Transient voltage stability rule mining method based on shapelet and inclined decision tree learning

Abstract

The method for transient voltage stability rule mining based on shapelet and inclined decision tree learning first mines a plurality of key local dynamic features related to a stable state from transient voltage time sequence samples to form a shapelet set with interpretability; then, constructs sample feature representation based on the shapelet set, and generates transient voltage stability decision rules by using inclined decision tree learning of a hierarchical decision relationship corresponding to the key time sequence features; finally, extracts, expresses and analyzes the generated decision rules in combination with the shapelet set and the inclined decision tree decision path to obtain key time sequence dynamic features related to transient voltage stability state and decision basis thereof. The method can extract key time sequence features with physical interpretability from transient voltage time sequence responses, mine clear transient voltage stability decision rules, and provide support for power system transient voltage stability mechanism analysis and auxiliary decision making.

Description

Technical Field

[0001] This invention relates to the field of transient voltage stability analysis technology in power systems, and in particular to a transient voltage stability rule mining method based on shapelet and skew decision tree learning. Background Technology

[0002] With the continuous expansion of new energy grid connection, the large-scale integration of power electronic equipment, and the increasingly complex dynamic characteristics of loads, the dynamic response process of modern power systems after large disturbances is more rapid and the coupling relationship is stronger, making transient voltage stability issues increasingly prominent. If the system cannot promptly restore sufficient voltage support capacity after fault clearing, time-series voltage instability may further expand, potentially even leading to widespread blackouts. Therefore, extracting physically interpretable key time-series dynamic features from the transient voltage response of the power system and developing clear and effective transient voltage stability decision rules has become a crucial technical issue supporting the analysis and decision-making for the safe and stable operation of the power grid.

[0003] Transient voltage stability in power systems involves multivariable dynamic response processes, exhibiting strong nonlinearity, time-varying characteristics, and coupling. Various transient voltage stability analysis methods have been proposed in existing technologies. Traditional methods typically rely on relatively sophisticated system models, but their ability to extract key dynamic information during transient responses is limited under complex operating modes and variable conditions. While data-driven methods can learn the discrimination rules of transient voltage stability states from samples, many existing methods employ neural networks, deep learning models, etc., whose internal discrimination mechanisms are not intuitive enough to clearly reveal the key time-series features on which the judgment results are based and their mechanisms of action. Furthermore, some methods use holistic modeling or compressed representations of transient time-series data, resulting in insufficient mining of key time-series features that are significant for post-fault discrimination. To enhance the interpretability of the analysis results, existing studies have also adopted models with transparent decision-making processes, such as decision trees. However, traditional decision trees usually use a single feature to split nodes. When dealing with high-dimensional transient time-series features, their ability to express the joint decision-making relationship of multiple features is limited. Therefore, it is difficult to effectively extract key time-series dynamic features related to the transient voltage steady state and form clear and interpretable decision rules. Summary of the Invention

[0004] To address the technical problems of insufficient extraction of key time-series features, weak rule mining capabilities, and lack of interpretability of decision-making basis in the current technology for power system transient voltage stability analysis, this invention provides a transient voltage stability rule mining method based on shapelet and skew decision tree learning.

[0005] To address the aforementioned technical problems, this invention employs the following technical method: a transient voltage stability rule mining method based on shapelet and skew decision tree learning, comprising: S1. Obtain transient voltage time series samples of the power system under disturbance, search for multiple key local dynamic features related to the transient voltage steady state, construct a shapelet set for extracting key time series features and a shapelet feature vector for feature representation of transient voltage time series samples. S2. Based on the shapelet feature vector and the corresponding transient voltage stability state label, a slanted decision tree model is constructed. The samples in the new feature space are divided by the slanted hyperplane. The hierarchical judgment relationship between the key time-series features representing the transient voltage stability state is learned. The feature combination weight, bias term and temperature parameter of each decision node are solved according to the node optimization objective function. The node splitting parameter is updated. The tree structure is determined by splitting layer by layer, and the slanted decision tree and its corresponding transient voltage stability decision rules are generated. S3, based on the decision path of shapelet set and oblique decision tree model, extracts, expresses and analyzes the generated transient voltage stability decision rules, and obtains the key time-series dynamic features related to the transient voltage stability state and their judgment basis.

