Power grid scene spatio-temporal data generation method based on conditional diffusion model

By extracting load and renewable energy output data from grid data, and using cubic polynomial fitting and conditional diffusion models, combined with denoising networks and penalty loss functions, the generated spatiotemporal data of the grid scenario outperforms existing technologies in terms of power range width and coverage. This solves the problem that existing methods are insufficient in comprehensively considering multivariate time series data, graph structure information, and the influence of covariates, and achieves accurate simulation of real grid scenarios.

CN121808686APending Publication Date: 2026-04-07HOHAI UNIV +3
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-12-29
Publication Date
2026-04-07

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Abstract

The invention discloses a power grid scene spatio-temporal data generation method based on a conditional diffusion model. According to the method, load and new energy output data are extracted from power grid operation data, multi-dimensional key information is acquired, modeling is performed on time sequence data by using a cubic polynomial fitting method, scene constraint information is extracted, a generative model is constructed based on a conditional diffusion model, and a denoising network is designed. The time dependence and the space dependence are modeled by using the time convolution network and the graph convolution network respectively, a penalty loss function is introduced to ensure that the generated data conform to the scene constraint, the generated spatio-temporal data is evaluated through two indexes of the power interval width and the coverage rate, and the accuracy of the generated data is verified. According to the method, the influence of multivariate time series data, graph structures and covariables is comprehensively considered, a real power grid scene can be accurately simulated, and reliable data support is provided for power system optimization scheduling decisions.
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Description

Technical Field

[0001] This invention relates to the fields of power system and computer data mining technology, specifically to a method for generating spatiotemporal data of power grid scenarios based on a conditional diffusion model. Background Technology

[0002] With the widespread application of new energy power generation in power systems, the randomness, volatility, and intermittency of new energy sources such as wind power and photovoltaics have brought numerous challenges to the safe and stable operation of the power grid. The unpredictability and instability of these new energy power generation sources not only increase the complexity of power grid operation but also place higher demands on power system dispatching and operation. During power grid operation, different operating conditions (such as season, weather, and date type) significantly affect the output characteristics of new energy sources and the grid's absorption capacity, resulting in high volatility in both grid load demand and new energy power generation in time and space. Therefore, how to generate spatiotemporal data that can accurately simulate real power grid scenarios has become an important research direction in the current power system field.

[0003] Traditional power system optimization and dispatch decisions rely on real-world spatiotemporal power grid data. However, real-world data often involves privacy and security restrictions, and the scale of publicly available data is limited, making it difficult to cover diverse power grid operation scenarios. Furthermore, uncertainties such as random load changes and fluctuations in renewable energy output make it difficult for real-world data to comprehensively represent all possible scenarios the power grid may face. Therefore, it is necessary to utilize data generation techniques to generate simulated data to supplement the complex real-world scenarios in power grid operation. In recent years, diffusion models, as an emerging generative model, have achieved significant success in fields such as image generation and audio synthesis, and are gradually being introduced into the research of time series data generation. However, traditional diffusion models mainly focus on unconditional generation tasks, making it difficult to guarantee key conditions such as time series characteristics during the generation process, which limits their application effectiveness in the field of spatiotemporal data generation. Conditional diffusion models have emerged to address this, but existing time series data generation methods based on conditional diffusion models have many limitations. For example, they are limited to the generation of only a single type of time series data, failing to cover the comprehensive consideration of multivariate time series data; or they only focus on some factors in multivariate time series data, such as multivariate time series data composed of multiple variables, the graph structure information of the system in which the time series data resides, and covariates that have a significant impact on the dynamics of the time series. The combined effect of these factors is crucial for generating spatiotemporal data that can accurately simulate real power grid scenarios. However, existing methods still have shortcomings in comprehensively considering the influence of multivariate time series data, graph structure information, and covariates, resulting in generated data that fails to accurately reflect the complexity of power grid operation.

