Power grid risk assessment method based on integrated power flow calculation and topology analysis

Abstract

The application relates to the technical field of power grid risk assessment, and discloses a power grid risk assessment method based on integrated power flow calculation and topology analysis, which comprises the following steps: collecting power grid operation data and preprocessing, organizing the preprocessed data into a four-dimensional high-order tensor structure; constructing a power grid topology relation tensor network; constructing an optimization problem in the form of L1 norm, and solving the optimization problem by using an augmented Lagrange multiplier method; analyzing the relationship between different dimension factor matrices to reveal the complex coupling relationship between time, space and parameters; performing risk assessment on different granularity levels under a multi-scale tensor analysis framework, and coordinating the analysis results of each level to form a comprehensive assessment; designing a tensor completion estimation algorithm, constructing an optimization model by using a low-rank assumption, and solving a complete data set by using a tensor low-rank decomposition method; by adopting high-order tensor representation and tensor network decomposition technology, the application effectively reduces the dimension and complexity of data, and the calculation complexity is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power grid risk assessment, more particularly, it relates to a power grid risk assessment method based on integrated power flow calculation and topology analysis. BACKGROUND

[0002] With the development of power systems towards large-scale and high complexity, the scale of modern power grids is continuously expanding and the structure is increasingly complex, and the traditional power grid risk assessment method is facing severe challenges. The existing technology has the following technical problems in processing power grid risk assessment:

[0003] The power grid risk data presents typical high-dimensional characteristics, including time series, geographical spatial distribution, multiple parameter types and different operation scenarios, and there are complex interaction patterns between these dimensions, forming a large-scale multi-dimensional spatio-temporal data structure, and the existing data processing technology cannot effectively store and analyze such large-scale multi-dimensional data, resulting in insufficient information utilization in the risk assessment process; the traditional spatio-temporal data processing method has an exponential growth in computational complexity when processing high-dimensional power grid data, and when the data size reaches a certain level, the computational resource consumption is huge and the processing time is prolonged, which cannot meet the demand of real-time or quasi-real-time risk assessment of power grids, and cannot realize integrated analysis of full spatio-temporal data; the power grid risk patterns are usually hidden in the interaction relationship among multiple dimensions, and the existing data analysis methods are mostly designed for single or double dimensions, which can only analyze single-dimensional characteristics such as time trend or spatial distribution, and cannot effectively capture the interaction patterns among multiple dimensions, which may lead to key risk patterns being ignored and reduce the accuracy of risk identification; the actual power grid monitoring data generally has quality problems such as missing, noise and inconsistency, which will seriously affect the accuracy and reliability of risk assessment, and the existing methods lack effective mechanisms to handle incomplete or inaccurate observation data, which cannot guarantee the reliability of the evaluation results.

[0004] The above technical problems result in low efficiency and insufficient accuracy of the existing power grid risk assessment method, which cannot meet the demand of safe operation of modern smart grids. Therefore, a new evaluation method is needed to efficiently process large-scale multi-dimensional power grid data and accurately identify key risk patterns, in order to improve the efficiency and accuracy of power grid risk assessment. SUMMARY

[0005] The present application provides a power grid risk assessment method based on integrated power flow calculation and topology analysis, which solves the technical problems of high computational complexity, weak pattern extraction ability, difficulty in multi-dimensional interaction analysis and data quality in related technologies when processing multi-dimensional power grid data.

[0006] The present application provides a power grid risk assessment method based on integrated power flow calculation and topology analysis, which includes:

[0007] Collect power grid operation data and pre-process, organize the pre-processed data into a four-dimensional high-order tensor structure;

[0008] Construct a power grid topology relationship tensor network, and decompose the constructed four-dimensional high-order tensor structure into low-dimensional core tensors and factor matrices using an alternating least squares algorithm;

[0009] Apply sparsity constraints to the decomposition results, construct an optimization problem in the form of L1 norm, and solve the optimization problem using the augmented Lagrange multiplier method to extract key risk patterns;

[0010] Inter-modal interaction analysis is performed on the extracted risk patterns to reveal the complex coupling relationship between time, space and parameters by analyzing the relationship between different dimension factor matrices;

[0011] Based on the revealed complex coupling relationship, a multi-scale tensor analysis framework is constructed, and risk assessment is performed on different granularity levels under the multi-scale tensor analysis framework, and the analysis results of each level are coordinated to form a comprehensive assessment;

[0012] For the data missing problem in the comprehensive assessment process, a tensor completion estimation algorithm is designed, an optimization model is constructed using the low-rank assumption, and the complete data set is solved by tensor low-rank decomposition method.

[0013] Further, the pre-processing includes:

[0014] Standardize the power parameters of different dimensions of voltage, power and frequency;

[0015] Convert the parameter type dimension to a numerical representation using onehot encoding;

[0016] The scene type dimension is encoded with a risk degree weight.

[0017] Further, the high-order tensor structure is defined as a four-dimensional tensor space, wherein the four dimensions represent the dimensions of time, space, parameter type and scene.

