Line loss correction analysis method and system

Abstract

The invention discloses a line loss correction analysis method and system, and the method comprises the steps: receiving original line loss data collected by a power grid system, and generating a group of initial line loss feature sets based on the original line loss data; performing spatial-temporal feature mapping on the initial line loss feature set, constructing a line loss feature tensor, and decomposing the line loss feature tensor into a plurality of sub-tensors to capture different spatial-temporal features of line loss; a distributed optimization algorithm is utilized to carry out multi-target collaborative optimization on the sub-tensor, an optimized line loss feature set is generated, and the distributed optimization algorithm optimizes all targets in parallel through edge computing nodes; and performing physical rationality and data consistency screening on the optimized line loss feature set, and determining a plurality of groups of final line loss correction parameters as an execution basis of power grid line loss correction. According to the embodiment of the invention, accurate and efficient line loss correction analysis can be realized, and the accuracy and practicability of power grid line loss management are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric power, and particularly relates to a method and system for line loss correction analysis. Background Art

[0002] With the rapid development of the construction of smart grids, the problem of grid line loss has increasingly become a key factor affecting the economic operation of power systems. Traditional line loss analysis methods mainly rely on centralized data processing and static parameter models, and it is difficult to effectively cope with the complex spatio-temporal variation characteristics in grid operation. In the prior art, line loss feature extraction is mostly based on single-dimensional statistical analysis, lacking the deep integration of multi-source heterogeneous data in the grid, resulting in incomplete characterization of line loss characteristics. At the same time, line loss optimization methods often adopt single-objective optimization strategies, unable to take into account multiple requirements such as minimizing the line loss rate, regional load balancing, and suppressing sudden fluctuations. The optimization results often have problems such as physical unreasonableness or difficulty in execution in practical applications. Summary of the Invention

[0003] The purpose of the present invention is to provide a method and system for line loss correction analysis to solve the deficiencies in the prior art, and to be able to achieve accurate and efficient line loss correction analysis, and improve the accuracy and practicality of grid line loss management.

[0004] An embodiment of the present application provides a method for line loss correction analysis, the method comprising:

[0005] Receiving the original line loss data collected by the power grid system, and generating a set of initial line loss feature sets based on the original line loss data, wherein each initial line loss feature is associated with a feature dimension of grid operation;

[0006] Performing spatio-temporal feature mapping on the initial line loss feature set, constructing a line loss feature tensor, and decomposing the line loss feature tensor into several sub-tensors to capture different spatio-temporal characteristics of the line loss;

[0007] Using a distributed optimization algorithm to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set, wherein the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes;

[0008] Performing screening on the optimized line loss feature set for physical reasonableness and data consistency to determine several groups of final line loss correction parameters as the execution basis for grid line loss correction.

[0009] Optionally, the receiving the original line loss data collected by the power grid system, and generating a set of initial line loss feature sets based on the original line loss data, wherein each initial line loss feature is associated with a feature dimension of grid operation, includes:

[0010] Based on the original line loss data collected from the power grid system, the multi-source data fusion technology is adopted to align the heterogeneous data of the SCADA system, smart meters, and PMU devices. Through the timestamp matching algorithm, a spatio-temporally synchronized original data set is generated;

[0011] For the spatio-temporally synchronized original data set, a feature encoding method based on the power grid topology structure is adopted to map the electrical parameters of each line to the feature dimension. Through the feature weight allocation mechanism, a preliminary line loss feature vector is generated;

[0012] For the preliminary line loss feature vector, a feature selection algorithm based on mutual information is adopted. Combining with the operating characteristics of the power grid, the features strongly related to line loss are screened out. Through the non-linear dimensionality reduction technology, the final initial line loss feature set is generated.

[0013] Optionally, perform spatio-temporal feature mapping on the initial line loss feature set, construct a line loss feature tensor, and decompose the line loss feature tensor into several sub-tensors to capture different spatio-temporal characteristics of line loss, including:

[0014] According to the initial line loss feature set, define a three-dimensional tensor structure. Among them, the time dimension of the three-dimensional tensor structure is divided by hour granularity, and the space dimension is divided by substation / line partition to generate a preliminary line loss feature tensor;

[0015] Perform CP decomposition on the line loss feature tensor, decompose it into a time series sub-tensor, a space sub-tensor, and a feature sub-tensor. Through the sparse constraint term, separate the periodic, regional, and sudden characteristics of line loss;

[0016] For each decomposed sub-tensor, adopt tensor reconstruction error evaluation to verify the decomposition effectiveness. Through spatio-temporal correlation analysis, generate the final sub-tensor set.

[0017] Optionally, use the distributed optimization algorithm to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set. Among them, the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes, including:

[0018] According to the sub-tensor set, define multiple optimization objectives. Through the Pareto optimal front theory, generate multiple objective optimization problems;

[0019] Divide the sub-tensors by the space dimension and allocate them to edge computing nodes. Each node is responsible for a spatial region. Through the consistent hashing algorithm, ensure load balancing and task fault tolerance;

[0020] At each edge node, adopt the alternating direction multiplier method to parallelly solve the corresponding objective optimization problem. At the same time, coordinate the results between nodes through the global consistency constraint. Through the asynchronous communication mechanism, generate preliminary optimized sub-tensors;

[0021] For the preliminary optimized sub-tensors, a weighted aggregation algorithm is adopted to integrate the optimization results of each edge node. Through robustness testing, a final optimized line loss feature set is generated.

[0022] Optionally, screening the optimized line loss feature set for physical rationality and data consistency to determine several groups of final line loss correction parameters as the execution basis for power grid line loss correction includes:

[0023] According to the optimized line loss feature set, use the physical rules of the power grid to construct constraint conditions. Through a mixed-integer programming model, eliminate parameter combinations that violate physical laws and generate a preliminary candidate parameter set;

[0024] For the candidate parameter set, use KL-divergence-based distribution consistency analysis to compare the historical line loss data distribution. Through an anomaly detection algorithm, eliminate parameters that deviate from the normal pattern and generate a refined parameter set;

[0025] For the refined parameter set, use the TOPSIS multi-criteria decision-making algorithm to rank them in combination with economic, feasibility, and effectiveness indicators. Through expert weight assignment, generate a priority parameter sequence;

[0026] For the priority parameter sequence, use Monte Carlo simulation to verify the parameter effectiveness. Through a version control mechanism, output the final line loss correction parameters.

[0027] Another embodiment of the present application provides a line loss correction analysis system, which includes:

[0028] A receiving module for receiving the original line loss data collected by the power grid system and generating an initial line loss feature set based on the original line loss data, where each initial line loss feature is associated with the characteristic dimension of the power grid operation;

[0029] A decomposition module for performing spatio-temporal feature mapping on the initial line loss feature set, constructing a line loss feature tensor, and decomposing the line loss feature tensor into several sub-tensors to capture different spatio-temporal characteristics of the line loss;

[0030] An optimization module for using a distributed optimization algorithm to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set, where the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes;

[0031] A determination module for screening the optimized line loss feature set for physical rationality and data consistency to determine several groups of final line loss correction parameters as the execution basis for power grid line loss correction.

[0032] Another embodiment of the present application provides a storage medium in which a computer program is stored, where the computer program is set to execute the method described in any one of the above when running.

[0033] Another embodiment of the present application provides an electronic device, including a memory and a processor. A computer program is stored in the memory, and the processor is configured to run the computer program to execute the method described in any one of the above.

[0034] Compared with the prior art, a line loss correction analysis method provided by the present invention receives the original line loss data collected by the power grid system, and generates a set of initial line loss feature sets based on the original line loss data; performs spatio-temporal feature mapping on the initial line loss feature sets, constructs a line loss feature tensor, and decomposes the line loss feature tensor into several sub-tensors to capture different spatio-temporal characteristics of the line loss; uses a distributed optimization algorithm to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set, where the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes; performs physical rationality and data consistency screening on the optimized line loss feature set to determine several sets of final line loss correction parameters as the execution basis for power grid line loss correction, so as to be able to achieve accurate and efficient line loss correction analysis and improve the accuracy and practicability of power grid line loss management. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a hardware structure block diagram of a computer terminal for a line loss correction analysis method provided by an embodiment of the present invention;

[0036] Figure 2 It is a schematic flowchart of a line loss correction analysis method provided by an embodiment of the present invention;

[0037] Figure 3 It is a schematic structural diagram of a line loss correction analysis system provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0038] The embodiments described below by referring to the drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0039] An embodiment of the present invention first provides a line loss correction analysis method, which can be applied to an electronic device, such as a computer terminal, specifically, an ordinary computer, etc.

[0040] The following takes running on a computer terminal as an example to describe it in detail. Figure 1 It is a hardware structure block diagram of a computer terminal for a line loss correction analysis method provided by an embodiment of the present invention. As Figure 1 shown, the computer device includes a processor, a memory, and a network interface connected through a system bus. Among them, the memory may include a non-volatile storage medium and an internal memory.