[0004] In summary, there is an urgent need for a generation method in the field of spatiotemporal data generation for power grid scenarios that can comprehensively consider multivariate time series data, graph structure information, and covariates, in order to overcome the limitations of existing technologies, generate high-quality simulation data, and provide reliable support for power system optimization scheduling decisions. Summary of the Invention

[0005] The purpose of this invention is to provide a method for generating spatiotemporal data for power grid scenarios based on a conditional diffusion model, aiming to address the shortcomings of existing generation techniques in comprehensively modeling multivariate time series, graph structure information, and covariates. The method of this invention can generate spatiotemporal data that conforms to the constraints of power grid scenarios, improving the accuracy and reliability of power system optimization scheduling decisions.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A method for generating spatiotemporal data of power grid scenarios based on a conditional diffusion model, comprising the following steps: Load and renewable energy output time series data are extracted from power grid operation data to construct a multidimensional time series dataset. The cubic polynomial fitting method is used to model the time series data in the multidimensional time series dataset and extract scene constraint information; A generative model is constructed based on a conditional diffusion model. In the forward process, the generative model gradually perturbs the original spatiotemporal data of the power grid until it becomes noise. In the reverse process, a denoising network is used to recover the original data from the noise. Spatiotemporal data generated by a generative model are used, and the accuracy of the generated spatiotemporal data is verified by evaluating it using two metrics: power interval width and coverage. Specifically, the average power interval width and coverage of the generated data are calculated, and the average value of the power interval width and coverage of each node is used as the final evaluation metric.

[0007] Among them, the power interval width index reflects the range of the generated scene data. A smaller average power interval width indicates that the generated data is more concentrated, while a larger value indicates that the data is more dispersed. Coverage reflects the degree to which the generated scene data includes the real data. A higher coverage indicates that the generated data can cover the fluctuation range of the real data well, while a lower coverage indicates that the generated data may have omissions or excessively wide intervals.

[0008] According to the above technical solution, the multidimensional time series dataset includes time series data of load, time series data of wind power output, and time series data of photovoltaic power output.

[0009] Specifically, the process involves extracting time-series data of the load from the load data, including the load power value and its variation over time; extracting time-series data of wind power output from the wind power data, including the wind power power value and its variation over time; and extracting time-series data of photovoltaic output from the photovoltaic data, including the photovoltaic power value and its variation over time. The extracted time-series data of the load, wind power, and photovoltaic are then combined into a multi-dimensional time-series dataset for subsequent spatiotemporal data generation tasks.

[0010] According to the above technical solution, for a point in the time series data, the cubic polynomial fitting method is used to model the data. The optimal cubic polynomial coefficients are obtained by minimizing the loss function and solving the least squares method. The fitted cubic polynomial is used to characterize the overall trend of the time series, and spatiotemporal data with scene constraint characteristics are obtained as scene constraint information.

[0011] Based on the above technical solution, assuming the time series is represented as follows: The time point is represented as Then the cubic polynomial model is expressed as ,in Let t be the coefficient to be determined, and t represent time.

[0012] According to the above technical solution, the forward process of the generative model gradually degenerates the original data into pure noise data by progressively adding Gaussian noise. In each step of the noise addition process, the noise intensity is gradually increased according to the noise ratio, while maintaining the basic structure and distribution characteristics of the data, until the data is completely submerged in noise and becomes pure noise data. This process simulates the degradation process of data from ordered to disordered, providing a foundation for the subsequent reverse denoising process.

[0013] According to the above technical solution, the reverse process of the generative model gradually removes noise and recovers the original data through a denoising network. In each step of the denoising process, historical spatiotemporal data and power grid diagram structure information are used as conditions to guide the generative model to gradually recover the spatiotemporal structure and features of the data.