[0006] Further, in step S2, the shapelet feature vector is matched with the corresponding transient voltage stability state label to construct a slanted decision tree learning sample set. The input is the shapelet feature vector of the sample, and the output is the corresponding transient voltage stability state label, which includes stable and unstable classes. Starting from the root node, the training samples contained in the current node are input into the slanted decision tree model. At the current node, a node splitting function is constructed using a linear combination of the input features. Based on the splitting function of the current node, the training samples arriving at that node are divided. Combining the sample class distribution of the divided child nodes, the change in node purity, and the improvement of the objective function, it is determined whether the current node meets the conditions for continued splitting. If the conditions for continued splitting are met, the corresponding child node is generated. If the conditions for continuing splitting are not met, splitting is stopped and the current node is set as a leaf node. The node parameter learning and sample partitioning process is repeated for each generated child node, recursively determining the splitting parameters of each decision node and the hierarchical connection relationship between parent and child nodes, until all nodes meet the preset stopping conditions, thereby completing the construction of the oblique decision tree structure. The stopping conditions include at least one of the following: the number of samples of the current node is lower than a preset threshold, the node purity reaches a preset threshold, the tree depth reaches the upper limit, or the improvement of the objective function brought by continuing splitting is lower than a preset threshold. After completing the learning of splitting parameters of all nodes and the determination of the tree structure, the splitting parameters, node hierarchical relationship, leaf node output category and sample decision path information of each decision node are retained to form an oblique decision tree and its decision path representation for transient voltage stability rule mining.

[0007] Furthermore, in step S2, the splitting function is expressed as: (1) in, Input features; For the feature combination weight vector, The number of input features, The first in the weight vector One component; For bias terms; A temperature-controlled soft partitioning mechanism is used in each decision node, and the weights of samples assigned to the left child nodes are determined. and the weights of the samples assigned to the right child nodes. They are represented as follows: (2) (3) in, For the Sigmoid function; For temperature parameters; Sample weights of the left child node The sum of sample weights of the right child node They are represented as follows: (4) (5) in, This represents the total number of samples in the current node. For the current node Input features of each sample; The objective function is constructed based on the weighted entropy of the left and right child nodes and the sparse regularization term, and is expressed as follows: (6) in, and These are the entropies of the left and right child nodes, respectively. For sparse regularization coefficients, For the feature combination weight vector Norm; By minimizing the objective function, the splitting parameters of each decision node are determined, and a slanted decision tree structure is generated by recursive splitting. The node splitting conditions from the root node to the leaf node are connected in series to obtain the corresponding transient voltage stability decision rules.

[0008] Furthermore, in step S3, the transient voltage stability decision rules are extracted, expressed, and analyzed using the key temporal features of the shapelet extracted in step S2 and the decision path of the oblique decision tree formed in step S4. Specifically, the node splitting conditions from the root node to the leaf node in the oblique decision tree are combined in the order of the path to form corresponding rule expressions. The key temporal feature combinations corresponding to each rule path and their impact on the determination of the transient voltage stability state are analyzed, thereby obtaining the key temporal dynamic features related to the transient voltage stability state and their determination basis.

[0009] Furthermore, in step S1, the transient voltage timing sample includes transient response data collected during actual operation and multivariate timing data obtained from simulation.

[0010] Furthermore, in step S1, before extracting key time-series features, the transient voltage time-series samples are preprocessed, including normalization, outlier handling, and label sorting, to form a standardized sample set for key time-series feature extraction and decision rule mining.

[0011] Preferably, in step S1, for the preprocessed transient voltage time series sample, multiple key time series features related to the transient voltage steady state are searched on each input feature dimension. The length range of the candidate shapelet is set, and candidate subsequences of different lengths are traversed within this length range. Candidate shapelets are extracted for each input feature dimension to obtain the overall candidate shapelet set. Then, the candidate shapelets and the time series segments to be matched are symbolized, and the matching distance between the candidate shapelet and the corresponding time series trajectory is calculated. Based on the preset evaluation index, the optimal shapelet set with class discrimination ability is selected. Then, based on the optimal shapelet set, the transient voltage time series sample is mapped to a new feature space composed of shapelets. By calculating the matching relationship between each sample and each optimal shapelet with class discrimination ability, the shapelet feature vector representing the time series dynamic features of the sample is obtained.

[0012] This invention provides a transient voltage stability rule mining method based on shapelet and oblique decision tree learning. Aiming at interpretable rule mining of transient voltage stability states, it constructs an evaluation system comprising key time-series feature extraction, decision rule generation, and decision rule analysis. Compared with existing technologies, this invention has significant advantages. Specifically, firstly, by extracting a set of shapelets characterizing key time-series features from the transient voltage response, this invention effectively mines transient voltage stability-related time-series features, overcoming the problem of difficulty in identifying key time-series information under traditional holistic modeling methods. Secondly, by combining shapelet feature representation with oblique decision tree learning, this invention can learn the hierarchical decision relationships between key time-series features and form clear transient voltage stability decision rules, improving rule expressiveness. Thirdly, through a temperature soft partitioning mechanism and sparse regularization constraints, this invention can reduce redundant feature interference, enhancing the stability of the rule learning process and the compactness of the rule structure. Finally, by extracting and reflecting decision paths, key time-series feature combinations, and their corresponding key time-series features, this invention can obtain judgment criteria related to transient voltage stability states, thus possessing strong interpretability and engineering application value. Attached Figure Description