[0041] The non-volatile storage medium can store an operating system and a computer program. The computer program includes program instructions that, when executed, can cause the processor to execute any one of the line loss correction analysis methods.

[0042] The processor is used to provide computing and control capabilities to support the operation of the entire computer device.

[0043] The internal memory provides an environment for the operation of the computer program in the non-volatile storage medium. When the computer program is executed by the processor, it can cause the processor to execute any one of the line loss correction analysis methods.

[0044] The network interface is used for network communication, such as sending assigned tasks, etc. Those skilled in the art can understand that Figure 1 the structure shown in

[0045] is only a block diagram of some structures related to the solution of this application, and does not constitute a limitation on the computer device to which the solution of this application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0046] See Figure 2 , the embodiments of the present invention provide a line loss correction analysis method, which may include the following steps:

[0047] S201, receiving the original line loss data collected by the power grid system, and generating a set of initial line loss feature sets based on the original line loss data, where each initial line loss feature is associated with a feature dimension of the power grid operation;

[0048] This method first receives the original line loss data collected by the power grid system and generates an initial line loss feature set through feature engineering. Each feature is associated with a specific dimension of power grid operation (such as voltage, current, power factor, etc.), establishing a data foundation for subsequent analysis. This step realizes the conversion from original data to structured features. The original data is transformed into an analyzable feature set, providing a standardized input for subsequent spatio-temporal feature analysis. Through feature dimension association, it ensures that the analysis results have clear physical meanings and interpretability, laying a data foundation for accurate line loss correction.

[0049] Specifically, based on the original line loss data collected by the power grid system, multi-source data fusion technology can be adopted to align the heterogeneous data of the SCADA system, smart meters, and PMU devices, and generate a spatio-temporally synchronized original data set through a timestamp matching algorithm;

[0050] Integrate heterogeneous data such as SCADA, smart meters, and PMU through multi-source data fusion technology, and use the timestamp matching algorithm to achieve spatio-temporal alignment of data, solving the problems of multi-source data acquisition delay and accuracy differences. Establish a high-precision spatio-temporal reference data set, eliminate the inconsistencies of multi-source data, and provide a reliable data source for subsequent feature engineering. Spatio-temporal synchronization processing ensures that the analysis results accurately reflect the actual operating state of the power grid.

[0051] For the spatio-temporally synchronized original data set, adopt a feature encoding method based on the power grid topological structure, map the electrical parameters of each line to the feature dimension, and generate a preliminary line loss feature vector through a feature weight allocation mechanism;

[0052] Perform feature encoding based on the power grid topological structure, map the electrical parameters to the feature space, and highlight the key line features through weight allocation. This method considers the influence of the power grid connection relationship on line loss. Incorporate physical topological information into feature engineering, making the features have clear power grid physical meanings. The weight allocation mechanism highlights the contributions of key lines and enhances the representation ability of the feature set.

[0053] For the preliminary line loss feature vector, adopt a feature selection algorithm based on mutual information, combine with the power grid operation characteristics, screen out the features strongly related to line loss, and generate the final initial line loss feature set through a non-linear dimensionality reduction technique.

[0054] Adopt the mutual information feature selection algorithm to screen out strongly related features, and combine with non-linear dimensionality reduction technology to eliminate redundant information. This step considers both the statistical correlation between features and the power grid operation characteristics. Improve the sparsity and effectiveness of the feature set, reduce the subsequent computational complexity. Retain the most discriminative line loss features, providing high-quality input for accurate analysis.

[0055] I. Multi-source Data Fusion and Spatio-temporal Synchronized Data Set Generation:

[0056] 1. Heterogeneous data alignment:

[0057] In the power grid system, the raw data from the SCADA system (data frequency 1Hz), smart meters (15 minutes / time) and PMU devices (50Hz) have differences in time and space scales. The dynamic time warping (DTW) algorithm is used to align the time series:

[0058] Timestamp matching: Using the SCADA system as the reference time axis (timestamp accuracy 1 second), linear interpolation is performed on smart meter data (15 minutes → 1 second granularity), and sliding window averaging (50Hz → 1Hz) is used for PMU data.

[0059] Spatial alignment: According to the grid topology (GIS coordinates), the node-level data of the PMU is mapped to the line level (e.g., the voltage difference between nodes A and B is mapped to the voltage drop of line AB).

[0060] Example: The SCADA voltage data of a 10kV line is [230V, 231V, 229V] (timestamps t1-t3), and the power data of the smart meter during the same period is [100kW, 105kW] (timestamps t1 and t3). The power estimate of 103kW at time t2 is generated by interpolation.

[0061] 2. Data cleaning and verification:

[0062] The outliers are removed by using Z-score-based anomaly detection (threshold ±3σ), and the missing data are repaired by the KNN filling algorithm. For example, the current data of a certain line is missing the value at time t2, and it is filled with 51A based on the adjacent time (t1: 50A, t3: 52A) and similar line data.

[0063] 3. Generation of spatiotemporal synchronized datasets:

[0064] The cleaned data is integrated into a structured table according to the time-space dimension. Each row represents a complete parameter set of a line at a certain moment (1 second granularity), including voltage, current, power factor, impedance, etc. An example of the format of the final generated data set is shown in Table 1:

[0065] Table 1

[0066] Timestamp Line ID Voltage (V) Current (A) Power factor Impedance t1 L001 230 50 0.92 0.15 t2 L001 231 51 0.91 0.15

[0067] 2. Feature coding and weight allocation based on power grid topology:

[0068] 1. Topological feature mapping:

[0069] According to the grid topology (tree or ring), a graph neural network (GNN) is used to model the line relationship. The feature vector of each line includes:

[0070] Electrical parameters: voltage, current, power factor, impedance (normalized to the range [0,1]);

[0071] Topological attributes: line level (main / branch), number of adjacent lines, load contribution.

[0072] Example: The feature vector of line L001 (main line) is [0.85, 0.72, 0.91, 0.15, 1.0, 3, 0.6], corresponding to normalized voltage, current, power factor, impedance, level, number of adjacent lines, and load contribution respectively.

[0073] 2. Feature weight assignment:

[0074] Use the entropy weight method to calculate the weights of each feature:

[0075] Information entropy calculation: Calculate the information entropy for each feature column. The smaller the entropy value, the higher the weight;

[0076] Weight assignment: For example, the weight of voltage V is 0.3, the weight of current I is 0.25, the weight of power factor cosθ (θ is the phase difference angle between voltage and current) is 0.2, the weight of impedance Z is 0.15, and the weight of topological attributes is 0.1. Formula:

[0077]

[0078] where \(E_j\) is the information entropy of the \(j\)th feature, and the number of features is \(k\).

[0079] 3. Feature vector generation:

[0080] Perform a linear combination of the weighted features to generate a preliminary line loss feature vector. For example:

[0081] Line loss feature = 0.3·V + 0.25·I + 0.2·cosθ + 0.15·Z + 0.1·topological attributes.

[0082] III. Feature selection and non-linear dimensionality reduction

[0083] 1. Mutual information feature selection:

[0084] Use the mutual information (MI) algorithm to quantify the correlation between features and the line loss rate:

[0085] MI calculation: Calculate the mutual information value for each feature and the line loss rate, and retain the features with MI ≥ 0.2;

[0086] Example: The MI of voltage = 0.35 (strong correlation), the MI of impedance = 0.18 (weak correlation), so the impedance feature is removed.

[0087] 2. t-SNE non-linear dimensionality reduction:

[0088] For the selected features (such as voltage, current, power factor, topology score), the t-SNE algorithm (perplexity = 30, iterations = 1000) is used to reduce them to 2 dimensions, while preserving the non-linear relationships. An example of the features after dimensionality reduction is shown in Table 2:

[0089] Table 2

[0090] Original feature dimension t-SNE dimension 1 t-SNE dimension 2 [0.85,0.72,0.91,0.6] -1.2 0.8 [0.82,0.68,0.89,0.5] -1.0 0.7

[0091] 3. Generation of the initial feature set:

[0092] The features after dimensionality reduction are combined with time and space labels (such as line ID, time period) to generate an initial line loss feature set, which is stored as a structured database table or an HDF5 format file.

[0093] Exemplarily, a complete application scenario is as follows:

[0094] Generation of line loss features for a certain urban distribution network:

[0095] Scenario description: A certain urban distribution network contains 200 10kV lines, and its daily line loss features need to be analyzed.

[0096] Data sources include:

[0097] SCADA system: Voltage and current are collected at 1Hz;

[0098] Smart meters: 15-minute power data;

[0099] PMU device: 50Hz node voltage phase data.

[0100] Detailed steps:

[0101] 1. Multi-source data fusion:

[0102] Time alignment: Based on the 1-second timestamp of SCADA, the smart meter data is converted to 1-second granularity through cubic spline interpolation, and the PMU data is averaged over a 1-second window.

[0103] Space alignment: The node data of PMU is mapped to the line level. For example, node A (230V∠0°) and node B (228V∠5°) are mapped to a voltage drop of 2V∠-5° for line AB.