[0014] According to the above technical solution, the specific structure of the denoising network is as follows: The data processing flow of the denoising network starts from the constraint extraction module. After the historical data trend constraints are extracted by this module, the spatiotemporal data with scene constraint features will flow into the linear projection layer for feature dimension adaptation and transformation. The output of the linear projection layer is added to the output of the diffusion step encoding module (including the fully connected layer) to realize the embedding of diffusion step size information and feature enhancement. Subsequently, the feature data will enter the spatiotemporal dependency capture module: First, the long temporal dependency relationship is captured through the temporal convolutional network (including gated causal convolution). The processed features are then fed into the graph convolutional network (including the normalized adjacency matrix layer and the weight mapping layer) after the normalization layer to mine the spatial correlation features between power grid nodes. Residual connections are set between the spatiotemporal dependency capture modules. Finally, the outputs of each spatiotemporal dependency capture module are sent to the fully connected output layer to obtain the predicted noise.

[0015] The specific steps of denoising using a denoising network include: Spatiotemporal data with scene constraints are input into the linear projection layer, and the feature dimension is transformed by the linear mapping mechanism, mapping the original features into intermediate feature tensors that are adapted to subsequent network processing. For the diffusion step, sine and cosine functions are used to encode the diffusion step size. The encoded diffusion step size features are first processed by a fully connected layer and SiLU activation function, and then fused with the intermediate feature tensor obtained in the previous step to finally generate enhanced features carrying diffusion step size information. The fused enhanced features are input into a temporal convolutional network, and long-term temporal dependencies are modeled using gated causal convolution. Specifically, based on the initial intermediate feature tensor, two sets of convolutional kernels are used to generate feature matrices. One set of feature matrices is then processed by a sigmoid activation function and multiplied element-wise with the other set of feature matrices. The feature tensor output by the temporal convolutional network is input into the graph convolutional network, and combined with the normalized adjacency matrix corresponding to the power grid topology graph to complete spatial feature aggregation. Specifically, the feature tensor is first mapped to the weight matrix for calculation, then combined with the normalized adjacency matrix to complete the feature interaction between nodes, and finally processed by the ReLU activation function to extract the spatial correlation features between the nodes of the power grid. Residual connections are set between the spatiotemporal dependency capture modules, which consist of temporal convolutional networks and graph convolutional networks. Finally, the outputs of each spatiotemporal dependency capture module are fed into a fully connected output layer to obtain the predicted noise.

[0016] Based on the above technical solution, a penalty loss function is introduced, combined with generation error and constraint loss, to ensure that the generated data conforms to the scene constraints. A denoising network is trained to fit the denoising function by optimizing the objective function.

[0017] The objective function is expressed as follows: ; In the formula, To generate error, To limit losses, This is the coefficient of the constraint penalty term. In the generation error, Represents real noise. This represents the noise predicted by the denoising network. For the diffusion step, , , The first The generated data, historical data, and power grid topology structure are considered. In the constrained loss, Indicates scenario constraints. This represents the final generated data.

[0018] Specifically, generation error measures the difference between generated data and real data, while constraint loss assesses whether the generated data meets the scenario constraints. By adjusting the weight parameters in the penalty loss function, the relative importance of generation error and constraint loss is balanced, ensuring that the generated data meets the constraint requirements of a specific power grid scenario while maintaining data distribution consistency.

[0019] Including another technical solution, the present invention further provides an electronic device, comprising: one or more processors; and a storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to execute the spatiotemporal data generation method for power grid scenarios based on a conditional diffusion model as described in any of the above technical solutions.

[0020] Another technical solution is also provided in this invention: a storage medium is provided in which at least one instruction is stored, which is loaded and executed by a processor to implement the spatiotemporal data generation method for power grid scenarios based on a conditional diffusion model as described in any of the above technical solutions.