[0013] Figure 1 A flowchart illustrating the transient voltage stability rule mining method based on shapelet and skew decision tree learning provided by this invention; Figure 2 This is a schematic diagram illustrating the principle of generating decision rules based on shapelet extraction of key temporal features and combined with oblique decision tree in this invention; Figure 3This is a schematic diagram of the transient voltage timing sample of the power system under disturbance in this invention (wherein, Figure 3 (a) is a schematic diagram of stable samples. Figure 3 (b) is a schematic diagram of unstable samples); Figure 4 This is a schematic diagram of the oblique decision tree obtained using the method proposed in this invention during a simulation experiment of an embodiment of this invention (wherein, Figure 4 (a) is a schematic diagram of the decision-making criteria for the oblique decision tree; Figure 4 (b) is a schematic diagram showing the specific composition of the linear combination Y0 of features in the oblique decision tree. Figure 5 This is a schematic diagram of a common decision tree in a simulation experiment of an embodiment of the present invention; Figure 6 This is a comparison chart of the model performance evaluation of oblique decision trees and univariate decision trees in the simulation experiment of the embodiments of the present invention; Figure 7 This is a comparison of the classification accuracy of the proposed method and mainstream deep learning models (RNN, CNN, LSTM, GRU, TF) on the same dataset in simulation experiments of embodiments of the present invention. Detailed Implementation

[0014] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0015] As mentioned in the background section, traditional decision trees typically use a single feature for node splitting, essentially relying on hierarchical judgments based on a single shapelet distance or a single physical quantity threshold. For example, voltage recovery rate reaching a certain range indicates stability, while reactive power injection exceeding a threshold indicates instability. Transient voltage instability is often not determined by a single local trajectory feature, but rather by the combined effects of multiple temporal dynamic features such as node voltage, reactive power response, and recovery rate. Ordinary decision trees require progressively approximating this multi-feature coupling relationship through multiple layers of nodes, easily leading to a deep tree structure, fragmented rules, and difficulty in directly expressing the joint judgment relationship between multiple key shapelets. Therefore, this invention introduces a combination of shapelets and oblique decision trees. At each decision node, instead of simply judging whether the distance to a single shapelet is less than a threshold, an oblique splitting boundary is constructed using a linear combination of multiple shapelet features. That is, the shapelet feature space is partitioned using an oblique hyperplane, thereby learning the joint judgment relationship between multiple key stability features, significantly increasing efficiency compared to traditional decision trees. Specifically, this invention provides a transient voltage stability rule mining method based on shapelet and oblique decision tree learning, such as... Figure 1The transient voltage stability rule mining method based on shapelet and oblique decision tree learning mainly consists of three parts: key time series feature extraction, decision rule generation, and decision rule analysis.

[0016] Part 1: Key Temporal Feature Extraction.

[0017] S101, acquire transient voltage time series samples of the power system under disturbance.

[0018] The transient voltage time-series samples used include transient response data collected during actual operation and multivariate time-series data obtained from simulation. The actual data is used to characterize the dynamic response characteristics of the power system under real disturbance conditions. The simulation samples are used to supplement transient response scenarios under different operating modes, fault scenarios, and disturbance conditions. Specifically, a target power grid model is constructed based on the power system transient simulation platform, and a transient simulation case set is built according to the actual system operating mode and transient fault information. Time-domain simulations are performed on each transient simulation case, and voltage data is collected within a preset observation time window after the disturbance. Active power and reactive power The time-series trajectories are used as multi-dimensional time-series input data for samples. Stability is labeled for each transient simulation case based on transient voltage stability engineering criteria, thus constructing a labeled transient time-series sample set. Each transient simulation case corresponds to one sample, and the total number of samples is denoted as . , No. Each sample is represented as ,in, For the first Multidimensional time-series input data for each sample For the first The stability label corresponding to the nth sample, when the nth sample Each sample corresponds to the system when the transient voltage is stable. When the first Each sample corresponds to a transient voltage instability in the system. Therefore, let the sample dataset be... for: (7) Among them, the Multidimensional time-series input data of one sample Represented as: (8) in, Indicates the first Time in each sample Next The measurement value of each feature, The total number of sampling points for the sample time series. The input feature dimension.

[0019] Preprocessing operations such as outlier handling, normalization, and labeling are performed on transient voltage time series samples to construct a standardized sample set for key time series feature extraction and decision rule mining. Outlier handling is used to reduce the interference of abnormal disturbances, measurement noise, or distorted samples on time series feature extraction; normalization is used to reduce the impact of differences in different units and numerical ranges on shapelet feature representation and oblique decision tree learning; and labels are used to check the transient voltage steady state corresponding to the sample.