[0104] Anomaly handling: It is detected that the current of line L023 suddenly increases to 200A (Z-score = 4.1) at 09:00, which is determined to be an anomaly and replaced with the average value of the previous and subsequent moments (105A).

[0105] 2. Feature encoding and weight assignment:

[0106] Topological Modeling: Use GNN to model the power grid topology. The feature vector of line L101 (main line) is [0.88, 0.75, 0.93, 1.0, 4, 0.7];

[0107] Calculation by Entropy Weight Method: Voltage weight 0.28, current 0.23, power factor 0.19, topological attribute 0.12;

[0108] Generation of Weighted Features: The line loss feature of line L101 = 0.28×0.88 + 0.23×0.75 +... = 0.742.

[0109] 3. Feature Selection and Dimensionality Reduction:

[0110] Mutual Information Screening: Voltage (MI = 0.32), current (MI = 0.28), power factor (MI = 0.21) are retained, and impedance (MI = 0.15) is excluded;

[0111] t-SNE Dimensionality Reduction: Input 4-dimensional features, output 2-dimensional projections, forming clusters (high-loss lines cluster in the lower left, and low-loss lines cluster in the upper right);

[0112] Storage of Feature Sets: Generate a line loss feature matrix containing 200 lines × 86400 seconds, and store it as an HDF5 file. Example of each row of data:

[0113] {Timestamp: 09:00:00, Line ID: L101, Feature 1: -1.2, Feature 2: 0.8}.

[0114] Technical Effects

[0115] Data Fusion Precision: Time alignment error ≤ 0.1 second, spatial mapping error ≤ 1V;

[0116] Feature Interpretability: Features after dimensionality reduction can clearly distinguish high / low-loss lines (cluster silhouette coefficient ≥ 0.7);

[0117] Computing Efficiency: The full-process processing time is shortened from 12 hours of the traditional method to 2 hours (based on Spark distributed computing).

[0118] S202. Perform spatio-temporal feature mapping on the initial line loss feature set, construct a line loss feature tensor, and decompose the line loss feature tensor into several sub-tensors to capture different spatio-temporal characteristics of line loss;

[0119] Perform spatio-temporal feature mapping on the initial features to construct a three-dimensional line loss feature tensor (time × space × feature), and decompose it into several sub-tensors through tensor decomposition techniques. This step uses methods such as higher-order singular value decomposition to capture the spatio-temporal variation laws of line loss. Through tensor decomposition, different spatio-temporal characteristics of line loss (such as periodic fluctuations, regional differences, etc.) are effectively separated, providing a structured analysis object for multi-objective optimization. This decomposition method can reveal complex line loss patterns that are difficult to discover by traditional methods.

[0120] Specifically, according to the initial line loss feature set, a three-dimensional tensor structure can be defined. Among them, the time dimension of the three-dimensional tensor structure is divided by hour granularity, and the space dimension is divided by substation / line partition to generate a preliminary line loss feature tensor.

[0121] Define a three-dimensional tensor structure including time, space, and features, and construct an initial tensor through higher-order singular value decomposition. The time dimension is divided by hour, and the space dimension is divided by power grid partition. Structurally represent the spatio-temporal evolution law of line loss and establish a mathematical model for multi-dimensional analysis. The refined spatio-temporal division ensures that the line loss characteristics at different time scales and spatial ranges can be captured.

[0122] Perform CP decomposition on the line loss feature tensor, decompose it into a time series sub-tensor, a space sub-tensor, and a feature sub-tensor, and separate the periodic, regional, and sudden characteristics of line loss through sparse constraint terms.

[0123] Use CP tensor decomposition to decompose the original tensor into three sub-tensors: time series, space, and features, and separate the components with different characteristics through sparse constraints. Realize the decoupled analysis of line loss characteristics and separately study different patterns such as periodicity, regionality, and suddenness. The sparse constraint enhances the interpretability and facilitates the identification of dominant factors.

[0124] For each of the decomposed sub-tensors, use tensor reconstruction error evaluation to verify the effectiveness of the decomposition, and generate a final set of sub-tensors through spatio-temporal correlation analysis.

[0125] Evaluate the decomposition quality through reconstruction error and verify the physical meaning of each sub-tensor based on spatio-temporal correlation analysis. Ensure that the decomposition result not only maintains mathematical rationality but also conforms to the physical laws of the power grid, providing a credible intermediate result for subsequent optimization.

[0126] I. Definition of Three-Dimensional Tensor Structure and Construction of Line Loss Feature Tensor

[0127] 1. Data Dimension Division:

[0128] Time Dimension: Divide the time axis by hour granularity. For example, divide a day into 24 time windows (00:00 - 01:00, 01:00 - 02:00, etc.), and aggregate the average value, maximum value, and standard deviation of line loss data within each window.

[0129] Spatial dimension: Divide the spatial region according to the power grid topology. For example, divide the power grid into the jurisdiction scope of several substations or line partitions (such as "Substation A - Line Group 1", "Substation B - Line Group 2").

[0130] Feature dimension: Define the feature axis based on the initial line loss feature set. For example, it includes features such as "line loss rate", "load rate", "three - phase unbalance degree", "temperature influence coefficient", etc.

[0131] Example: A power grid system contains 3 substations, a 24 - hour time window, and 10 feature dimensions. Then the size of the constructed three - dimensional tensor is 24×3×10.

[0132] 2. Tensor data filling:

[0133] Data alignment: Fill each feature value in the initial line loss feature set to the corresponding position of the tensor according to the timestamp and spatial location. For example, the feature values such as the line loss rate and load rate of Substation A in the time period from 00:00 to 01:00 are filled to the position [0,0,:] of the tensor.

[0134] Missing value processing: For the data missing in some time periods or regions, use a spatio - temporal interpolation algorithm (such as Kriging interpolation) for supplementation. For example, if there is no data for Substation B from 03:00 to 04:00, interpolation filling is performed according to the data of adjacent time periods (from 02:00 to 03:00 and from 04:00 to 05:00) and adjacent substations (Substation A and C).

[0135] Output: The preliminary line loss feature tensor [T×S×F], where T = time dimension, S = spatial dimension, and F = feature dimension.

[0136] II. CP decomposition and sub - tensor generation

[0137] Perform CP decomposition (Canonical Polyadic Decomposition) on the line loss feature tensor. The specific implementation method is as follows:

[0138] 1. CP decomposition principle and parameter setting:

[0139] Decomposition objective: Decompose the three - dimensional tensor into three factor matrices (temporal factor matrix A, spatial factor matrix B, feature factor matrix C) and a core tensor G, such that the original tensor ≈ G×1A×2B×3C.

[0140] Decomposition rank selection: Determine the optimal decomposition rank through the alternating least squares method (ALS) and model fitting error (such as RMSE). For example, select the rank R = 5 through cross - validation.

[0141] Sparse constraint term: Add an L1 regularization term during the decomposition process to enforce the sparsity of the factor matrices, in order to separate different characteristics (periodicity, regionality, suddenness) of line losses.

[0142] 2. Decomposition process and characteristic separation:

[0143] Temporal sub-tensor extraction: Each column of the temporal factor matrix A represents a time pattern. For example, the first column may correspond to daily periodic fluctuations (such as morning and evening load peaks), and the second column corresponds to weekly periodic fluctuations (such as differences between weekdays and weekends).

[0144] Spatial sub-tensor extraction: Each column of the spatial factor matrix B represents a spatial distribution pattern. For example, the first column may correspond to high-loss regions (such as suburban lines), and the second column corresponds to low-loss regions (such as downtown lines).

[0145] Characteristic sub-tensor extraction: Each column of the characteristic factor matrix C represents an association pattern of different characteristic dimensions. For example, the first column may associate "line loss rate" with "load rate", and the second column associates "three-phase unbalance degree" with "temperature influence coefficient".

[0146] Output: The set of decomposed sub-tensors, including the temporal sub-tensor (A×G), the spatial sub-tensor (B×G), and the characteristic sub-tensor (C×G).

[0147] 3. Optimization of decomposition results:

[0148] Iterative optimization: Iteratively update the factor matrices through the ALS algorithm until convergence (such as iterating 50 times or the RMSE change rate < 0.1%).

[0149] Verification of physical meaning: Manually analyze the physical meaning of the factor matrices. For example, verify whether the temporal sub-tensor truly reflects the daily / weekly load cycle, and whether the spatial sub-tensor matches the known high-loss regions.

[0150] III. Verification of decomposition effectiveness and generation of sub-tensor set

[0151] Verify the effectiveness of the decomposed sub-tensors, and the specific implementation methods are as follows:

[0152] 1. Reconstruction error evaluation:

[0153] Error calculation: Reconstruct the sub-tensors into the original tensor according to the CP decomposition formula, and calculate the root mean square error (RMSE) between the reconstructed tensor and the original tensor. For example, if the RMSE of a power grid tensor after reconstruction is 4.2% (threshold ≤ 5%), it is determined that the decomposition is effective.

[0154] Analysis of error sources: If the RMSE exceeds the standard, check the data quality (such as noise, missing values) or adjust the decomposition rank (such as increasing R from 5 to 6).

