction).

[0177] For line L2, node 1 receives 13.2 kW of active power and 1.6 kvar of reactive power from upstream; node 2 transmits 12.6 kW of active power downstream and absorbs 1.3 kvar of reactive power. This indicates that during line transmission, some active and reactive power is consumed or allocated to other components. The power flow at both ends of line L2 is as follows: Figure 7 As shown (taking one set of data as an example, the power value marked on the left arrow is "4.3913 + j 0.529635kVA", indicating that in each set of power data, 4.3913 kW of active power and 0.529635 kvar of reactive power flow to line L2; the power value marked on the right arrow is "-4.20162 + j -0.420162 kVA", indicating that in each set of power data, -4.20162 kW of active power and -0.420162 kvar of reactive power flow out of line L2, and the negative sign indicates that the power direction is opposite to the set reference direction).

[0178] For load LP1, node 1 absorbs 12.6 kW of active power and 1.3 kvar of reactive power from the system. The power flow of the three sets of data received by load point LP1 (also referred to as LP01) is as follows: Figure 8 As shown (taking one set of data as an example, the value is "4.20162 + j 0.420162 kVA", indicating that in each set of power data, there is 4.20162 kW of active power and 0.420162 kvar of reactive power flowing to the load point LP01).

[0179] For load LP2, node 1 absorbs 2.8 kW of active power and 0.1 kvar of reactive power from the system. The power flow of the three sets of data received by load point LP2 (also referred to as LP02) is as follows: Figure 9 As shown (taking one set of data as an example, the value is "0.931533 + j 0.0186307 kVA", indicating that in each set of power data, there is 0.931533 kW of active power and 0.0186307 kvar of reactive power flowing to the load point LP02).

[0180] Therefore, by introducing probabilistic power flow calculations, we can understand the power flow of various components in the power system, including power injection, consumption, and losses during line transmission. This allows us to generate targeted power regulation response strategies. For example, interruptible load control can be implemented at nodes with high loads to reduce unnecessary power consumption; loads can be rationally allocated based on the active power demand of each node to avoid overloading of certain lines or transformers; compensation equipment can be added at nodes with high reactive power demand (such as transformer terminals); and transformer tap changes can be rationally set based on voltage change trends in power flow calculations to ensure that voltage levels are within allowable ranges and avoid damage to equipment caused by excessively high or low voltage.

[0181] Therefore, this embodiment organically combines high-precision load forecasting with probabilistic power flow calculation, and provides a comprehensive, dynamic, and operable power regulation strategy generation method under the premise of considering the complex topology and load characteristics of the distribution area. It can not only improve the accuracy and reliability of forecasting and power flow analysis, but also enhance the pertinence, flexibility and risk resistance of the dispatching strategy, thereby improving the operational safety and economy of the distribution area-level power distribution system.

[0182] Example 4:

[0183] Based on the same inventive concept, this invention also provides a transformer area load prediction system based on a long short-term memory network, the structural composition of which is shown in the schematic diagram below. Figure 10 As shown, it includes:

[0184] The data acquisition module is used to acquire real-time load data for the target transformer area;

[0185] The feature extraction module is used to extract features from the real-time load data to obtain load feature data;

[0186] The load forecasting module is used to forecast the load of the target transformer area based on the load characteristic data and using a pre-built forecasting model to obtain the load demand data of the target transformer area.

[0187] The prediction model is constructed based on the Long Short-Term Memory (LSTM) network and the topology parameter data of the target transformer area.

[0188] In one implementation, the feature extraction module may include:

[0189] The kurtosis detection submodule is used to perform frequency domain kurtosis detection on the real-time load data to obtain the mode separation data corresponding to the real-time load data.

[0190] The spatial reconstruction submodule is used to reconstruct the phase space of the modal separation data to obtain a multimodal component matrix;

[0191] The feature aggregation submodule is used to perform spatiotemporal aggregation of the multimodal component matrix using a temporal graph convolutional network to obtain load feature data;

[0192] The modal separation data includes one or more of the following: fundamental mode, harmonic mode, and noise mode;

[0193] For example, the load characteristic data may include one or more of the following: physical characteristic data, spatiotemporal characteristic data, and correlation coupling characteristic data;

[0194] The physical characteristic data may include: fundamental mode components and nonlinear dynamic parameter data;

[0195] The spatiotemporal feature data may include: phase space trajectory tensor and multi-scale fluctuation patterns;

[0196] The associated coupling feature data may include: node correlation matrix and source-load interaction factor;

[0197] The topology parameter data may include one or more of the following: transformer capacity data, feeder impedance data, and the location of distributed photovoltaic access points.