[0018] Further, the alternating least squares algorithm includes the following iteration process:

[0019] Fix the core tensor, the spatial dimension factor matrix, the parameter type dimension factor matrix and the scene dimension factor matrix, and update the time dimension factor matrix;

[0020] Fix the core tensor, the time dimension factor matrix, the parameter type dimension factor matrix and the scene dimension factor matrix, and update the spatial dimension factor matrix;

[0021] Fix the core tensor, the time dimension factor matrix, the spatial dimension factor matrix and the scene dimension factor matrix, and update the parameter type dimension factor matrix;

[0022] Fixing the core tensor, time dimension factor matrix, space dimension factor matrix and parameter type dimension factor matrix, updating the scene dimension factor matrix;

[0023] Fixing the time dimension factor matrix, space dimension factor matrix, parameter type dimension factor matrix and scene dimension factor matrix, updating the core tensor;

[0024] Calculate the current reconstruction error and check the convergence condition.

[0025] Further, the inter-modal interaction analysis on the extracted risk patterns comprises:

[0026] Analyzing the relationship between different dimension factor matrices to reveal the complex coupling relationship between time, space and parameters;

[0027] Z-score standardization processing is performed on the time series data of different dimensions and scales to ensure the comparability between different types of parameters.

[0028] Further, the risk assessment on different granularity levels under the multi-scale tensor analysis framework comprises:

[0029] Building a multi-scale tensor analysis framework to perform risk assessment at different granularity levels;

[0030] Integrating local details and global patterns by coordinating the analysis results of different scales.

[0031] Further, the multi-scale tensor analysis framework comprises:

[0032] Scale management module, responsible for managing the definition and configuration of different analysis scales;

[0033] Tensor representation generator, generating corresponding tensor representation for each scale level;

[0034] Scale selector, automatically selecting the most suitable analysis scale according to the analysis target and data characteristics;

[0035] Multi-scale coordination unit, coordinating the analysis results of different scales.

[0036] It should be noted that the adaptive logic of the scale selector is based on the risk entropy of each scale data. First, calculate the variance and computational complexity of the data tensor at each scale, then calculate the risk entropy, which is the quotient of the logarithm of the data variance at this scale and the logarithm of the computational complexity. The scale with the maximum risk entropy is selected as the current optimal analysis scale.

[0037] Further, the design tensor completion estimation algorithm comprises:

[0038] The missing data in the power grid monitoring data is processed by using a tensor completion algorithm;

[0039] An optimization model is constructed based on a low-rank assumption, a tensor low-rank decomposition method is used for solving, and the completion precision is evaluated through cross-validation.

[0040] Further, the application of the decomposition result to the sparsity constraint includes preprocessing and normalization of the sparsity weight coefficient, so that the factor matrices of different dimensions can contribute equally in the optimization process, and the weight coefficient is determined by an adaptive adjustment method based on the performance of the validation set and a prior distribution method based on expert knowledge.

[0041] The application provides a computer storage medium, comprising a memory and one or more processors, the memory stores executable code, and the one or more processors execute the executable code to implement the power grid risk assessment method based on integrated power flow calculation and topology analysis.

[0042] The application has the following beneficial effects:

[0043] By adopting high-order tensor representation and tensor network decomposition technology, the method can effectively reduce the dimension and complexity of data, and the calculation complexity is reduced compared with traditional methods, and this structural breakthrough makes the integrated analysis of full-time and space power grid risk data possible, and overcomes the calculation bottleneck of traditional methods in processing high-dimensional data.

[0044] The tensor decomposition optimization method based on sparsity constraint can effectively extract the key space-time mode of power grid risk, compared with traditional methods, the method can consider multiple dimensional factors such as time, space, parameter type and scene, prevent the key risk mode from being ignored, especially in complex fault scenarios, the power grid risk assessment method can identify the risk mode that is difficult to be found by traditional methods.

[0045] Through the inter-modal interaction analysis module, the method can reveal the complex coupling relationship between time, space and parameters, and this multi-modal analysis capability is not possessed by traditional single-dimensional or double-dimensional analysis methods, which helps to deeply understand the formation mechanism and propagation path of power grid risk.

[0046] Through the multi-scale tensor analysis framework, risk assessment is carried out at different granularities, which can not only pay attention to local abnormal points, but also grasp the overall risk situation, and adapt to different levels of decision-making requirements, and this multi-scale analysis capability enables power grid operators to flexibly monitor and analyze risks at macro and micro levels.

[0047] The missing data estimation algorithm based on tensor completion can effectively handle the data missing and abnormal problems in actual power grid monitoring. Compared with the traditional method, the method can utilize the internal correlation in the tensor structure to more accurately repair the data and improve the reliability of risk assessment. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 is a flowchart of the power grid risk assessment method based on integrated power flow calculation and topology analysis in the present application;

[0049] Figure 2 is a column chart comparing the capabilities of the three analysis methods in identifying different types of faults;

[0050] Figure 3 is a column chart comparing the performance of the three data completion methods in handling missing power grid data. DETAILED DESCRIPTION

[0051] The subject matter described herein will now be discussed with reference to example implementations. It should be understood that discussions of these implementations are merely provided to give a more fuller understanding of the subject matter described herein and are not intended to limit the scope of the protection of this specification. The functions and arrangements of the elements discussed can be varied from those described and the various implementations can omit, substitute, or add various procedures or components as appropriate. Additionally, features described in relation to some examples can also be combined in other examples.

[0052] A power grid risk assessment method based on integrated power flow calculation and topology analysis is disclosed in at least one embodiment of the present application, as shown in Figure 1 , including:

[0053] Step 1, collect power grid operation data and pre-process, organize the pre-processed data into a four-dimensional high-order tensor structure;

[0054] Data collection and preprocessing: Collect power grid operation data, including node voltage, line flow, device state and other parameters, and perform standardization and denoising processing.