[0155] 2. Spatiotemporal Correlation Analysis:

[0156] Temporal Correlation: Calculate the Pearson correlation coefficient between the time-series sub-tensor and historical line loss data. For example, if the correlation coefficient between a certain time-series sub-tensor and the historical daily load curve is ≥ 0.85, it indicates that the periodic characteristics are successfully captured.

[0157] Spatial Correlation: Perform regression analysis on the spatial sub-tensor and power grid geographic information (such as line length, user density) to verify the rationality of the spatial distribution. For example, the coincidence degree between the high-weight area in a certain spatial sub-tensor and the actual high-loss area (such as the line aging area) reaches 90%.

[0158] Verification of Sudden Characteristics: Detect abnormal fluctuations in the sub-tensor through a sliding window and compare with actual fault records. For example, a significant peak appears in a certain sudden sub-tensor during a known fault period (such as thunderstorm weather).

[0159] 3. Generation of Sub-tensor Set:

[0160] Data Formatting: Store the verified sub-tensors in a standard format (such as HDF5) and label their physical meanings (such as "daily periodic time-series sub-tensor", "spatial sub-tensor of high-loss area").

[0161] Attachment of Metadata: Add descriptive metadata to each sub-tensor, such as decomposition rank, correlation coefficient, verification timestamp.

[0162] Output: A set of sub-tensors containing time-series, spatial, and feature sub-tensors for subsequent optimization analysis.

[0163] Exemplarily, an application scenario of the decomposition of line loss feature tensor of a certain provincial power grid includes:

[0164] Step 1: Data Preparation and Tensor Construction

[0165] A certain provincial power grid includes 5 main substations (S1 - S5), 72-hour (3 days) line loss data, and 8 feature dimensions (line loss rate, load rate, three-phase unbalance degree, temperature, humidity, voltage deviation, power factor, harmonic distortion rate).

[0166] 1. Time Dimension Division: Divide the 72 hours into 72 time windows at an hourly granularity, and calculate the mean value of each feature for each window.

[0167] 2. Spatial Dimension Division: Divide it into 5 regions (S1 - S5) according to the jurisdiction scope of the substations.

[0168] 3. Feature Dimension Definition: After standardization processing, the 8 feature dimensions are mapped to the range of [0, 1].

[0169] 4. Tensor filling: Construct a three-dimensional tensor of size 72×5×8, and fill the missing data (such as the power outage of S3 from 1:00 to 2:00 in the early morning) using spatio-temporal Kriging interpolation.

[0170] Step 2: CP decomposition and feature separation

[0171] 1. Decomposition parameter setting:

[0172] The decomposition rank R = 6 (determined by cross-validation), and L1 regularization (λ = 0.1) is added. The ALS algorithm is implemented using the TensorLy library in Python, with a maximum of 100 iterations and a convergence threshold of ΔRMSE < 0.1%.

[0173] 2. Decomposition process:

[0174] After the first iteration, RMSE = 15.3%, after the 20th iteration, RMSE = 5.1%, after the 50th iteration, RMSE = 4.6%, and finally it converges. The decomposition rank is R = 6, so all factor matrices contain 6 columns, and the specific corresponding relationships are shown in Table 3 below:

[0175] Table 3

[0176]

[0177]

[0178] Among them, in the time series factor matrix A:

[0179] The first column shows an obvious 24-hour periodic fluctuation (with peaks at 18:00 - 20:00), representing the daily load cycle; the second column shows a 7-day periodic trend (the load increases from the first day to the third day), representing the weekly load pattern.

[0180] In the spatial factor matrix B:

[0181] The weight of the first column in the S2 area is significantly higher than that in other areas, corresponding to the known high-loss suburban lines; the weight of the third column is prominent in the S4 area, corresponding to the harmonic distortion problem in the industrial area.

[0182] In the feature factor matrix C:

[0183] The first column is strongly correlated with "line loss rate" and "load rate"; the fourth column is correlated with "temperature" and "humidity", reflecting the influence of environmental factors.

[0184] Step 3: Verification of decomposition results

[0185] 1. Reconstruction error evaluation: The RMSE of the reconstructed tensor = 4.6% (< 5% threshold), determining that the decomposition is effective.

[0186] 2. Space-time correlation verification: The correlation coefficient between the time-series sub-tensor 1 and the historical daily load curve is 0.89, and the correlation coefficient between the time-series sub-tensor 2 and the weekly load plan is 0.82.

[0187] In the spatial sub-tensor 1, the weight proportion of the line loss rate in the S2 area is 35%, which is consistent with the high-loss report of on-site detection.

[0188] The burst sub-tensor detected an abnormal peak at the 48th hour (thunderstorm weather in the S3 area), which matches the actual fault record.

[0189] 3. Output of the sub-tensor set:

[0190] Generate 6 sub-tensors (R = 6), labeled as "daily cycle time-series", "weekly trend time-series", "high-loss space", "industrial harmonic space", "load-loss characteristics", "environmental correlation characteristics".

[0191] Store as an HDF5 file, with additional metadata: "decomposition time 2023-10-01", "RMSE = 4.6%", "correlation coefficient ≥ 0.8".

[0192] Step 4: Application and value

[0193] This sub-tensor set is input into the subsequent distributed optimization module, for example:

[0194] The time-series sub-tensor is used to predict the line loss trend in the next 24 hours;

[0195] The spatial sub-tensor guides the line transformation for the S2 area;

[0196] The burst sub-tensor triggers the preventive maintenance strategy during the thunderstorm season.

[0197] Through the decomposition results, grid managers can accurately locate the root cause of line loss, formulate differentiated correction plans, and are expected to reduce the overall line loss rate by 15% - 20%.

[0198] S203, use the distributed optimization algorithm to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set. Among them, the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes;

[0199] Use the distributed optimization algorithm to perform parallel optimization on the sub-tensors, and achieve multi-objective collaborative optimization through edge computing nodes. Each node processes the sub-tensors of a specific spatial area, and finally integrates to form an optimized line loss feature set. Using distributed computing improves the optimization efficiency and ensures the real-time processing ability of large-scale grid data. Multi-objective collaborative optimization balances the contradictions between different space-time characteristics and obtains the globally optimal line loss feature set.

[0200] Specifically, multiple optimization objectives can be defined according to the set of sub-tensors, and multiple objective optimization problems can be generated through the Pareto optimal frontier theory;

[0201] Define multiple optimization objectives according to the characteristics of sub-tensors (such as minimizing line loss, balancing regional differences, etc.), and establish a multi-objective optimization problem based on the Pareto optimal theory. Transform the line loss correction into a quantifiable multi-objective optimization problem, and balance the trade-off relationship between different optimization objectives through the Pareto frontier.

[0202] Divide the sub-tensors according to the spatial dimension and allocate them to the edge computing nodes. Each node is responsible for a spatial region, and through the consistent hashing algorithm, ensure load balancing and task fault tolerance;

[0203] Partition the sub-tensors according to the spatial dimension and allocate them to the edge computing nodes through the consistent hashing algorithm to achieve load balancing and fault tolerance processing. Use edge computing to achieve distributed parallel optimization, significantly improving the computing efficiency. Intelligent task allocation ensures load balancing of each node and enhances the robustness of the system.

[0204] At each edge node, use the alternating direction multiplier method to solve the corresponding objective optimization problem in parallel, and at the same time coordinate the results between nodes through global consistency constraints. Through the asynchronous communication mechanism, generate preliminary optimized sub-tensors;

[0205] At each edge node, use the ADMM algorithm to solve in parallel, coordinate the node results through global consistency constraints, and use the asynchronous communication mechanism to improve efficiency. Distributed optimization not only ensures local computing autonomy but also ensures global consistency through the coordination mechanism. Asynchronous communication reduces waiting time and improves the overall computing speed.

[0206] For the preliminary optimized sub-tensors, use the weighted aggregation algorithm to integrate the optimization results of each edge node, and through the robustness test, generate the final optimized line loss feature set.

[0207] Perform weighted aggregation on the node optimization results, exclude outliers through the robustness test, and generate the final optimized feature set. Integrate the distributed optimization results to ensure the stability and reliability of the output. The robustness test ensures that the final result is not affected by the anomalies of individual nodes.

[0208] I. Definition of Multi-Objective Optimization Problem and Construction of Pareto Model

[0209] According to the set of sub-tensors, define multiple optimization objectives, and generate multi-objective optimization problems through the Pareto optimal frontier theory. The specific implementation method is as follows:

[0210] 1. Objective Definition and Quantification:

[0211] Objective 1 (Minimizing line loss rate): The weighted average of the line loss rates of each region is used as the objective function, with the weight being the proportion of the regional electricity consumption. For example, if the electricity consumption in Region A accounts for 30% of the total network, the weight of its line loss rate is 0.3.

[0212] Objective 2 (Regional load balancing): The difference between the maximum regional line loss rate and the minimum regional line loss rate is used as the objective function to ensure that the difference between regions ≤ 2%.