[0021] Compared with existing technologies, the beneficial effects achieved by this invention are as follows: This invention extracts load and renewable energy output data from power grid operation data to obtain multi-dimensional key information. It uses a cubic polynomial fitting method to model time series data, extracts scenario constraint information, constructs a generative model based on a conditional diffusion model, designs a denoising network, and models temporal and spatial dependencies using temporal convolutional networks and graph convolutional networks respectively. A penalty loss function is introduced to ensure that the generated data conforms to scenario constraints. The generated spatiotemporal data is evaluated using two indicators: power range width and coverage, verifying the accuracy of the generated data. This invention comprehensively considers the influence of multivariate time series data, graph structure, and covariates. The generated spatiotemporal data of the power grid scenario outperforms existing technologies in terms of power range width and coverage, accurately simulating real power grid scenarios and providing reliable data support for power system optimization and scheduling decisions. Attached Figure Description

[0022] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of the steps of a method for generating spatiotemporal data of a power grid scenario based on a conditional diffusion model, according to the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Taking the Ningxia power grid operation data as an example, this invention applies a method for generating spatiotemporal data of power grid scenarios based on a conditional diffusion model to generate spatiotemporal data. Specific steps include (…). Figure 1 )include: S1. Extract relevant data on load, wind power generation, and photovoltaic power generation from the Ningxia power grid's operational data from December 1, 2021 to April 8, 2022. Specifically: The bus matrix is ​​parsed from the MATPOWER format data file, and the Pd attribute (active load demand) is extracted as the load power value. The load power value at each time point is recorded with a time resolution of 15 minutes to form a complete load time series data.

[0025] Wind turbines were selected from the gen matrix in the MATPOWER format data file, and their Pg attribute (active power output) was extracted as the wind power output value. Complete time series data of wind power output was generated with a time resolution of 15 minutes.

[0026] Photovoltaic units were selected from the gen matrix in the MATPOWER format data file, and their Pg attribute (active power output) was extracted as the photovoltaic power output value. Complete photovoltaic power output time series data was generated with a time resolution of 15 minutes.

[0027] The extracted time-series data of load, wind power, and photovoltaic power are merged into a single dataset, forming a multi-dimensional time-series dataset containing timestamps, load power values, photovoltaic power output values, and wind power output values, providing comprehensive data support for subsequent scenario modeling and data generation.

[0028] S2. The time series data is modeled using a cubic polynomial fitting method to obtain spatiotemporal data with scene constraint characteristics. Step S2 further includes: Step S21: For a given point in the time series data, model the data using a cubic polynomial fitting method. Determine the coefficients of the cubic polynomial by minimizing the loss function based on quadratic error. Specifically, assume the time series is represented as... The time point is represented as Then the cubic polynomial model is expressed as ,in The coefficients are to be determined. This is achieved by minimizing the loss function. The optimal cubic polynomial coefficients are obtained by using the least squares method, so that the fitted curve can best approximate the original time series data.

[0029] The overall trend of the time series is characterized by the fitted cubic polynomial, resulting in spatiotemporal data with scenario-constrained features. This data serves as scenario-constrained information, providing trend constraints for subsequent data generation. By analyzing the shape and trend of the fitted curve, long-term trend features of the time series data can be extracted, such as the seasonal variation trend of load and the intraday fluctuation trend of wind power. These trend features will serve as scenario constraints, guiding the subsequent data generation process and ensuring that the generated data conforms to the changing patterns of a specific power grid scenario.

[0030] S3. Construct a generative model based on the conditional diffusion model. In the forward process, the generative model gradually perturbs the original spatiotemporal data of the power grid until it becomes noise. In the reverse process, a denoising network is used to recover the original data from the noise.

[0031] Specifically, the generative model progressively adds Gaussian noise during the forward pass, gradually degrading the original data into pure noise data. In each noise addition step, the noise intensity is gradually increased according to a certain noise ratio, while maintaining the basic structure and distribution characteristics of the data, until the data is completely submerged in noise, becoming pure noise data. This process simulates the degradation of data from ordered to disordered, providing a foundation for the subsequent reverse denoising process.

[0032] The original data is recovered from the noise during the reverse process, and historical spatiotemporal data and the power grid diagram structure are introduced as conditions. A denoising function is learned through a denoising network to gradually remove noise and reconstruct the original data. In each step of the denoising process, the time series context information provided by historical data and the inter-node connection relationships described by the power grid diagram structure are used to constrain the spatial distribution and temporal variation patterns of the generated data, so that the generated data can conform to the actual operation of the power grid.