[0020] S102: Search for multiple key local dynamic features related to the stable state of transient voltage from the preprocessed transient voltage time series samples, extract multiple shapelets with discriminative ability, construct a shapelet set, and realize the extraction of key stable features.

[0021] like Figure 2 As shown, for the preprocessed transient voltage time series samples, key time series features related to the transient voltage steady state are searched across each input feature dimension. These key time series features mainly refer to local subsequences with classification and discrimination capabilities identified from the time series of features such as voltage, such as voltage drop segments, recovery segments, or fluctuation segments within a certain time window. A range of candidate shapelet lengths is set, and candidate subsequences of different lengths are traversed within this range. Candidate shapelets are extracted separately for each input feature dimension. In the nth sample Temporal trajectory on each feature dimension for: (9) Set the lower bound of the length of the candidate shapelet and upper bound of length and satisfy ≥3、 ≤T, within the candidate length interval Iterate through consecutive candidate subsequences of different lengths and extract candidate shapelets for each input feature dimension.

[0022] For the length corresponding to each value within the candidate length interval From the time-series trajectory Extract all lengths of The continuous subsequences are used as candidate shapelets, and the corresponding candidate shapelets are used with It means that its expression is: (10) in, Let be the starting position of the candidate shapelet, and satisfy . .

[0023] After extracting candidate shapelets across all input feature dimensions of all samples, the overall candidate shapelet set is obtained. : (11) Time series corresponding to each candidate shapelet for: (12) Due to the large number of candidate shapelets, SAX symbolization is performed on the candidate shapelets and their matching time series to improve the computational efficiency of the candidate shapelet matching calculation process.

[0024] First, the candidate shapelets and their matching time series sequences are normalized respectively, resulting in a normalized set of candidate shapelets. Represented as: (13) Normalized matching time series Represented as: (14) Divide the above sequence into Given a set of consecutive subintervals of equal or approximately equal length, the average value of the data within each subinterval is taken to obtain a candidate shapelet set. and the corresponding piecewise aggregation approximation sequence PAA represents a sequence, which is: (15) (16) Define symbol set The PAA sequences are mapped to corresponding symbols according to their intervals, ultimately yielding a set of candidate shapelets. and the symbol sequence of the corresponding sequence : (17) (18) Based on the above symbol sequence The similarity between candidate shapelets and matching subsequences is calculated in the symbol space to reduce the computational burden of shapelet matching.

[0025] Information gain (IG) is used as the evaluation metric to measure the ability of each candidate shapelet to distinguish between sample classes. The calculation is as follows: (19) In the formula, The initial entropy for the sample category, The set of categories for all samples; The subset is obtained by partitioning the candidates based on a distance threshold. These correspond to two different types of samples; For subset The entropy. Setting an information gain threshold. Filter out The candidate shapelets are used to form the optimal shapelet set with class discrimination ability. Let the optimal shapelet set be denoted as . for: (20) in, This represents the optimal number of shapelets obtained through selection. The optimal shapelet set is used to characterize key temporal dynamic features related to the transient voltage steady state, thereby enabling the extraction of key temporal features.

[0026] In simple terms, step S102 first standardizes the multivariate time-series data and transforms it into a digitized vector. Then, the SAX method is used to approximate and symbolically represent the curve in segments, converting the continuous curve into a discrete symbolic sequence. The optimal segment is selected by calculating the similarity or distance between segments. This segment reflects the most significant change pattern in the curve and represents its main trend characteristics. The results show that the selected segment is highly representative in terms of morphological changes, fluctuation amplitude, or pattern matching, and therefore can serve as a key region for subsequent analysis and interpretation.

[0027] S103, based on the shapelet set, perform feature representation on the transient voltage time series samples to obtain the shapelet feature vector characterizing the time series dynamic features of the samples.

[0028] Specifically, based on the optimal shapelet set obtained in S102, transient voltage time-series samples are mapped to a new feature space composed of shapelets. By calculating the matching relationship between each sample and each optimal shapelet with class discrimination capability, shapelet feature vectors characterizing the temporal dynamic features of the samples are obtained. The shapelet feature vectors formed after mapping all samples are used to characterize the temporal dynamic features related to the transient voltage steady state in the transient voltage time-series samples and serve as the input to the subsequent oblique decision tree model.

[0029] Step S2: Construct a slanted decision tree model based on shapelet feature vectors and corresponding transient voltage stability state labels. Divide the samples in the new feature space through the slanted hyperplane, learn the hierarchical decision relationship between key time-series features representing transient voltage stability state, solve the feature combination weights, bias terms and temperature parameters of each decision node according to the node optimization objective function, complete the node splitting parameter update, and determine the tree structure through layer-by-layer splitting to generate the slanted decision tree and its corresponding transient voltage stability decision rules.