[0055] Dimension definition: Organize power grid risk data into a four-dimensional tensor structure:

[0056] Time dimension: including data at different time points or time windows;

[0057] Spatial dimension: including data of different geographical locations, substations or lines;

[0058] Parameter type dimension: including different types of power parameters such as voltage, power and frequency;

[0059] Scenario dimension: including different operation scenarios such as normal operation, fault and high load;

[0060] Among them, for non-numerical data of parameter type dimension and scene dimension, encoding preprocessing is needed. The parameter type is converted into numerical representation by one-hot encoding, and the scene type is encoded by label and given risk degree weight, to ensure that different types of data can be uniformly processed in the tensor structure.

[0061] Data mapping: map the preprocessed power grid data into the defined four-dimensional tensor space to form a unified high-order tensor representation. The constructed tensor can be represented as:

[0062] ;

[0063] Among them represents the high-order tensor of power grid risk data; represents the real number set; I, J, K, L represent the dimension sizes of time, space, parameter type and scene respectively.

[0064] Further, the data collection and preprocessing steps include three sub-steps of outlier detection and processing, data standardization and missing value preliminary filling, to ensure the data quality of subsequent tensor construction.

[0065] Further, the dimension definition step needs to consider the sampling rate, coverage range and granularity level of each dimension to balance the relationship between computational complexity and model accuracy.

[0066] Further, the data mapping step includes feature normalization processing to unify power parameters of different dimensions to the same scale, avoiding some parameters from occupying too large weight in the model.

[0067] Step 2, construct the power grid topology relationship tensor network, and decompose the constructed four-dimensional high-order tensor structure into low-dimensional core tensor and factor matrix by alternating least squares algorithm;

[0068] Network topology construction: based on the physical connection relationship of power grid, construct the tensor network structure to reflect the physical constraints and correlation between data.

[0069] Tensor decomposition model design: decompose the high-dimensional tensor into low-dimensional core tensor and a series of factor matrices:

[0070] ;

[0071] Among them represents the high-order tensor of power grid risk data; G is the core tensor, representing the interaction between dimensions; A, B, C, D are the factor matrices of time, space, parameter type and scene dimension respectively; 、 、 、 Tensor matrix product along the 1st, 2nd, 3rd, 4th dimension.

[0072] Tensor matrix product along the nth dimension A special kind of multi-linear operation, which is implemented as follows: unfolding a tensor along its nth dimension, multiplying with the corresponding factor matrix, and then reorganizing it into the original tensor structure. This operation keeps the structure of all dimensions except the nth dimension unchanged, only linearly transforms the specified dimension, allowing the tensor to be processed and decomposed dimension by dimension, and is one of the core operations of multi-dimensional data processing.

[0073] Optimization algorithm design: design an alternating least squares algorithm to optimize the core tensor and factor matrices through iteration to minimize the reconstruction error.

[0074] Further, the network topology construction step includes graph structure representation of power grid connection relationship and weight distribution process based on connection strength, ensuring that physical constraints can be accurately reflected in the mathematical model.

[0075] Further, the tensor decomposition process includes the following sub-steps:

[0076] Determine the number of core features of each dimension, i.e., determine the number of columns of each factor matrix;

[0077] Initialize the core tensor and each factor matrix, which can use random initialization or eigenvalue decomposition results as initial values;

[0078] Calculate the initial reconstruction error to establish the benchmark value for optimization.

[0079] Further, the alternating least squares algorithm performs the following iteration process:

[0080] Update the time dimension factor matrix A by fixing other parameters;

[0081] Update the spatial dimension factor matrix B by fixing other parameters;

[0082] Update the parameter type dimension factor matrix C by fixing other parameters;

[0083] Update the scenario dimension factor matrix D by fixing other parameters;

[0084] Update the core tensor G by fixing all factor matrices;

[0085] Calculate the current reconstruction error and check the convergence condition. If it has not been reached, continue iteration.

[0086] Step 3, apply sparsity constraints to the decomposition results, construct an optimization problem in the form of L1 norm, and solve the optimization problem using the augmented Lagrange multiplier method to extract key risk patterns;

[0087] Sparse constraint definition: For the risk characteristics of power grid, define the sparse constraint function to ensure that the decomposition result can accurately extract the key risk patterns:

[0088] ;

[0089] wherein represents the high-order tensor of power grid risk data; G is the core tensor, representing the interaction relationship between dimensions; A, B, C, and D are respectively the factor matrices of time, space, parameter type, and scenario dimension; 、 、 、 represents the tensor matrix product along the 1st, 2nd, 3rd, and 4th dimensions; is the sparse constraint function, is the balance parameter; represents the Frobenius norm of the matrix; represents the minimization.

[0090] Constraint optimization solution: design an algorithm based on the augmented Lagrange multiplier method to solve the constrained optimization problem, ensuring that the decomposition result meets the sparsity requirement.

[0091] Pattern extraction: based on the decomposition result, extract the key spatio-temporal patterns of power grid risk, and sort the patterns according to their importance.

[0092] Further, the sparse constraint function can choose L1 norm, group sparsity, or structured sparsity, etc. in different forms, and can be flexibly adjusted according to the prior knowledge of power grid risk, enhancing the ability of the model in extracting key features. Specifically, the sparse constraint function is defined as the weighted sum of each factor matrix:

[0093] ;

[0094] wherein represents the L1 norm of the matrix, which calculates the sum of the absolute values of all elements of the matrix; 、 、 、 and represent the sparsity weights of time, space, parameter type, scenario dimension, and core tensor respectively; represents the sparse constraint function; A, B, C, and D are respectively the factor matrices of time, space, parameter type, and scenario dimension; G is the core tensor, representing the interaction relationship between dimensions.