[0033] By optimizing the objective function The denoising network is trained to fit the denoising function.

[0034] In the formula, To generate error, To limit losses, This is the coefficient of the constraint penalty term. In the generation error, Represents real noise. This represents the noise predicted by the denoising network. For the diffusion step, , , The first The generated data, historical data, and power grid topology structure are considered. In the constrained loss, Indicates scenario constraints. This represents the final generated data.

[0035] For the input historical spatiotemporal data, the constraint extraction module completes the trend constraint extraction. Specifically, it fits a cubic polynomial curve to the data. The coefficients of each term of the polynomial are solved by minimizing the quadratic loss, thereby accurately capturing the overall trend of data change and obtaining spatiotemporal data with scene constraint characteristics. Its dimension is consistent with the input historical spatiotemporal data.

[0036] The denoising process using a denoising network includes the following steps: Spatiotemporal data with scene constraints are input into the linear projection layer, and the feature dimension is transformed by the linear mapping mechanism, mapping the original features into intermediate feature tensors that are adapted to subsequent network processing. For the diffusion step, the diffusion step encoding module uses sine and cosine functions to encode the diffusion step size. The encoded diffusion step size features are first processed by a fully connected layer and the SiLU activation function. The outputs of the linear projection layer and the diffusion step encoding module are added together to generate an enhanced feature carrying diffusion step size information; The enhanced features carrying diffusion step size information enter the temporal convolutional network of the spatiotemporal dependency capture module. The temporal convolutional network generates feature matrices based on the initial intermediate feature tensor through two sets of gated causal convolutional kernels. Then, one set of feature matrices is processed by the Sigmoid activation function and then element-wise multiplied with the other set of feature matrices to achieve long temporal dependency modeling. The feature tensor output by the temporal convolutional network is input into the graph convolutional network of the spatiotemporal dependency capture module, and spatial feature aggregation is completed by combining it with the normalized adjacency matrix corresponding to the power grid topology graph. Specifically, the feature tensor is first mapped and calculated with the weight matrix, then combined with the normalized adjacency matrix to complete the feature interaction between nodes, and finally processed by the ReLU activation function to extract the spatial correlation features between the nodes of the power grid. The output of the spatiotemporal dependency capture module is input to the spatiotemporal dependency capture module, and residuals are set between the two modules for residual connection optimization. Then, the output is input to the fully connected output layer to obtain the predicted noise.

[0037] S4. Utilize the spatiotemporal data generated by the generative model, and evaluate the generated spatiotemporal data using two metrics: power range width and coverage, to verify the accuracy of the generated spatiotemporal data. Specifically: For each time point, the difference between the upper and lower bounds of the generated scene data is calculated to obtain the power interval width at that time point. Then, the average power interval width is obtained by averaging the power interval widths across all time points. This metric reflects the range of the generated scene data; a smaller average power interval width indicates a more concentrated distribution of the generated data, while a larger value indicates a more dispersed distribution.

[0038] The coverage rate of the generated data is calculated by counting the proportion of real data points that fall within the power range of the generated scene data. The coverage rate reflects the degree to which the generated scene data includes the real data. A higher coverage rate indicates that the generated data can cover the fluctuation range of the real data well, while a lower coverage rate indicates that the generated data may have omissions or excessively wide ranges.

[0039] The average power range width and coverage of each node are used as the final evaluation index to comprehensively assess the quality of the generated data. By averaging the power range width and coverage of all nodes, a comprehensive evaluation index for the spatiotemporal data of the entire power grid is obtained. If the generated data can achieve the minimum deviation between the power range width and the true value, while maintaining a high coverage, the accuracy of the generated data can be comprehensively measured, providing a basis for model optimization and improvement.