[0030] Specifically, the shapelet feature vector is matched with the corresponding transient voltage stability state label to construct a slanted decision tree learning sample set. The input is the shapelet feature vector of the sample, and the output is the corresponding transient voltage stability state label, which includes stable and unstable classes. Starting from the root node, the training samples contained in the current node are input into the slanted decision tree model. At the current node, a node splitting function is constructed using a linear combination of the input features. The feature combination weights, bias terms, and temperature parameters are solved according to the node optimization objective function to determine the splitting parameters of the current node.

[0031] Based on the splitting function of the current node, the training samples arriving at that node are divided. The distribution of sample categories in the child nodes after splitting, the change in node purity, and the improvement of the objective function are considered to determine whether the current node meets the conditions for further splitting. If the conditions are met, corresponding child nodes are generated; otherwise, splitting stops and the current node is set as a leaf node. The node parameter learning and sample partitioning process is repeated for each generated child node, recursively determining the splitting parameters of each decision node and the hierarchical connection relationship between parent and child nodes, until all nodes meet the preset stopping conditions, thus completing the construction of the oblique decision tree structure. The aforementioned stopping conditions include at least one of the following: the number of samples in the current node is lower than a preset threshold, the node purity reaches a preset threshold, the tree depth reaches an upper limit, or the improvement in the objective function resulting from further splitting is lower than a preset threshold. After completing the learning of all node splitting parameters and the determination of the tree structure, the splitting parameters, node hierarchical relationships, leaf node output categories, and sample decision path information of each decision node are retained to form an oblique decision tree and its decision path representation for transient voltage stability rule mining.

[0032] Furthermore, the learning process of the aforementioned oblique decision tree specifically includes: At each decision node, a splitting function is constructed based on a linear combination of the input features, and a diagonal hyperplane splitting rule is constructed. The splitting function is expressed as: (1) in, For input features; For feature combination weight vector, The number of input features, The first in the weight vector One component; This is a bias term.

[0033] Based on the output of the splitting function, the samples are divided into left and right child nodes. Compared with traditional decision trees that perform axial parallel splitting based on only a single feature, this invention uses a multi-feature linear combination method to form oblique splitting boundaries, which can more fully characterize the coupling relationship between different features and improve the ability to characterize complex transient voltage stability modes. To solve the problem of non-differentiability and difficulty in continuous optimization of the splitting function under the traditional hard partitioning method, a temperature-based soft partitioning mechanism is introduced during the node splitting process, transforming the discrete partitioning relationship into a continuous weight allocation relationship.

[0034] Specifically, for any sample, the weight assigned to its left child node and the weights of the samples assigned to the right child nodes. They are represented as follows: (2) (3) in, For the Sigmoid function; This is a temperature parameter used to adjust the degree of soft partitioning. When the value is small, soft partitioning is closer to traditional hard partitioning; when... When the value is larger, the assignment of samples between the left and right child nodes is smoother, which is beneficial to the stable optimization of model parameters.

[0035] Sample weights of the left child node The sum of sample weights of the right child node They are represented as follows: (4) (5) in, This represents the total number of samples in the current node. For the current node Input features of each sample; Based on the previous soft partitioning results, the weighted sample size and entropy of the left and right child nodes of the current node are calculated, and a node optimization objective function is constructed by combining it with a sparse regularization term. The expression of this objective function is as follows: (6) in, and These are the entropies of the left and right child nodes, respectively. For sparse regularization coefficients, For the feature combination weight vector Norm.

[0036] By minimizing the objective function, the splitting parameters of each decision node are determined, and a slanted decision tree structure is generated by recursive splitting. The node splitting conditions from the root node to the leaf node are connected in series to obtain the corresponding transient voltage stability decision rules.

[0037] Based on the constructed node optimization objective function, the feature combination weight vector and bias term of the current node are optimized to determine the optimal splitting parameters corresponding to that node. The parameter solution can be implemented using gradient descent, quasi-Newton methods, or other continuous optimization methods to obtain the oblique splitting hyperplane of the current node. During the oblique decision tree learning process, the splitting features, linear combination coefficients, and node hierarchical relationships corresponding to each decision node are recorded to form a traceable decision path representation, providing a foundation for subsequent decision rule extraction, rule expression, and judgment basis analysis.