[0095] It should be particularly noted that the above sparse weight coefficients 、 , , and In practical applications, appropriate preprocessing and normalization are required. Since factor matrices of different dimensions have different numerical ranges and physical meanings, directly using the original weights may lead to some dimensions becoming overly dominant during optimization. Therefore, these weight coefficients need to be normalized according to the characteristics and importance of the data in each dimension. Adaptive weight adjustment methods based on validation set performance or prior weight allocation methods based on expert knowledge can be used to ensure a balanced contribution of each dimension to the sparsity constraints.

[0096] Furthermore, the constraint optimization solution step employs an iterative shrinking threshold algorithm, including the following operations:

[0097] By fixing the core tensor, a soft threshold shrinkage operation is performed on each factor matrix to promote sparsity.

[0098] Dynamically adjust balance parameters A warm-start strategy is used to accelerate convergence;

[0099] Set an early stopping criterion to avoid overfitting caused by excessive iteration.

[0100] Furthermore, the pattern extraction step includes three sub-processes: importance score calculation, cluster analysis, and feature interpretation, ensuring that the extracted risk patterns are both accurate and interpretable. Before performing pattern cluster analysis, the eigenvalues ​​of each factor matrix are subjected to maximum and minimum normalization, scaling the values ​​to the [0, 1] interval to ensure that features of different dimensions have the same weight and to avoid certain features with large numerical ranges dominating the clustering results.

[0101] like Figure 2 As shown, the capabilities of three analysis methods (traditional single-dimensional analysis, traditional two-dimensional analysis, and the proposed method) in identifying different types of faults are compared. The proposed method achieves a 100% identification rate for voltage fluctuation faults and cascading faults, and a 75% identification rate for equipment overload faults, outperforming traditional methods. In particular, for complex cascading faults, traditional single-dimensional analysis fails to identify them at all (0%), while the proposed method achieves full identification, demonstrating the advantages of multidimensional tensor analysis.

[0102] Step 4: Perform intermodal interaction analysis on the extracted risk patterns. By analyzing the relationship between factor matrices of different dimensions, the complex coupling relationship between time, space and parameters is revealed.

[0103] The intermodal interaction analysis module consists of the following components:

[0104] Cross-correlation analyzer: Calculates cross-correlation functions between different dimensions, quantifies the coupling strength between time, space, and parameters, and generates inter-dimensional correlation maps. Before performing cross-correlation analysis, time-series data of different dimensions and scales are Z-score standardized to ensure comparability between different types of parameters (such as voltage, power, frequency, etc.) and eliminate the influence of dimensions on correlation calculation.

[0105] Factor correlation analysis unit: Analyzes factor matrices of different dimensions generated by tensor decomposition, extracts potential correlation patterns, and identifies outliers and special patterns.

[0106] Multidimensional interactive visualization engine: Transforms complex high-dimensional relationships into intuitive visual representations, including heatmaps, network diagrams, and spatiotemporal evolution diagrams.

[0107] Association Pattern Miner: Automatically discovers and extracts typical association patterns between different dimensions, providing interpretable results for risk assessment.

[0108] Furthermore, before conducting cross-correlation analysis on time series data across different dimensions, all time series data were first Z-score standardized to eliminate the influence of dimensions. The lag cross-correlation coefficients between the time dimension and the parameter type dimension factor matrices were calculated, with the maximum lag step set to twenty-four, to identify cross-dimensional time series dependencies.

[0109] Furthermore, the cross-correlation analyzer includes lag analysis capabilities, which can detect temporal dependencies between different dimensions and reveal the propagation path of risk events.

[0110] Furthermore, the factor association analysis unit employs a graph-based representation learning method to represent the relationships between factors of different dimensions as a weighted graph structure, and uses graph algorithms to uncover implicit risk associations.

[0111] Step 5: Based on the revealed complex coupling relationships, construct a multi-scale tensor analysis framework, conduct risk assessments at different granular levels under the multi-scale tensor analysis framework, and coordinate the analysis results at each level to form a comprehensive assessment.

[0112] The multiscale tensor analysis framework consists of the following components:

[0113] The scale management module is responsible for managing the definition and configuration of different analysis scales, including multiple scale levels such as substation internal, regional power grid, and network-wide. This module stores the characteristic parameters and interrelationships of each scale.

[0114] Tensor representation generator: Generates corresponding tensor representations for each scale level and maintains the mapping relationship between different scales to achieve cross-scale data transformation.

[0115] Scale selector: Includes an adaptive algorithm that automatically selects the most suitable analysis scale based on the current analysis objective and data characteristics. When comparing features at different scales, scale-adaptive data scaling preprocessing is used, applying independent logarithmic or power transformations to the data at each scale level to make the data distribution more consistent across different scales, providing a fair benchmark for scale selection.

[0116] Multi-scale collaborative unit: coordinates analysis results at different scales, integrates local details with global patterns, and forms a unified risk assessment view.