[0040] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0041] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for generating spatiotemporal data of power grid scenarios based on a conditional diffusion model, characterized in that, The steps include: Load and renewable energy output time series data are extracted from power grid operation data to construct a multidimensional time series dataset. The cubic polynomial fitting method is used to model the time series data in the multidimensional time series dataset and extract scene constraint information; A generative model is constructed based on a conditional diffusion model. In the forward process, the generative model gradually perturbs the original spatiotemporal data of the power grid until it becomes noise. In the reverse process, the generative model uses a denoising network to recover the original data from the noise. The spatiotemporal data generated by the generative model were used, and the accuracy of the generated spatiotemporal data was verified by evaluating the power range width and coverage.

2. The method for generating spatiotemporal data of power grid scenarios based on a conditional diffusion model according to claim 1, characterized in that, The multidimensional time series dataset includes time series data of load, time series data of wind power output, and time series data of photovoltaic power output.

3. The method for generating spatiotemporal data of power grid scenarios based on a conditional diffusion model according to claim 1, characterized in that, For a point in the time series data, the data is modeled using the cubic polynomial fitting method. The optimal cubic polynomial coefficients are obtained by minimizing the loss function and solving using the least squares method. The fitted cubic polynomial is used to characterize the overall trend of the time series, resulting in spatiotemporal data with scene constraints.

4. The method for generating spatiotemporal data of a power grid scenario based on a conditional diffusion model according to claim 3, characterized in that, The cubic polynomial model represents: ; in, Let t be the coefficient to be determined, and t represent time.

5. The method for generating spatiotemporal data of power grid scenarios based on a conditional diffusion model according to claim 1, characterized in that, The forward process of the generative model gradually degenerates the original data into pure noise data by progressively adding Gaussian noise. In each step of the noise addition process, the noise intensity is gradually increased according to the noise ratio, while maintaining the basic structure and distribution characteristics of the data, until the data is completely submerged in noise and becomes pure noise data.

6. The method for generating spatiotemporal data of power grid scenarios based on a conditional diffusion model according to claim 1, characterized in that, The reverse process of the generative model gradually removes noise and recovers the original data through a denoising network. In each step of the denoising process, historical spatiotemporal data and power grid diagram structure information are used as conditions to guide the generative model to gradually recover the spatiotemporal structure and features of the data.

7. The method for generating spatiotemporal data of a power grid scenario based on a conditional diffusion model according to claim 6, characterized in that, The denoising network execution steps include: Spatiotemporal data with scene constraints are input into the linear projection layer of the denoising network. The feature dimension is transformed by using a linear mapping mechanism, and the original features are mapped into intermediate feature tensors that are adapted to subsequent network processing. The diffusion step size is encoded using sine and cosine functions. The encoded diffusion step size features are first processed by a fully connected layer and a SiLU activation function, and then fused with the intermediate feature tensor to finally generate an enhanced feature carrying diffusion step size information. The enhanced features carrying diffusion step size information are fed into the temporal convolutional network in the spatiotemporal dependency capture module, and long temporal dependency modeling is achieved by using gated causal convolution. The feature tensor output by the temporal convolutional network is input into the graph convolutional network of the spatiotemporal dependency capture module, and spatial feature aggregation is completed by combining it with the normalized adjacency matrix corresponding to the power grid topology graph. The outputs of each spatiotemporal dependency capture module, after being optimized by residual connections, will be aggregated and input into the fully connected output layer. Through nonlinear transformation and dimension mapping, the predicted noise will be obtained.

8. The method for generating spatiotemporal data of a power grid scenario based on a conditional diffusion model according to claim 7, characterized in that, The denoising network is trained to fit the denoising function by optimizing the objective function; the optimized objective function : ; In the formula, To generate error, To limit losses, It is the coefficient of the constraint penalty term; in the generation error, Represents real noise. This represents the noise predicted by the denoising network. For the diffusion step, , , The first The generation of step data, historical data, and power grid topology structure; in the constrained loss, Indicates scenario constraints. This represents the final generated data.

9. An electronic device, characterized in that, include: One or more processors; A storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to perform the method according to any one of claims 1-8.

10. A storage medium, characterized in that, The storage medium stores at least one instruction, which is loaded and executed by a processor to implement the method as described in any one of claims 1-8.