[0038] It is worth mentioning that this invention introduces a temperature-based soft partitioning mechanism and a sparse regularization term. By optimizing node splitting parameters through continuous weight allocation and suppressing the interference of redundant shapelet features on the rules, the mined rules are both highly expressive and relatively compact and interpretable. Traditional decision trees, on the other hand, use a hard partitioning method, where a sample at a given node can only be assigned to either the left or right child node. While this method is intuitive, it introduces two problems in oblique decision trees: first, node splitting conditions are discrete, making it difficult to stably solve the splitting parameters through continuous optimization; second, for samples near the splitting boundary, even small perturbations can cause their splitting direction to change, leading to unstable rule learning results. Transient voltage response data itself contains perturbations, noise, and operating condition differences. Directly using hard partitioning can easily cause the mined rules to be affected by individual boundary samples, resulting in insufficient generalization and stability. Temperature-based soft partitioning does not change the interpretable form of the final rules, but rather improves the rule learning process. During training, samples near the boundary are not suddenly and absolutely assigned to one side, but participate in the category distribution and entropy calculation of the left and right child nodes with continuous weights. This reduces the abrupt impact of boundary samples, noisy samples, or individual abnormal transient trajectories on the node splitting results, making the final rules more stable. The role of the sparse regularization term is to control the number of shapelets participating in the splitting in the oblique decision tree node. Since the shapelet extraction stage may obtain a large number of candidate key time series segments, these may include both key local dynamic features that are truly related to the transient voltage steady state and redundant, highly correlated, or weakly discriminative shapelets. If the oblique decision tree node allows all shapelet features to participate in linear combination, although the expressive power is enhanced, it will lead to each rule involving too many features, making the rule form complex and not conducive to engineers' understanding and use.

[0039] Step S3, as follows Figure 1 and Figure 2 As shown, based on the decision path of the shapelet set and the oblique decision tree model, the generated transient voltage stability decision rules are extracted, expressed, and analyzed. Preferably, the node splitting conditions from the root node to the leaf node in the oblique decision tree are combined according to the path order to form corresponding rule expressions. The key time-series feature combinations corresponding to each rule path and their impact on the transient voltage stability state determination are analyzed, thereby obtaining the key time-series dynamic features related to the transient voltage stability state and their determination criteria. The key time-series dynamic features are vector sets composed of time series of multiple features (such as voltage, reactive power, and active power). Figure 3 Two transient voltage time series samples of the power system under disturbance are presented. Figure 3 (a) The red time series and Figure 3In (b), the purple time series represent a stable sample and an unstable sample, respectively. The black line in the yellow box represents a selected shapelet with discriminative effect, that is, a feature time series in the key time series dynamic features. If a certain time series is more similar to the shapelet selected by this method, that is, the Euclidean distance is smaller, it can be judged that the sample system is stable; otherwise, it is unstable. Similarly, a shapelet that can be judged to be unstable can also be selected.

[0040] Next, a simulation test was conducted on the method proposed in this invention. The test system includes 74 nodes, 102 branches and 20 synchronous generators, covering three voltage levels: 400kV, 220kV and 130kV. This simulation test focuses on the central heavy load center area, which accounts for more than 50% of the total load of the system. This area is the core sensitive area for voltage stability issues, containing 11 key load nodes. The load types include voltage-sensitive loads (α=1.0, β=2.0) and induction motor loads, and it concentrates a large number of industrial and residential loads, which are prone to voltage instability after disturbances.

[0041] Based on the BPA simulation platform, batch case generation was achieved using MATLAB, covering multi-dimensional scenario variable combinations: 100 power flow modes were set, simulating actual load fluctuations by randomly adjusting the load rates (0.8~1.2 pu) of 11 key load nodes; dynamic load ratios were set to three scenarios: 0.6, 0.75, and 0.9; fault scenarios included three-phase short-circuit faults on 18 key lines, with fault clearing times of 0.1s and 0.2s as typical values. The simulation time step was 0.01s, with each case simulation lasting 2s, focusing on recording time-series data after 0.2s of the fault, including key electrical quantities such as bus voltage and branch power. During the simulation, the BPA power flow calculation program and transient stability calculation program were automatically invoked, generating 100×3×18×2=10800 complete simulation cases, providing comprehensive dataset support for subsequent time-series data processing and model training.

[0042] In this simulation experiment, the key time-series dynamic features obtained by the method proposed in this invention should have been a vector set consisting of 39 feature time series, including 13 voltage time series, 13 reactive power time series, and 13 active power time series. However, since two of the active power time series contain outliers (null values) that need to be removed, the final key time-series dynamic features obtained are actually a vector set consisting of 37 feature time series.

[0043] like Figure 4 As shown, this is the oblique decision tree obtained using the method proposed in this invention in this simulation experiment. Figure 4 (a) and Figure 4 In (b), each decision node of the oblique decision tree is composed of a linear combination of multiple nodes, using the feature linear combination Y.i This indicates that the linear combination of features of the first decision node (i.e., the root decision node) is Y0, the explicit combination of features of the second decision node is Y1, and so on. The oblique decision tree obtained using the method proposed in this invention only requires 3 layers to achieve a 98% stability accuracy rate, which is highly efficient and beneficial for practical system applications. Furthermore, during the visualization process… Figure 4 In the diagram, non-leaf nodes marked in green are split through linear combinations of multiple features. Leaf nodes are marked in red and blue to clearly distinguish different types of nodes. This intuitive visualization of the tree structure allows for a clearer understanding of the model's decision-making process and a more tangible appreciation of the high interpretability offered by the decision tree model.