[0117] Multi-scale collaborative units require special preprocessing to address incompatibility issues between data at different scales when integrating data results from different scales. First, standard score transformation (z-score) or percentile normalization is performed on the risk indicators of each scale to eliminate dimensional differences between scales. Second, a weight matrix is ​​applied to adjust the results at each scale; this weight matrix, determined through supervised learning or expert knowledge, reflects the importance of different scales in various risk assessments. Finally, nonlinear fusion methods (such as fusion machines based on neural networks or fuzzy logic) are used to handle the interaction effects between results from different scales, avoiding complex relationships that might be overlooked by simple linear combinations. This multi-level preprocessing strategy ensures that risk information from macro, meso, and micro scales can be integrated in an optimal way, improving the comprehensiveness and accuracy of risk assessment.

[0118] In an optional embodiment, the "nonlinear fusion method" specifically employs a three-layer feedforward neural network as the fusion processor. Its input layer has the same number of nodes as the sum of the number of risk indicators across all scales, the hidden layer contains sixty-four nodes using the ReLU activation function, and the output layer has one node using the Sigmoid activation function. The network is trained using historical event data to learn how to optimally weight and fuse risk scores from different scales.

[0119] Furthermore, the scale management module includes a scale definition submodule and a scale parameter configuration submodule. The former is responsible for establishing the scale system, while the latter is responsible for setting appropriate parameters for each scale.

[0120] Furthermore, the tensor representation generator contains two functional units: a feature extractor and an inter-scale mapping builder, which enable the extraction and transformation of features at different scales.

[0121] Step 6: To address the data missing problem in the comprehensive evaluation process, a tensor completion estimation algorithm is designed. An optimization model is constructed using the low-rank assumption, and the complete dataset is solved using the tensor low-rank decomposition method.

[0122] Missing Data Detection and Preprocessing: An algorithm was developed to automatically detect missing points and outliers in power grid monitoring data. Detected outliers were preprocessed by replacing them with the median or local mean. Small-scale missing data were initially filled using nearest neighbor interpolation. Large-scale or structured missing data were used as target areas for completion, and local normalization was applied to surrounding observations to eliminate boundary discontinuities.

[0123] Tensor Completion Model Design: Constructing a tensor completion model based on the low-rank assumption:

[0124] ;

[0125] Where Y represents the complete power grid risk data tensor to be completed; This represents a tensor of observed power grid risk data containing missing values; Indicates the location already observed. Projection operation on; Indicates minimization; Represents the rank of a tensor; Indicates constraints.

[0126] Projection operation here It is a selective data extraction function, specifically implemented as follows: among all elements of a tensor, only a set of specified indices is retained. The function selects the element value within the specified range and sets the values ​​of the elements in the remaining positions to zero. This operation allows the optimization process to focus only on the fitting error of the existing observation data, while deriving reasonable values ​​for the missing positions through rank constraints. This function is the foundation of the tensor completion algorithm, enabling the algorithm to distinguish between known data and data to be completed.

[0127] Specifically, this projection operation The definition of is:

[0128] ;

[0129] in Indicates the location already observed. Projection operation on; Tensor At coordinate position The values ​​at the specified locations, i, j, k, and l, represent the dimensions of time, space, parameter type, and scene, respectively. This represents the set of indices for the observed data. The projection operation preserves the values ​​at observed locations while setting the values ​​at unobserved locations to zero.

[0130] In an optional embodiment, the weight coefficients of the nuclear norm of each dimension in the tensor completion model are determined based on the proportion of the sum of singular values ​​after the tensor is matrixed along each dimension. That is, the dimension with more information has a higher corresponding weight coefficient.

[0131] Algorithm solution and verification: The tensor low-rank decomposition method is used to solve the completion problem, and the completion accuracy is evaluated through cross-validation.

[0132] Furthermore, the missing data detection algorithm includes three stages: data consistency check, outlier identification, and spatiotemporal correlation analysis, which can accurately identify missing data regions and outlier locations.

[0133] Furthermore, the tensor completion model is based on the following key assumptions: power grid data has strong spatiotemporal correlation and low-rank characteristics. Even in high-dimensional space, the intrinsic structure of the power grid data can be approximated by a low-rank representation with a dimension much smaller than that of the original data.

[0134] Furthermore, the solution steps for the tensor completion model include:

[0135] The rank minimization problem is transformed into a nuclear norm minimization problem, and a convex optimization model is constructed:

[0136] ;

[0137] Where Y represents the complete power grid risk data tensor to be completed; This represents a tensor of observed power grid risk data containing missing values; Indicates the location already observed. Projection operation on; Indicates minimization; Indicates constraints; Let the nuclear norm of a tensor be defined as the sum of the singular values ​​of all matrix forms of the tensor expansion:

[0138] ;

[0139] in This represents the matrix transformation of tensor Y along the nth dimension. Representation matrix The A singular value, These are the weighting coefficients for each dimension, used to balance the contributions of different dimensions; Indicates the total number of dimensions; The summation symbol is used.

[0140] Weight coefficients of each dimension The values ​​of these weights have a significant impact on the completion result and require scientific preprocessing. Specifically, these weighting coefficients need to consider the feature distribution, variability, and physical meaning of each dimension. Preprocessing methods include:

[0141] Automatic weight allocation based on the distribution of singular values ​​in each dimension: the greater the information content of a dimension, the higher its corresponding weight.

[0142] Based on the standardization of the coefficient of variation of data in each dimension, the dimensions with larger coefficients of variation are assigned higher weights.

[0143] By incorporating power grid expertise into the initial weighting, dimensions such as time and parameter type, which are often more critical for estimating missing data, can be assigned higher initial weights. These preprocessing steps ensure that dimensions with different physical dimensions and importance play a reasonable role in the tensor completion process.