[0198] In this implementation, the spatial reconstruction submodule may include:

[0199] The feature parsing unit is used to parse time delay information and embedding dimension information from the modality separation data;

[0200] A trajectory output unit is used to determine the trajectory tensor of the modality separation data based on the time delay information and the embedding dimension information.

[0201] Tensor folding unit is used to fold the trajectory tensor of the modal separation data to obtain a multimodal component matrix.

[0202] In one implementation, the transformer area load forecasting system may further include: a model building module, specifically including:

[0203] The graph encoding submodule is used to perform graph encoding on the topology parameter data of the target station area to obtain a topology embedding vector.

[0204] An initialization submodule is used to take the historical load data of the target transformer area as the input data of the Long Short-Term Memory (LSTM) network and take the topology embedding vector as the initial state of the LSTM network.

[0205] The output setting submodule is used to use the load demand corresponding to the historical load data as the output data of the LSTM network.

[0206] The model training submodule is used to train the LSTM network based on the input data, the initial state, and the output data to obtain a prediction model.

[0207] In one implementation, the transformer area load forecasting system may further include: a data preprocessing module, which may specifically include:

[0208] The data cleaning submodule is used to clean the real-time load data to obtain cleaned load data.

[0209] The normalization submodule is used to normalize the cleaning load data using the minimum-maximum scaling method to obtain normalized data.

[0210] The time slicing submodule is used to extract time series data from the normalized processed data, slice the time series data to obtain time slice data, and use the time slice data as preprocessed real-time load data.

[0211] In one implementation, the transformer area load forecasting system may further include: a scheduling response module, specifically including:

[0212] The constraint construction submodule is used to construct a dynamic constraint tensor based on the load demand data, real-time load data and topology parameter data of the target transformer area;

[0213] The power flow calculation submodule is used to perform probabilistic power flow calculation on the dynamic constraint tensor to obtain the power flow calculation results.

[0214] The strategy generation submodule is used to generate the power regulation response strategy for the target transformer area based on the power flow calculation results.

[0215] Example 5:

[0216] like Figure 11 As shown, the present invention also provides an electronic device, which may be a computer device, a microcontroller device, a smart mobile device, etc. The electronic device in this embodiment may include a processor, a memory, a transceiver component, etc. The memory, processor, and transceiver component are connected via a bus; the memory can be used to store executable programs, and an exemplary executable program may include instructions; the processor is used to execute the instructions stored in the memory. The memory can also be used to store data, which can be accessed and / or modified when instructions are executed.

[0217] The processor may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, and it is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions in the storage medium to realize the corresponding method flow or corresponding function, so as to realize the steps of the transformer area load prediction method based on long short-term memory network in the above embodiment.

[0218] Example 6:

[0219] Based on the same inventive concept, this invention also provides a readable storage medium, specifically an electronic device readable storage medium (Memory). This readable storage medium is a memory device within an electronic device used to store programs and data. It is understood that the storage medium here can include both built-in storage media within the electronic device and extended storage media supported by the electronic device. The storage medium provides storage space, which stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more executable programs (including program code). It should be noted that the storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. Loading and executing one or more instructions stored in the storage medium by the processor can implement the steps of the transformer load prediction method based on a long short-term memory network in the above embodiments.

[0220] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0221] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0222] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0223] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0224] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or equivalent substitutions to the specific implementation methods of the application, but these changes, modifications or equivalent substitutions are all within the scope of protection of the claims pending approval.