[0044] Figure 4 (b) shows the relevant information of the linear combination feature Y0 of the non-leaf nodes in the first-level if-then form, including the splitting basis, current node samples, splitting threshold, etc. The leaf nodes contain information such as the number of current node samples, support rate, confidence, etc. Here, Y0 is the linear combination of features after linear transformation of input feature X0, W0 is the feature combination weight vector, that is, the feature coefficient matrix, b0 is the bias term, and the rule generated by the skew decision tree judges the stability as the result of multiple feature weights. The positive and negative signs of the feature coefficients reflect the positive and negative effects of the features on voltage stability, and the magnitude of the feature coefficients reflects the degree of influence of the features on stability. Therefore, the feature coefficients can reflect the joint influence of multiple features on voltage stability. Figure 4 (b) shows the rule Y0=0.65P 4043 +0.58Q 1041 +0.53Q 1043 ≤0.04, node 1043 is directly connected to generator g7 and is the main source of dynamic reactive power support in the central area. Node 1041 is located near node 1043 and is connected to a key regional transmission corridor. Node 4043 is an important hub for inter-regional active power transmission. These three nodes together constitute the topological core that governs the system voltage stability. The sign of each characteristic coefficient accurately reflects the directional influence of the corresponding variable on voltage stability. For example, Q 1043 A positive eigenvalue indicates that the higher the eigenvalue, the greater the likelihood that Y0 will exceed the threshold, thus causing the model to classify the system as unstable. This behavior is consistent with the underlying physical mechanism: generator g7 injects excessive reactive power into node 1043, indicating that it is in a state of deep overexcitation, which reduces the available excitation margin and thus weakens dynamic reactive power support.

[0045] To verify the superiority of the proposed method, this simulation experiment also included a comparative experiment between the oblique decision tree obtained by the proposed method and the traditional univariate decision tree (DT). Compared to the stability rules generated by the oblique decision tree based on combined features, the stability rules generated by the univariate decision tree can only analyze the correlation between a single variable and stability, and its ability to analyze the correlation between features is insufficient. For example... Figure 5 As shown, each decision node in a conventional decision tree is a single node, which would be very redundant in a real system. Only two layers are shown here. To achieve a similar effect to a slanted decision tree (accuracy of 96.5%), at least five layers or even more are needed, which is very unfavorable for practical power system applications.

[0046] The comparative experimental results of the oblique decision tree (Ours) and the traditional univariate decision tree (DT) are shown in Table 1 and 2, respectively. Figure 6 Numerical data and visualizations clearly compare the performance of the improved multivariate decision tree algorithm of this invention with that of the traditional univariate decision tree comparison model on the same dataset. As shown in Table 1, a horizontal comparison of the test set results for each model leads to the clear conclusion that the method proposed in this invention exhibits significant advantages in all core evaluation indicators, fully demonstrating the effectiveness of the proposed method in power system transient stability assessment.

[0047] Table 1. Performance Comparison of Oblique Decision Trees and Univariate Decision Trees ; Furthermore, this simulation experiment further compared the classification accuracy of the proposed method with mainstream deep learning models (RNN recurrent neural networks, CNN convolutional neural networks, LSTM long short-term memory networks, GRU gated recurrent unit structures, Transformer, TF) on the same dataset, such as... Figure 7 As shown, the accuracy of evaluating the transient stability of power systems using the method proposed in this invention is close to that of deep learning models, and the overall accuracy is stable at over 98%, demonstrating excellent practicality and reliability. This invention effectively avoids the inherent "black box" problem of deep learning models and can achieve higher and more stable accuracy without large-scale hyperparameter tuning.

[0048] The above embodiments are preferred implementations of the present invention. In addition, the present invention can be implemented in other ways. Any obvious substitutions without departing from the concept of the present technical solution are within the protection scope of the present invention.

[0049] To facilitate understanding by those skilled in the art of the improvements of this invention over the prior art, some of the accompanying drawings and descriptions have been simplified, and for clarity, some other elements have been omitted from this application. Those skilled in the art should realize that these omitted elements may also constitute the content of this invention.