[0144] The optimization problem is solved using an accelerated proximal gradient descent algorithm.

[0145] We design an adaptive regularization parameter adjustment strategy to balance reconstruction accuracy and model complexity.

[0146] Furthermore, the accuracy evaluation of tensor completion adopts the K-fold cross-validation method, performs manual occlusion tests on existing data, calculates indicators such as mean square error and mean absolute error, and improves the stability of tensor completion through model ensemble technology.

[0147] like Figure 3 As shown, the performance of three data completion methods (traditional interpolation, matrix completion, and tensor completion using the proposed method) in processing missing power grid data is compared. From the three evaluation metrics—Mean Squared Error (MSE), Mean Absolute Error (MAE), and Peak Signal-to-Noise Ratio (PSNR)—the proposed method outperforms the other methods in all metrics. Particularly noteworthy is the PSNR, where the proposed method achieves 36.98 dB, an improvement of 10.56 dB over the traditional interpolation method, indicating improved data quality and providing a more reliable data foundation for power grid risk assessment. The MSE and MAE data are standardized by multiplying by 100 to bring the numerical ranges of the three metrics closer together, facilitating comparison within the same chart.

[0148] A computer storage medium includes a memory and one or more processors, wherein the memory stores executable code, and when the one or more processors execute the executable code, it is used to implement the above-described power grid risk assessment method based on integrated power flow calculation and topology analysis.

[0149] Based on the content of the above embodiments, in an optional embodiment:

[0150] It should also be added that:

[0151] Regarding the details of tensor construction and preprocessing, for outlier detection, a robust method based on moving median and absolute deviation is specifically employed. Specifically, the moving median and moving absolute deviation of the data sequence are first calculated. For any data point, if its deviation from the moving median exceeds three times the moving absolute deviation, the point is marked as an outlier and replaced with the median within the corresponding time window.

[0152] For initial imputation of missing values, specifically for small-scale random missing values, spatiotemporal bilinear interpolation is used. This method is based on known data from adjacent time and spatial locations of the missing points, and a reasonable estimate is calculated through weighted averaging for imputation.

[0153] For data standardization, specifically, Z-score standardization is applied to all numerical parameters. That is, for any parameter, its mean and standard deviation are first calculated across the entire dataset. Then, the mean is subtracted from each data value and the result is divided by the standard deviation, ultimately yielding standardized data that conforms to a standard normal distribution.

[0154] Regarding the settings of the core parameters for tensor decomposition:

[0155] 1. Determination of Decomposition Rank: This invention employs a heuristic method based on explained variance to determine the rank (i.e., the number of feature points) of each dimension factor matrix. The specific process is as follows: the original four-dimensional tensor is matrix-expanded according to the time, space, parameter, and scene dimensions; the singular values ​​of each expanded matrix and their cumulative contribution rate are calculated; the index value corresponding to the first time the cumulative contribution rate exceeds 95% is selected as the decomposition rank of that dimension. Thus, the ranks of the time, space, parameter, and scene dimensions are determined to be 80, 50, 8, and 4, respectively.

[0156] Second, ALS algorithm configuration: The alternating least squares algorithm uses random initialization to generate the factor matrix. The iteration stopping condition is set as follows: the maximum number of iterations is 200, or the relative change in reconstruction error between two adjacent iterations is less than one part per million. The regularization parameter is set to 0.01 to prevent overfitting;

[0157] Regarding the specific implementation of sparsity constraints, the following additional points need to be added:

[0158] Weight coefficient settings: The weight coefficients in the sparsity constraint function are set using an adaptive method based on the initial decomposition results. Specifically, each weight coefficient is taken as the reciprocal of the initial L1 norm value of the corresponding factor matrix or core tensor. To avoid division by zero errors, a very small constant value is added to the denominator during calculation. This setting ensures that the larger the initial value of the matrix or tensor, the smaller the relative constraint force is applied, thereby balancing the sparsity of each part;

[0159] Optimization Solver: An iterative shrinking thresholding algorithm is employed to solve optimization problems with the L1 norm. This algorithm performs a soft thresholding operation on each row of the factor matrix, which is essentially a mathematical operation that promotes sparsity based on gradient descent. The balancing parameter adopts a warm-start strategy, with an initial value of 0.1, and decays by multiplying by 0.9 every ten iterations.

[0160] Furthermore, in an optional embodiment:

[0161] The "graph-based representation learning method" is specifically implemented as a graph attention network. A fully connected graph is constructed using factor matrices of different dimensions as node features; two graph attention layers are used, each containing four attention heads, with a hidden layer dimension of 64; by calculating the attention coefficients between nodes, a low-dimensional embedding representation of risk patterns is learned and output for subsequent clustering and anomaly detection.

[0162] Here, the present invention provides an implementation example:

[0163] A provincial power grid company manages a large ultra-high voltage transmission network, comprising 32 500kV substations, 128 220kV substations, and approximately 350 transmission lines. This power grid company faces the following challenges:

[0164] The increasing power grid load, coupled with factors such as aging equipment and weather conditions, has increased the risks.

[0165] Existing assessment methods struggle to simultaneously process massive amounts of multidimensional data from different substations and lines;

[0166] It is difficult to effectively identify the risk patterns hidden in the complex interactions between different dimensions;

[0167] The monitoring data contains a large number of missing values, which affects the accuracy of the assessment.