[0213] Objective 3 (Suppressing sudden fluctuations): The total fluctuation intensity of the sudden sub-tensor is used as the objective function, and it is statistically analyzed through a sliding window (e.g., the number of fluctuations per hour ≤ 3 times).

[0214] Constraints: Include physical rules such as line capacity limits (e.g., current ≤ 500A), voltage deviation (≤ 5%), power factor (≥ 0.9), etc.

[0215] 2. Pareto optimal front modeling:

[0216] Non-dominated solution set generation: Use NSGA-II (Non-dominated Sorting Genetic Algorithm) to optimize multiple objectives. The algorithm parameters include population size (e.g., 200 individuals), crossover probability (0.8), and mutation probability (0.1).

[0217] Frontier screening strategy: Select solutions from the solution set that satisfy all constraints and are non-dominant to form the Pareto front. For example, a certain solution may satisfy a 12% reduction in line loss rate and a 1.8% regional difference, but the effect of suppressing sudden fluctuations is average.

[0218] 3. Model verification and adjustment:

[0219] Sensitivity analysis: By adjusting the objective weights (e.g., the line loss rate weight increases from 0.5 to 0.7), observe the changes in the Pareto front to ensure the robustness of the model.

[0220] Physical feasibility pre-check: Perform a pre-verification of the power flow calculation for the front solutions to eliminate solutions that cause voltage violations or line overloads.

[0221] II. Distributed task allocation and load balancing

[0222] The sub-tensor is divided according to the spatial dimension and assigned to the edge computing nodes. The specific implementation method is as follows:

[0223] 1. Spatial segmentation of sub-tensor:

[0224] Regional division rule: According to the weight distribution of the spatial sub-tensor, the high-weight regions (e.g., line loss rate > 5%) are preferentially assigned to the high-performance edge nodes. For example, Region S2 (high-loss suburb) is assigned to the node equipped with GPU acceleration.

[0225] Data Chunk Format: Each sub-tensor data chunk contains time series, feature vectors, and metadata (such as region ID, decomposition rank), and is stored in Parquet format to improve reading efficiency.

[0226] 2. Implementation of Consistent Hashing Algorithm:

[0227] Virtual Node Mapping: Map edge nodes (such as Node1 - Node5) to the hash ring (0 - 2 32 -1), and each node corresponds to multiple virtual nodes (such as 1000) to ensure load balancing.

[0228] Data Chunk Allocation: Allocate the sub-tensor based on the hash value of the region ID to the nearest virtual node. For example, the hash value of region S3 is 1987654321, and it is allocated to the virtual node under the jurisdiction of Node2.

[0229] Fault Tolerance Mechanism: If a node fails (such as Node3 goes down), its virtual nodes are taken over by adjacent nodes (Node4), and the data is automatically migrated.

[0230] 3. Task Assignment Verification:

[0231] Load Monitoring: Monitor the CPU / memory usage rate of each node through Prometheus to ensure load balancing (such as the difference between nodes ≤ 15%).

[0232] Data Integrity Verification: Use CRC32 checksum to verify the integrity of the transmitted sub-tensor data.

[0233] III. Edge Node Parallel Optimization and ADMM Solution

[0234] At each edge node, use the Alternating Direction Method of Multipliers (ADMM) to solve the objective optimization problem in parallel.

[0235] The specific implementation method is as follows:

[0236] 1. ADMM Framework Design:

[0237] Variable Splitting: Separate global variables (such as the overall network line loss rate) from local variables (such as the regional line loss rate). For example, define the global consistency variable z (representing the average value of the overall network line loss rate) and the local variable x_i (representing the line loss rate of region i).

[0238] Alternating Update Rule:

[0239] Local Optimization: Each node updates x_i to minimize the local objective (such as the regional line loss rate) and satisfy local constraints.

[0240] Global Coordination: All nodes submit x_i to the coordination center to update the global variable

[0241] Lagrange multiplier update: Adjust the multiplier according to the deviation between \(x_i\) and \(z\) to strengthen the consistency.

[0242] 2. Parallel computing implementation:

[0243] Local solver selection: At each edge node, use IPOPT (Interior Point Optimization Library) to solve the local optimization problem, supporting the handling of non-linear constraints.

[0244] Asynchronous communication mechanism: Nodes exchange data through the RabbitMQ message queue, allowing some nodes to delay updates (e.g., tolerate ≤ 10% node delay).

[0245] 3. Convergence guarantee:

[0246] Residual monitoring: Define the residual \(r = ||x_i - z||^2\), and terminate the calculation when the residual < threshold (e.g., 1e-4) or the number of iterations exceeds the limit (e.g., 100 times).

[0247] Dynamic step size adjustment: Adaptively adjust the ADMM step size according to the residual change rate (e.g., halve the step size when the residual increases).

[0248] IV. Aggregation of optimization results and robustness test

[0249] Perform weighted aggregation and robustness test on the preliminary optimized sub-tensors. The specific implementation methods are as follows:

[0250] 1. Weighted aggregation algorithm:

[0251] Weight definition: Allocate weights according to the proportion of electricity consumption in each region (e.g., Region A accounts for 30%, weight 0.3), ensuring that high-load regions have a greater impact.

[0252] Aggregation calculation: For each optimized sub-tensor (e.g., line loss rate, load balance degree), calculate the weighted average. For example, the line loss rate in Region A is 4%, and the line loss rate in Region B is 5%. The weighted average line loss rate of the whole network = 0.3×4% + 0.7×5% = 4.7%.

[0253] 2. Robustness test method:

[0254] Monte Carlo simulation: Randomly perturb the input data (e.g., ±5% load fluctuation), run 1000 simulations, and statistically analyze the stability of the optimization results (e.g., the line loss rate fluctuation ≤ 0.5%).

[0255] Extreme scenario test: Simulate extreme events (e.g., a power outage in a certain region) to verify whether the optimization scheme still meets the constraints (e.g., the line loss rate in other regions ≤ 6%).

[0256] 3. Generation of final results:

[0257] Data Formatting: Store the optimized line loss feature set in JSON format, including fields: region ID, optimized line loss rate, load balance degree, burst suppression rate, confidence interval.

[0258] Visualization Report: Generate a dynamic dashboard through Grafana to display the comparison of optimization effects and historical trends in each region.

[0259] A complete example of multi-objective optimization for a certain city's power grid is as follows:

[0260] Step 1: Problem Definition and Data Preparation

[0261] A certain city's power grid is divided into 5 regions (S1 - S5), including the following sub-tensors:

[0262] Temporal Sub-tensor: Line loss rate and load rate time series data for 72 hours (R = 6 decomposition rank).

[0263] Spatial Sub-tensor: Line loss characteristic weights for 5 regions (S2 high-loss weight 0.35, S4 harmonic weight 0.28).

[0264] Feature Sub-tensor: Strong correlation between line loss rate and load rate (weight 0.6).

[0265] Step 2: Task Allocation and Edge Computing

[0266] 1. Sub-tensor Allocation:

[0267] Use the consistent hashing algorithm to allocate S1 - S5 to 3 edge nodes (Node1 - Node3), where S2 and S4 are allocated to Node3 (high-performance node).

[0268] Data Block Size: Each regional sub-tensor is approximately 50MB, and the total data volume is 250MB.

[0269] 2. ADMM Parameter Settings:

[0270] Local Solver: IPOPT (maximum iteration 100 times, tolerance error 1e-5).

[0271] Communication Protocol: MQTT topic subscription (e.g., Node1 subscribes to "global line loss rate update").

[0272] Step 3: Parallel Optimization Process

[0273] 1. Local Optimization Example (Node3 - S2 Region):

[0274] Objective Function: Minimize the line loss rate (weight 0.5) and burst fluctuations (weight 0.3), with constraints of current ≤ 450A and voltage deviation ≤ 4%.

[0275] Solution result: The line loss rate drops from 5.2% to 4.1%, and the sudden fluctuation events drop from 7 times per day to 3 times per day.

[0276] 2. Global coordination and update:

[0277] The coordination center aggregates the line loss rates of each node: S1: 3.8%, S2: 4.1%, S3: 4.3%, S4: 4.5%, S5: 3.9%.

[0278] Calculate the global mean value z = 4.12% and broadcast it to all nodes.

[0279] 3. Convergence determination:

[0280] The residual of the 10th iteration = 0.08, the residual of the 20th iteration = 0.02, the residual of the 25th iteration = 0.005 (< the threshold 0.01), terminate the calculation.

[0281] Step 4: Result aggregation and verification

[0282] 1. Weighted aggregation:

[0283] The electricity consumption weights of each region: S1 (20%), S2 (30%), S3 (15%), S4 (25%), S5 (10%).

[0284] The weighted average line loss rate of the whole network = 3.8% × 0.2 + 4.1% × 0.3 +... = 4.07%.

[0285] 2. Robustness test:

[0286] The Monte Carlo simulation shows that the 95% confidence interval is [3.9%, 4.3%], meeting the requirement of ≤ 4.5%.