Claims

1. A method for predicting transformer load based on long short-term memory networks, characterized in that, include: Obtain real-time load data for the target transformer area; Frequency domain kurtosis detection is performed on the real-time load data to obtain the mode separation data corresponding to the real-time load data; The phase space of the modal separation data is reconstructed to obtain a multimodal component matrix; The multimodal component matrix is ​​spatiotemporally aggregated using a temporal graph convolutional network to obtain load characteristic data; Based on the load characteristic data, a pre-built prediction model is used to predict the load of the target transformer area, thereby obtaining the load demand data of the target transformer area. The prediction model includes the following construction process: The topology parameter data of the target transformer area is graph encoded to obtain a topology embedding vector; the topology parameter data includes: transformer capacity, feeder impedance, and location of distributed photovoltaic access point; The historical load data of the target transformer area is used as the input data of the Long Short-Term Memory (LSTM) network, and the topology embedding vector is used as the initial state of the LSTM network. The load demand corresponding to the historical load data is used as the output data of the LSTM network. The LSTM network is trained based on the input data, the initial state, and the output data to obtain a prediction model. The step of performing frequency domain kurtosis detection on the real-time load data to obtain the mode separation data corresponding to the real-time load data includes: Perform a Fourier transform on the load time series corresponding to the real-time load data to obtain the spectrum of the load time series, and then calculate the kurtosis value of the frequency domain signal based on the spectrum. Based on the kurtosis value of the frequency domain signal, mode separation data is obtained; the mode separation data includes one or more of the following: fundamental mode, harmonic mode, and noise mode; After the modal separation data corresponding to the real-time load data, before performing phase space reconstruction on the modal separation data to obtain the multimodal component matrix, a sliding window adaptive modal tracking is introduced to adjust the weights of each modality in real time, including: The energy distribution and kurtosis index of load data can be monitored in real time using a fixed window or a dynamic window. Based on the changes in modal energy ratios and kurtosis values ​​within the window, the weights of the modal components are redistributed to form a dynamic mode matrix; A Bayesian update or exponentially weighted moving average (EWMA) strategy is adopted to enable the modal components to respond to abrupt changes, forming a dynamically updated multimodal matrix, and the phase space is reconstructed based on the multimodal matrix.

2. The method as described in claim 1, characterized in that, The phase space reconstruction of the modal separation data to obtain the multimodal component matrix includes: Interpret time delay information and embedding dimension information from the modality separation data; The trajectory tensor of the modality separation data is determined based on the time delay information and the embedding dimension information. The trajectory tensor of the modal separation data is folded to obtain a multimodal component matrix.

3. The method as described in claim 1, characterized in that, After acquiring the real-time load data of the target transformer area, and before performing feature extraction based on the real-time load data to obtain load feature data, the method further includes: The real-time load data is cleaned to obtain cleaned load data; The cleaning load data is normalized using the minimum-maximum scaling method to obtain normalized data. Time series data is extracted from the normalized data, and the time series data is sliced ​​to obtain time slice data, which is then used as preprocessed real-time load data.

4. The method as described in claim 1, characterized in that, After obtaining the load demand data of the target transformer area by performing load forecasting on the target transformer area using a pre-built prediction model based on the load characteristic data, the method further includes: Based on the load demand data, real-time load data, and topology parameter data of the target transformer area, a dynamic constraint tensor is constructed. Probabilistic power flow calculations are performed on the dynamic constraint tensor to obtain power flow calculation results; Based on the power flow calculation results, a power regulation response strategy for the target transformer area is generated.

5. The method as described in claim 1, characterized in that, The load characteristic data includes one or more of the following: physical characteristic data, spatiotemporal characteristic data, and correlation and coupling characteristic data; The physical characteristic data includes: fundamental mode components and nonlinear dynamic parameter data; The spatiotemporal feature data includes: phase space trajectory tensor and multi-scale fluctuation patterns; The associated coupling feature data includes: node correlation matrix and source-load interaction factor; The topology parameter data includes one or more of the following: transformer capacity data, feeder impedance data, and the location of distributed photovoltaic access points.

6. A transformer area load forecasting system implementing the method of any one of claims 1-5, characterized in that, include: The data acquisition module is used to acquire real-time load data for the target transformer area; The feature extraction module is used to extract features from the real-time load data to obtain load feature data; The load forecasting module is used to forecast the load of the target transformer area based on the load characteristic data and using a pre-built forecasting model to obtain the load demand data of the target transformer area. The prediction model is constructed based on the Long Short-Term Memory (LSTM) network and the topology parameter data of the target transformer area.

7. The system as described in claim 6, characterized in that, The spatial reconstruction submodule includes: The feature parsing unit is used to parse time delay information and embedding dimension information from the modality separation data; A trajectory output unit is used to determine the trajectory tensor of the modality separation data based on the time delay information and the embedding dimension information. Tensor folding unit is used to fold the trajectory tensor of the modal separation data to obtain a multimodal component matrix.

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