[0168] The power grid company has decided to apply the power grid risk assessment method described in this implementation method to conduct a comprehensive risk assessment of the ultra-high voltage transmission network under its jurisdiction in order to improve the level of safe operation of the power grid.

[0169] The power grid company collected operational data at 48 time points each day (one sampling point every 30 minutes) over the past year (365 days), including the following parameters:

[0170] The original data dimensions and their sampling information are shown in Table 1:

[0171] Table 1: Dimensions of the original data and their sampling information:

[0172]

[0173] Various types of parameter data were standardized, and the Z-score method was used to convert data of different dimensions into a standard normal distribution. One-hot encoding was used for the parameter type dimension, and label encoding with risk weights was used for the scene type dimension. Finally, a four-dimensional high-order tensor with dimensions of 17520×160×12×5 was constructed.

[0174] Based on the actual physical connections of the power grid, the topology of the power grid was constructed, and a tensor network suitable for the characteristics of the power grid was designed. Using the alternating least squares algorithm, the high-dimensional tensor was decomposed into a low-dimensional core tensor and four factor matrices.

[0175] Table 2 shows an overview of the tensor decomposition results:

[0176] Table 2: Overview of Tensor Decomposition Results:

[0177]

[0178] In the optimization process, a decomposition optimization method based on sparsity constraints is applied to construct the optimization problem and solve it using the augmented Lagrange multiplier method. An iterative shrinkage threshold algorithm is employed to obtain decomposition results that satisfy the sparsity constraints, effectively extracting key risk patterns.

[0179] The intermodal interaction analysis module is used to process the decomposed factor matrix:

[0180] Cross-correlation analyzer: After performing Z-score normalization on data from different dimensions, it calculates the cross-correlation function, quantifies the strength of the coupling relationship between dimensions, and generates a correlation map between dimensions.

[0181] Factor association analysis unit: Using a graph-based representation learning method, the association between factors of different dimensions is represented as a weighted graph structure to identify key interaction patterns.

[0182] Multi-dimensional interactive visualization engine: Transforms analysis results into visualizations such as heatmaps, network diagrams, and spatiotemporal evolution diagrams, intuitively displaying complex relationships.

[0183] Association Pattern Miner: Through hysteresis analysis and association rule mining, it automatically extracts typical patterns and identifies three main types of risks:

[0184] The main risk patterns identified and their characteristics are shown in Table 3:

[0185] Table 3: Identified main risk patterns and their characteristics:

[0186]

[0187] Further risk pattern analysis identified the 10 most critical risk points in the power grid, which are distributed across 7 substations and are mainly related to regional cascading fault risks.

[0188] Based on the constructed multi-scale tensor analysis framework, risk assessments were conducted at three levels: substation internal, regional power grid, and the entire network.

[0189] Scale Management Module: A three-level scale system (internal substation, regional power grid, and the entire network) has been established, and parameters have been configured for each scale to maintain the characteristics and relationships of different scales.

[0190] Tensor representation generator: generates corresponding tensor representations for each scale. Feature extractor extracts features at the equipment level, substation group level and overall power grid level, and establishes mapping relationships between scales.

[0191] Scale selector: Uses an adaptive algorithm to dynamically select the analysis scale based on the risk type, applies logarithmic transformation to data at different scales to ensure the consistency of data distribution at each scale, and provides a fair comparison benchmark.

[0192] Multi-scale collaborative unit: coordinates and integrates analysis results at different scales, while capturing local anomalies and global trends to form a unified risk assessment view.

[0193] Through multi-scale analysis, power grid companies can simultaneously assess risks at different granularities: local risk assessments for key substations are accurate to the equipment level, regional power grid assessments focus on inter-regional risks, and overall network assessments provide a macro-level risk profile.

[0194] In the original data, approximately 8% of the monitoring data was missing, mainly distributed across irregular time periods at 11 substations. First, missing data detection and preprocessing were performed. Outliers were handled by replacing them with the median, and small-scale missing data were initially filled using nearest-neighbor interpolation. Then, a tensor completion algorithm was applied to the large-scale structured missing data.

[0195] In an optional embodiment, the learning rate for the accelerated proximal gradient descent algorithm is set to 0.05, and the maximum number of iterations is 1,000. The regularization parameter is selected from the set of values ​​0.001, 0.01, 0.1, and 1 through cross-validation.

[0196] Specifically, a tensor completion model based on the low-rank assumption was implemented, which completes the data by minimizing the rank of the tensor while keeping the observed data unchanged. The rank minimization problem is transformed into a nuclear norm minimization problem, which is solved using an accelerated proximal gradient descent algorithm, and the completion accuracy is evaluated using K-fold cross-validation (K=5).

[0197] The performance evaluation results of tensor completion are shown in Table 4:

[0198] Table 4: Tensor Completion Performance Evaluation Results (5-fold Cross-validation):

[0199]

[0200] Verification of reduced computational complexity

[0201] Using power grid data subsets of different sizes, the differences in computation time between our method and traditional methods are compared:

[0202] Table 5 shows a comparison of computational efficiency under different data sizes:

[0203] Table 5: Comparison of computational efficiency under different data sizes:

[0204]

[0205] The results show that this method requires only 43.7 minutes to process all power grid data (approximately 16.8 million data points), saving more than 97% of the computation time compared to traditional methods. It also reduces memory usage and computational complexity from O(N^2) to O(N^2). 4 The efficiency of processing ultra-large-scale power grid data has been reduced to the O(N) level.