[0287] In the extreme test, when S2 is powered off, the maximum line loss rate in other regions is 5.1% (still ≤ 6% constraint).

[0288] 3. Output and application:

[0289] Generate an optimized line loss feature set to guide the power grid adjustment measures:

[0290] Region S2: Replace the aging lines (expected to reduce losses by 1.2%).

[0291] Region S4: Install a harmonic filter (expected to reduce losses by 0.8%).

[0292] It is expected that the line loss rate of the whole network will drop from 4.7% to 4.0%, saving about 1.2 million yuan in electricity bills annually.

[0293] Beneficial effects:

[0294] 1. Advantages of distributed architecture: Through parallel computing of edge nodes, the optimization time-consuming is shortened from 8 hours in the centralized mode to 2 hours.

[0295] 2. Multi-objective coordination: Pareto front screening ensures the comprehensive optimization of line loss rate, balance degree, and burst suppression.

[0296] 3. Robustness guarantee: Monte Carlo simulation and extreme tests provide reliability endorsement for the implementation of the solution.

[0297] S204, perform physical rationality and data consistency screening on the optimized line loss feature set, determine several groups of final line loss correction parameters, and use them as the execution basis for power grid line loss correction.

[0298] Perform physical rationality and data consistency screening on the optimized features, exclude the results that do not conform to the physical laws of the power grid through constraint conditions, and finally determine the set of line loss parameters that can be used for actual correction. Ensure the physical realizability and engineering applicability of the correction parameters, and avoid non-physical solutions that may be generated by pure data-driven methods. The screened parameters can directly guide the power grid line loss correction operation and improve the feasibility of the solution implementation.

[0299] Specifically, according to the optimized line loss feature set, construct constraint conditions using the physical rules of the power grid, and through a mixed-integer programming model, eliminate the parameter combinations that violate the physical laws, and generate a preliminary candidate parameter set;

[0300] This step first constructs constraint conditions based on the physical rules of the power grid (such as Kirchhoff's law, power balance equation, etc.), and performs preliminary screening on the optimized line loss feature set through a mixed-integer programming model. This step transforms the physical laws of power grid operation into mathematical constraints to ensure that the parameter combinations conform to the basic operation principles of the power grid. Fundamentally ensure the physical realizability of the line loss correction parameters and avoid unreasonable solutions that violate the basic operation laws of the power grid. The mixed-integer programming model can effectively handle discrete and continuous variables to ensure that the screening results satisfy both physical constraints and maintain mathematical optimality.

[0301] For the candidate parameter set, use distribution consistency analysis based on KL divergence, compare the distribution of historical line loss data, and through anomaly detection algorithms, eliminate the parameters that deviate from the normal mode to generate a refined parameter set;

[0302] Use KL divergence (Kullback-Leibler divergence) to analyze the distribution differences between the candidate parameter set and historical line loss data, and identify and eliminate the parameter combinations that deviate from the normal statistical mode through anomaly detection algorithms. This step establishes a data-driven screening mechanism. Ensure that the correction parameters are statistically consistent with the historical operation characteristics of the power grid and avoid abnormal parameters generated during the optimization process. KL divergence quantifies the parameter distribution differences, and anomaly detection algorithms can effectively identify statistical outliers and improve the reliability of the parameter set.

[0303] For the refined parameter set, the TOPSIS multi-criteria decision-making algorithm is used to rank the parameters in combination with economic, feasibility, and effectiveness indicators. Through expert weight allocation, a priority parameter sequence is generated.

[0304] Apply the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) multi-criteria decision-making algorithm to evaluate the parameters considering three dimensions: economic cost, engineering feasibility, and expected effect. Quantify the importance differences of each dimension through an expert weight allocation mechanism to generate a priority ranking. Achieve the balance between technical indicators and engineering practice to ensure that the selected parameters have both theoretical superiority and implementation feasibility. The TOPSIS algorithm avoids the one-sidedness of single-index evaluation, and the introduction of expert weights incorporates domain knowledge, making the ranking more valuable for engineering guidance.

[0305] For the priority parameter sequence, use Monte Carlo simulation to verify the parameter effectiveness, and through a version control mechanism, output the final line loss correction parameters.

[0306] Perform Monte Carlo simulation verification on the priority parameters, simulate the parameter performance under different operating scenarios, manage the parameter iteration process through a version control mechanism, and finally output the comprehensively verified line loss correction parameters. Verify the robustness and adaptability of the parameters through random simulation to ensure good performance under actual complex operating conditions. Version control enables traceable management of parameters and provides an optimally verified solution for engineering implementation.

[0307] I. Physical Constraint Filtering and Candidate Parameter Generation

[0308] Based on the optimized line loss feature set, use power grid physical rules to construct constraint conditions, and eliminate parameter combinations that violate physical laws through a mixed-integer programming model. The specific implementation methods are as follows:

[0309] 1. Definition of physical rules:

[0310] Kirchhoff's law constraint: Ensure that the input current of the power grid node is equal to the output. For example, if the input current of a substation is 1000A, the sum of the branch line currents must be equal to 1000A.

[0311] Line capacity limit: The current of each line shall not exceed its rated capacity (e.g., the maximum current of line L1 is 500A).

[0312] Voltage deviation constraint: The voltage deviation of all nodes shall not exceed ±5% (e.g., for a nominal voltage of 10kV, the actual voltage shall be between 9.5kV and 10.5kV).

[0313] 2. Mixed-integer programming (MIP) modeling:

[0314] Variable Definition: Set the line loss correction parameters (such as line impedance compensation value, transformer tap position) as continuous variables or integer variables. For example, the tap position is an integer (tap positions 1 - 5), and the impedance compensation value is a continuous variable (±10%).

[0315] Objective Function: Minimize the total correction cost, such as line transformation cost + equipment adjustment cost.

[0316] Constraints: Convert physical rules into mathematical constraints, such as converting "the current of line L1 ≤ 500A" into a linear inequality.

[0317] 3. Model Solving and Filtering:

[0318] Solver Selection: Use Gurobi or CPLEX solver to handle the MIP model, and set the solving time limit (such as 2 hours) and the optimal gap (≤1%).

[0319] Result Screening: Eliminate the solutions that violate the constraints (such as in a certain solution, the current of line L1 = 520A), and retain the feasible solutions as the candidate parameter set.

[0320] Example: After optimizing a certain power grid, 10 groups of parameter combinations are proposed. After MIP filtering, 3 groups are eliminated (current exceeding the limit or voltage deviation exceeding the standard), and the remaining 7 groups enter the next step.

[0321] II. Data Consistency Check and Parameter Refinement

[0322] Conduct distribution consistency analysis based on KL divergence for the candidate parameter set, and combine with anomaly detection algorithms to eliminate the parameters that deviate from the normal mode. The specific implementation methods are as follows:

[0323] 1. KL Divergence Analysis:

[0324] Construction of Historical Data Distribution: Statistically analyze the distribution of line loss parameters in the past year (such as the impedance compensation value is mainly concentrated between -5% and +5%).

[0325] Comparison of Candidate Parameter Distributions: Calculate the KL divergence (a measure of difference) between the candidate parameter set and the historical distribution, and set a threshold (such as KL ≤ 0.1).

[0326] Anomaly Marking: Mark the parameters with KL divergence exceeding the limit (such as a certain parameter suggests an impedance compensation of +15%, far exceeding the historical range).

[0327] 2. Isolation Forest Anomaly Detection:

[0328] Feature Selection: Extract the numerical features of the candidate parameters (such as impedance compensation value, tap position, expected loss reduction rate).

[0329] Model Training: Use historical normal parameters to train the isolation forest model (number of trees = 100, number of samples = 256).

[0330] Abnormal score: Perform an abnormal score (0 - 1) on the candidate parameters, and eliminate the parameters with a score > 0.6.

[0331] Example: Among 7 groups of candidate parameters, 2 groups were eliminated due to exceeding the KL divergence (KL = 0.15) and an isolation forest score > 0.7, and the remaining 5 groups entered the refined parameter set.

[0332] III. Multi-criteria Decision-making and Priority Ranking

[0333] Apply the TOPSIS multi-criteria decision-making algorithm to the refined parameter set and rank them in combination with economic, feasibility, and effectiveness indicators. The specific implementation method is as follows:

[0334] 1. Definition of evaluation indicators:

[0335] Economy: The transformation cost (in ten thousand yuan), such as the line transformation cost and equipment procurement cost.

[0336] Feasibility: The implementation difficulty score (1 - 5 points, 1 = easy, 5 = difficult), based on the construction period and technical complexity.

[0337] Effect: The expected percentage reduction in line loss, such as from 5% to 4.2%.

[0338] 2. TOPSIS algorithm process:

[0339] Data standardization: Normalize each indicator (e.g., take the reciprocal of the cost and make the reduction percentage positive).

[0340] Weight assignment: Determine the weights through the expert scoring method (economy 40%, feasibility 30%, effect 30%).

[0341] Ideal solution calculation: Determine the optimal values of each indicator (lowest cost, lowest difficulty, largest reduction).

[0342] Distance ranking: Calculate the Euclidean distance between each parameter and the ideal solution, and arrange them in ascending order of distance.

[0343] 3. Priority generation:

[0344] Result output: Generate a parameter priority list, such as Table 4:

[0345] Table 4

[0346] Parameter ID Economy (10,000 yuan) Feasibility (points) Effect (reduction percentage%) Priority P3 50 2 0.8％ 1 P5 80 1 1.2％ 2 P1 120 3 1.5％ 3

[0347] Example: Parameter P3 ranked first due to its low cost (500,000 yuan), easy implementation (2 points), and medium effect (0.8%).

[0348] IV. Parameter Verification and Final Generation

[0349] Perform Monte Carlo simulation verification on the priority parameter sequence and output the final parameters through a version control mechanism. The specific implementation method is as follows:

[0350] 1. Monte Carlo simulation design:

[0351] Perturbation factors: load fluctuation (±10%), ambient temperature change (±5°C), equipment aging (±3% performance decay).

[0352] Number of simulations: 1000 times, record indicators such as line loss rate and voltage deviation for each simulation.

[0353] Success rate calculation: the proportion of simulations that meet all constraints (e.g., a qualified success rate is ≥90%).

[0354] 2. Version control and output:

[0355] Parameter versioning: Generate a unique version number for each set of parameters (e.g., V1.2.3) and attach metadata (simulation results, effective time).

[0356] Rollback mechanism: If a failure occurs after the new parameters are put online, they can be quickly switched to the historical stable version (e.g., V1.1.0).

[0357] Example: Parameter P3 passes the simulation verification with a success rate of 92%, and the output is "V2.0.1_Parameter P3", which is then deployed to the power grid in Area S2.

[0358] A complete example of parameter screening and decision-making for a certain regional power grid is as follows:

[0359] Step 1: Physical constraint filtering

[0360] A certain power grid optimization generates 10 groups of candidate parameters, and some of the parameters are shown in Table 5 below:

[0361] Table 5

[0362] Parameter ID Impedance compensation Tap position Expected loss reduction Current (A) Voltage deviation P1 +8％ 3 1.5％ 480 +4.2％ P2 +12％ 4 2.1％ 520 +5.3％ P3 +5％ 2 0.8％ 460 +3.8％

[0363] 1. MIP model construction:

[0364] Objective function: Min (cost) = line transformation cost + tap adjustment cost.

[0365] Constraints: current ≤ 500A, voltage deviation ≤ 5%.

[0366] 2. Solving and filtering:

[0367] Parameter P2 is excluded due to a current of 520A (>500A) and a voltage deviation of 5.3%.

[0368] Remaining parameters: P1, P3, P4 - P10 (a total of 7 groups).

[0369] Step 2: Data Consistency Check

[0370] 1. KL Divergence Analysis:

[0371] Historical Impedance Compensation Distribution: Mean 0%, Standard Deviation 3%.

[0372] A compensation of +8% for parameter P1 results in KL = 0.15 (> threshold 0.1) and is marked as abnormal.

[0373] 2. Isolation Forest Detection:

[0374] The anomaly score of parameter P1 is 0.75 (> 0.6) and it is excluded.

[0375] Remaining parameters: P3, P4 - P10 (a total of 6 groups).

[0376] Step 3: Multi - Criteria Decision - Making Ranking

[0377] 1. Index Assignment as shown in Table 6:

[0378] Table 6

[0379] Parameter ID Economy (10,000 yuan) Feasibility (points) Effect (loss reduction%) P3 50 2 0.8％ P5 80 1 1.2％ P7 120 3 1.5％

[0380] 2. TOPSIS Calculation:

[0381] Ideal Solution: Economy = 500,000, Feasibility = 1 point, Effect = 1.5%.

[0382] The distance of P3 from the ideal solution is 0.12 (the smallest), ranking first.

[0383] Step 4: Monte Carlo Simulation Verification

[0384] 1. Simulation Settings:

[0385] Perturbation Range: Load ±10%, Temperature ±5°C, Equipment Aging ±3%.

[0386] Success Rate Threshold: ≥90%.

[0387] 2. Result Analysis:

[0388] The simulation success rate of parameter P3 is 92% (926 successful times out of 1000), meeting the requirements.

[0389] The success rate of parameter P5 is 88%, not meeting the standard and needs to be re - optimized.

[0390] Step 5: Parameter Deployment and Effect

[0391] 1. Version Release: Parameter P3 is marked as "V2.0.1_Suburban Line Loss Optimization" and deployed to Area S2.

[0392] 2. Actual effect:

[0393] The line loss rate drops from 5.1% to 4.3%, saving about 800,000 yuan in electricity costs annually.

[0394] The voltage deviation is stabilized within ±4%, and there are no over-limit events.

[0395] Beneficial effects:

[0396] 1. Physical-data dual-driven screening: By combining MIP and KL divergence, ensure that the parameters simultaneously meet physical feasibility and historical laws.

[0397] 2. Multi-dimensional decision support: The TOPSIS algorithm quantifies the trade-off of economy, feasibility, and effect, improving the scientificity of decision-making.

[0398] 3. Simulation verification guarantee: Monte Carlo tests cover extreme scenarios, reducing the risk of scheme implementation.

[0399] It can be seen that the original line loss data collected by the receiving power grid system is received, and a set of initial line loss feature sets are generated based on the original line loss data; spatio-temporal feature mapping is performed on the initial line loss feature sets to construct a line loss feature tensor, and the line loss feature tensor is decomposed into several sub-tensors to capture different spatio-temporal characteristics of the line loss; a distributed optimization algorithm is used to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set, where the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes; physical rationality and data consistency screening are performed on the optimized line loss feature set to determine several sets of final line loss correction parameters as the execution basis for power grid line loss correction, so as to be able to achieve accurate and efficient line loss correction analysis and improve the accuracy and practicality of power grid line loss management.

[0400] Another embodiment of the present invention provides a line loss correction analysis system. Refer to Figure 3 , the system may include:

[0401] A receiving module 301, configured to receive the original line loss data collected by the power grid system, and generate a set of initial line loss feature sets based on the original line loss data, where each initial line loss feature is associated with the feature dimension of power grid operation;

[0402] A decomposition module 302, configured to perform spatio-temporal feature mapping on the initial line loss feature sets, construct a line loss feature tensor, and decompose the line loss feature tensor into several sub-tensors to capture different spatio-temporal characteristics of the line loss;

[0403] An optimization module 303, configured to use a distributed optimization algorithm to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set, where the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes;

[0404] A determination module 304 is configured to perform physical rationality and data consistency screening on the optimized line loss feature set, and determine several groups of final line loss correction parameters as the execution basis for power grid line loss correction.

[0405] It can be seen that the original line loss data collected by the power grid system is received, and an initial line loss feature set is generated based on the original line loss data; spatio-temporal feature mapping is performed on the initial line loss feature set to construct a line loss feature tensor, and the line loss feature tensor is decomposed into several sub-tensors to capture different spatio-temporal characteristics of the line loss; a distributed optimization algorithm is used to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set, where the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes; physical rationality and data consistency screening are performed on the optimized line loss feature set to determine several groups of final line loss correction parameters as the execution basis for power grid line loss correction, so as to achieve accurate and efficient line loss correction analysis and improve the accuracy and practicality of power grid line loss management.

[0406] An embodiment of the present invention further provides a storage medium, in which a computer program is stored, and the computer program is configured to execute the steps in any one of the above method embodiments when running.

[0407] Specifically, in this embodiment, the above storage medium can be configured to store a computer program for executing the following steps:

[0408] S201, receiving the original line loss data collected by the power grid system, and generating an initial line loss feature set based on the original line loss data, where each initial line loss feature is associated with a feature dimension of power grid operation;

[0409] S202, performing spatio-temporal feature mapping on the initial line loss feature set, constructing a line loss feature tensor, and decomposing the line loss feature tensor into several sub-tensors to capture different spatio-temporal characteristics of the line loss;

[0410] S203, using a distributed optimization algorithm to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set, where the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes;

[0411] S204, performing physical rationality and data consistency screening on the optimized line loss feature set, and determining several groups of final line loss correction parameters as the execution basis for power grid line loss correction.

[0412] It can be seen that the original line loss data collected by the power grid system is received, and a set of initial line loss feature sets are generated based on the original line loss data; spatio-temporal feature mapping is performed on the initial line loss feature sets to construct a line loss feature tensor, and the line loss feature tensor is decomposed into several sub-tensors to capture different spatio-temporal characteristics of the line loss; a distributed optimization algorithm is used to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set, wherein the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes; physical rationality and data consistency screening are performed on the optimized line loss feature set to determine several sets of final line loss correction parameters as the execution basis for power grid line loss correction, so as to achieve accurate and efficient line loss correction analysis and improve the accuracy and practicality of power grid line loss management.

[0413] An embodiment of the present invention further provides an electronic device, including a memory and a processor, wherein a computer program is stored in the memory, and the processor is configured to run the computer program to execute the steps in any one of the above method embodiments.