[0206] To verify the ability of this method to identify risk patterns, the power grid company selected 12 actual fault events that occurred in the past year and compared the performance of different methods in early warning:

[0207] The risk identification capabilities are compared in Table 6:

[0208] Table 6: Comparison of Risk Identification Capabilities

[0209]

[0210] The results show that this method can identify 91.7% of actual faults, which is superior to traditional single-dimensional analysis (25%) and two-dimensional analysis (50%) methods. In particular, for complex cascading faults, this method achieves a 100% identification rate and can provide an average early warning of 4.2 hours, giving power grid dispatchers sufficient response time and effectively improving the safe operation level of the power grid.

[0211] By applying the power grid risk assessment method of this implementation, the provincial power grid company has achieved a comprehensive risk assessment of its ultra-high voltage transmission network. This not only improves computational efficiency and resource utilization, but also enhances the ability to identify complex risk patterns, providing a strong guarantee for the safe operation of the power grid.

[0212] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A power grid risk assessment method based on integrated power flow calculation and topology analysis, characterized in that, include: Collect and preprocess power grid operation data, and organize the preprocessed data into a four-dimensional high-order tensor structure; The preprocessing includes: Standardize electrical parameters with different dimensions such as voltage, power, and frequency; The parameter type dimension is converted into a numerical representation using one-hot encoding. The scenario type dimension is coded with labels and assigned a risk level weight; A power grid topology tensor network is constructed based on the physical connection relationship of the power grid, and the constructed four-dimensional high-order tensor structure is decomposed into a low-dimensional core tensor and factor matrix using the alternating least squares algorithm. Sparse constraints are applied to the decomposition results, an optimization problem is constructed in the form of L1 norm, and the optimization problem is solved using the augmented Lagrange multiplier method, thereby extracting key risk patterns. The application of sparsity constraints to the decomposition results includes preprocessing and normalizing the sparsity weight coefficients so that the factor matrices of different dimensions can contribute in a balanced manner during the optimization process. The weight coefficients are determined by an adaptive adjustment method based on the performance of the validation set and a prior allocation method based on expert knowledge. Intermodal interaction analysis is performed on the extracted risk patterns, and the complex coupling relationship between time, space and parameters is revealed by analyzing the relationship between factor matrices of different dimensions. The intermodal interaction analysis of the extracted risk patterns includes: Analyze the relationships between factor matrices of different dimensions to reveal the complex coupling relationships between time, space, and parameters; Z-score standardization is performed on time series data of different dimensions and scales to ensure comparability between different types of parameters; A multi-scale tensor analysis framework is constructed based on the revealed complex coupling relationships; The multiscale tensor analysis framework includes: The scale management module is responsible for managing the definition and configuration of different analysis scales; Tensor representation generator, which generates the corresponding tensor representation for each scale level; The scale selector automatically selects the most suitable analysis scale based on the analysis objectives and data characteristics. Multi-scale collaborative units coordinate analysis results at different scales; Risk assessments are conducted at different granular levels within the framework of multi-scale tensor analysis, and the analysis results at each level are coordinated to form a comprehensive assessment. To address the data missing problem in the comprehensive evaluation process, a tensor completion estimation algorithm is designed. An optimization model is constructed using the low-rank assumption, and the complete dataset is solved by the tensor low-rank decomposition method.

2. The power grid risk assessment method based on integrated power flow calculation and topology analysis according to claim 1, characterized in that, The higher-order tensor structure is defined as a four-dimensional tensor space, where the four dimensions represent the size of time, space, parameter type, and scene, respectively.

3. The power grid risk assessment method based on integrated power flow calculation and topology analysis according to claim 1, characterized in that, The alternating least squares algorithm includes the following iterative process: Fix the core tensor, spatial dimension factor matrix, parameter type dimension factor matrix, and scene dimension factor matrix, and update the time dimension factor matrix; Fix the core tensor, time dimension factor matrix, parameter type dimension factor matrix, and scene dimension factor matrix, and update the spatial dimension factor matrix; Fix the core tensor, time dimension factor matrix, space dimension factor matrix, and scene dimension factor matrix, and update the parameter type dimension factor matrix; Fix the core tensor, time dimension factor matrix, space dimension factor matrix, and parameter type dimension factor matrix, and update the scene dimension factor matrix; Update the core tensor by fixing the time dimension factor matrix, space dimension factor matrix, parameter type dimension factor matrix, and scene dimension factor matrix; Calculate the current reconstruction error and check the convergence condition.

4. The power grid risk assessment method based on integrated power flow calculation and topology analysis according to claim 1, characterized in that, The risk assessment at different granularity levels within the multi-scale tensor analysis framework includes: Construct a multi-scale tensor analysis framework to conduct risk assessment at different granularity levels; It coordinates analysis results at different scales and integrates local details with global patterns.

5. The power grid risk assessment method based on integrated power flow calculation and topology analysis according to claim 1, characterized in that, The design tensor completion estimation algorithm includes: Using tensor completion algorithm to process missing data in power grid monitoring data; An optimization model is constructed based on the low-rank assumption, solved using the tensor low-rank decomposition method, and the completion accuracy is evaluated through cross-validation.

6. A computer storage medium, characterized in that, The device includes a memory and one or more processors, wherein the memory stores executable code, and the one or more processors execute the executable code to implement the power grid risk assessment method based on integrated power flow calculation and topology analysis as described in any one of claims 1-5.

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