[0414] Specifically, the above electronic device may further include a transmission device and an input / output device, wherein the transmission device is connected to the above processor, and the input / output device is connected to the above processor.

[0415] Specifically, in this embodiment, the above processor may be configured to execute the following steps through a computer program:

[0416] S201, receive the original line loss data collected by the power grid system, and generate a set of initial line loss feature sets based on the original line loss data, wherein each initial line loss feature is associated with a feature dimension of power grid operation;

[0417] S202, perform spatio-temporal feature mapping on the initial line loss feature sets, construct a line loss feature tensor, and decompose the line loss feature tensor into several sub-tensors to capture different spatio-temporal characteristics of the line loss;

[0418] S203, use a distributed optimization algorithm to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set, wherein the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes;

[0419] S204, perform physical rationality and data consistency screening on the optimized line loss feature set to determine several sets of final line loss correction parameters as the execution basis for power grid line loss correction.

[0420] It can be seen that the original line loss data collected by the power grid system is received, and a set of initial line loss feature sets are generated based on the original line loss data; the initial line loss feature sets are subjected to spatio-temporal feature mapping to construct a line loss feature tensor, and the line loss feature tensor is decomposed into several sub-tensors to capture different spatio-temporal characteristics of the line loss; a distributed optimization algorithm is used to perform multi-objective collaborative optimization on the sub-tensors to generate an optimized line loss feature set, wherein the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes; the optimized line loss feature set is screened for physical rationality and data consistency to determine several sets of final line loss correction parameters as the execution basis for power grid line loss correction, so as to be able to achieve accurate and efficient line loss correction analysis and improve the accuracy and practicality of power grid line loss management.

[0421] The above has detailedly described the structure, features and function effects of the present invention according to the illustrated embodiments. The above is only the preferred embodiment of the present invention, but the present invention is not limited to the scope defined by the drawings. Any changes made according to the concept of the present invention, or equivalent embodiments modified into equivalent changes, should still be within the protection scope of the present invention when they do not exceed the spirit covered by the specification and the drawings.

Claims

1. A line loss correction analysis method, characterized in that The method includes: Receiving the original line loss data collected by the power grid system, and generating an initial set of line loss features based on the original line loss data, where each initial line loss feature is associated with a characteristic dimension of the power grid operation; Performing spatio-temporal feature mapping on the initial set of line loss features, constructing a line loss feature tensor, and decomposing the line loss feature tensor into several sub-tensors to capture different spatio-temporal characteristics of the line loss; Using a distributed optimization algorithm to perform multi-objective collaborative optimization on the sub-tensors, generating an optimized set of line loss features, where the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes; Performing physical rationality and data consistency screening on the optimized set of line loss features to determine several sets of final line loss correction parameters as the execution basis for power grid line loss correction.

2. The method according to claim 1, wherein The receiving the original line loss data collected by the power grid system, and generating an initial set of line loss features based on the original line loss data, where each initial line loss feature is associated with a characteristic dimension of the power grid operation, includes: According to the original line loss data collected by the power grid system, adopting a multi-source data fusion technology to align the heterogeneous data of the SCADA system, smart meters, and PMU devices, and generating a spatio-temporally synchronized original data set through a timestamp matching algorithm; For the spatio-temporally synchronized original data set, adopting a feature encoding method based on the power grid topology structure to map the electrical parameters of each line to the characteristic dimension, and generating a preliminary line loss feature vector through a feature weight allocation mechanism; For the preliminary line loss feature vector, adopting a feature selection algorithm based on mutual information, combining the power grid operation characteristics, screening out the features strongly related to the line loss, and generating the final initial set of line loss features through a non-linear dimensionality reduction technology.

3. The method according to claim 2, wherein The performing spatio-temporal feature mapping on the initial set of line loss features, constructing a line loss feature tensor, and decomposing the line loss feature tensor into several sub-tensors to capture different spatio-temporal characteristics of the line loss, includes: According to the initial set of line loss features, defining a three-dimensional tensor structure, where the time dimension of the three-dimensional tensor structure is divided by hour granularity, and the space dimension is divided by substation / line partition, generating a preliminary line loss feature tensor; Performing CP decomposition on the line loss feature tensor, decomposing it into a time series sub-tensor, a space sub-tensor, and a feature sub-tensor, and separating the periodic, regional, and sudden characteristics of the line loss through a sparse constraint term; For each decomposed sub-tensor, adopting a tensor reconstruction error evaluation to verify the decomposition effectiveness, and generating the final set of sub-tensors through spatio-temporal correlation analysis.

4. The method according to claim 3, characterized in that, The using a distributed optimization algorithm to perform multi-objective collaborative optimization on the sub-tensors, generating an optimized set of line loss features, where the distributed optimization algorithm parallelly optimizes each objective through edge computing nodes, includes: According to the set of sub-tensors, defining multiple optimization objectives, and generating multiple objective optimization problems through the Pareto optimal front theory; Dividing the sub-tensors by the space dimension and allocating them to edge computing nodes, with each node responsible for a space region, and ensuring load balancing and task fault tolerance through a consistent hashing algorithm. At each edge node, the alternating direction multiplier method is used to solve the corresponding objective optimization problem in parallel. Meanwhile, the results between nodes are coordinated through global consistency constraints, and a preliminary optimized sub-tensor is generated through an asynchronous communication mechanism. For the preliminary optimized sub-tensor, a weighted aggregation algorithm is used to integrate the optimization results of each edge node, and a final optimized line loss feature set is generated through robustness testing.

5. The method according to claim 4, wherein The physical rationality and data consistency of the optimized line loss feature set are screened to determine several groups of final line loss correction parameters as the execution basis for power grid line loss correction, including: According to the optimized line loss feature set, constraint conditions are constructed using power grid physical rules, and a preliminary candidate parameter set is generated by eliminating parameter combinations that violate physical laws through a mixed-integer programming model. For the candidate parameter set, distribution consistency analysis based on KL divergence is used to compare the historical line loss data distribution, and parameters deviating from the normal pattern are eliminated through an anomaly detection algorithm to generate a refined parameter set. For the refined parameter set, the TOPSIS multi-criteria decision-making algorithm is used to rank them in combination with economic, feasibility, and effectiveness indicators, and a priority parameter sequence is generated through expert weight assignment. For the priority parameter sequence, Monte Carlo simulation is used to verify the parameter effectiveness, and the final line loss correction parameters are output through a version control mechanism.

6. A line loss correction analysis system, characterized in that The system includes: A receiving module, which is used to receive the original line loss data collected by the power grid system, and generate an initial line loss feature set based on the original line loss data. Each initial line loss feature is associated with the feature dimension of the power grid operation. A decomposition module, which is used to perform spatio-temporal feature mapping on the initial line loss feature set, construct a line loss feature tensor, and decompose the line loss feature tensor into several sub-tensors to capture different spatio-temporal characteristics of the line loss. An optimization module, which is used to perform multi-objective collaborative optimization on the sub-tensors using a distributed optimization algorithm to generate an optimized line loss feature set. The distributed optimization algorithm optimizes each objective in parallel through edge computing nodes. A determination module, which is used to screen the physical rationality and data consistency of the optimized line loss feature set to determine several groups of final line loss correction parameters as the execution basis for power grid line loss correction.

7. The system according to claim 6, wherein The receiving module is specifically used for: According to the original line loss data collected by the power grid system, a multi-source data fusion technology is used to align the heterogeneous data of the SCADA system, smart meters, and PMU devices, and a spatio-temporally synchronized original data set is generated through a timestamp matching algorithm. For the spatio-temporally synchronized original data set, a feature encoding method based on the power grid topological structure is used to map the electrical parameters of each line to the feature dimension, and a preliminary line loss feature vector is generated through a feature weight assignment mechanism. For the preliminary line loss feature vector, a feature selection algorithm based on mutual information is used to screen out the features strongly related to the line loss in combination with the power grid operation characteristics, and a final initial line loss feature set is generated through a non-linear dimensionality reduction technology.

8. The system according to claim 7, wherein The decomposition module is specifically used for: According to the initial line loss feature set, a three-dimensional tensor structure is defined. Among them, the time dimension of the three-dimensional tensor structure is divided by hour granularity, and the space dimension is divided by substation / line partition to generate a preliminary line loss feature tensor; Perform CP decomposition on the line loss feature tensor, decompose it into a time series sub-tensor, a space sub-tensor and a feature sub-tensor, and separate the periodic, regional and sudden characteristics of the line loss through a sparse constraint term; For each decomposed sub-tensor, use tensor reconstruction error evaluation to verify the effectiveness of the decomposition, and generate a final sub-tensor set through spatio-temporal correlation analysis.

9. A storage medium, characterized in that, A computer program is stored in the storage medium, wherein the computer program is set to execute the method described in any one of claims 1-5 when running.

10. An electronic device, comprising a memory and a processor, characterized in that, A computer program is stored in the memory, and the processor is set to run the computer program to execute the method described in any one of claims 1-5.

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