Claims

1. A transient voltage stability rule mining method based on shapelet and skew decision tree learning, characterized in that, Including the following steps: S1. Obtain transient voltage time series samples of the power system under disturbance, search for multiple key local dynamic features related to the transient voltage steady state, construct a shapelet set for extracting key time series features and a shapelet feature vector for feature representation of transient voltage time series samples. S2. Based on the shapelet feature vector and the corresponding transient voltage stability state label, a slanted decision tree model is constructed. The samples in the new feature space are divided by the slanted hyperplane. The hierarchical judgment relationship between the key time-series features representing the transient voltage stability state is learned. The feature combination weight, bias term and temperature parameter of each decision node are solved according to the node optimization objective function. The node splitting parameter is updated. The tree structure is determined by splitting layer by layer, and the slanted decision tree and its corresponding transient voltage stability decision rules are generated. The shapelet feature vector is matched with the corresponding transient voltage stability state label to construct a slanted decision tree learning sample set. The input is the shapelet feature vector of the sample, and the output is the corresponding transient voltage stability state label. Starting from the root node, the training samples contained in the current node are input into the slanted decision tree model. At the current node, a linear combination of the input features is used to construct the node splitting function, expressed as: （1） in, Input features; For feature combination weight vector, The number of input features, The first in the weight vector One component; For bias terms; Based on the splitting function of the current node, a temperature-controlled soft partitioning mechanism is used to partition the training samples arriving at this node, and the weights of the samples are assigned to the left child nodes. and the weights of the samples assigned to the right child nodes. They are represented as follows: （2） （3） in, For the Sigmoid function; For temperature parameters; Sample weights of the left child node The sum of sample weights of the right child node They are represented as follows: （4） （5） in, This represents the total number of samples in the current node. For the current node Input features of each sample; The objective function is constructed based on the weighted entropy of the left and right child nodes and the sparse regularization term, and is expressed as follows: （6） in, and These are the entropies of the left and right child nodes, respectively. For sparse regularization coefficients, For the feature combination weight vector Norm; Based on the sample category distribution of the child nodes after partitioning, the change in node purity, and the improvement of the objective function, it is determined whether the current node meets the conditions for continuing to split. If the conditions for continuing to split are met, the corresponding child node is generated; if the conditions for continuing to split are not met, the splitting is stopped and the current node is set as a leaf node. The node parameter learning and sample partitioning process is repeated for each generated child node. By minimizing the objective function, the splitting parameters of each decision node and the hierarchical connection relationship between parent and child nodes are recursively determined until all nodes meet the preset stopping conditions, thereby completing the construction of the oblique decision tree structure. After completing the learning of all node splitting parameters and the determination of the tree structure, the splitting parameters, node hierarchical relationship, leaf node output category, and sample decision path information of each decision node are retained to form an oblique decision tree and its decision path representation for transient voltage stability rule mining. S3, based on the decision path of shapelet set and oblique decision tree model, extracts, expresses and analyzes the generated transient voltage stability decision rules, and obtains the key time-series dynamic features related to the transient voltage stability state and their judgment basis.

2. The transient voltage stability rule mining method based on shapelet and skew decision tree learning according to claim 1, characterized in that: Step S3 involves extracting, expressing, and analyzing transient voltage stability decision rules using the key temporal features of the shapelet extracted in step S1 and the decision path of the oblique decision tree formed in step S2. Specifically, the node splitting conditions from the root node to the leaf node in the oblique decision tree are combined according to the path order to form corresponding rule expressions. The key temporal feature combinations corresponding to each rule path and their impact on the determination of transient voltage stability are analyzed, thereby obtaining the key temporal dynamic features related to transient voltage stability and their determination basis.

3. The transient voltage stability rule mining method based on shapelet and skew decision tree learning according to claim 1 or 2, characterized in that: In step S1, the transient voltage time series sample includes transient response data collected during actual operation and multivariate time series data obtained from simulation.

4. The transient voltage stability rule mining method based on shapelet and skew decision tree learning according to claim 3, characterized in that: In step S1, before extracting key time series features, the transient voltage time series samples are preprocessed, including normalization, outlier handling, and label sorting, to form a standardized sample set for key time series feature extraction and decision rule mining.

5. The transient voltage stability rule mining method based on shapelet and skew decision tree learning according to claim 4, characterized in that: In step S1, for the preprocessed transient voltage time series samples, multiple key time series features related to the transient voltage steady state are searched on each input feature dimension. The length range of the candidate shapelet is set, and candidate subsequences of different lengths are traversed within this length range. Candidate shapelets are extracted for each input feature dimension to obtain the overall candidate shapelet set. Then, the candidate shapelets and the time series segments to be matched are symbolized, and the matching distance between the candidate shapelet and the corresponding time series trajectory is calculated. Based on the preset evaluation index, the optimal shapelet set with class discrimination ability is selected. Then, based on the optimal shapelet set, the transient voltage time series samples are mapped to a new feature space composed of shapelets. By calculating the matching relationship between each sample and each optimal shapelet with class discrimination ability, the shapelet feature vector representing the dynamic features of the sample time series is obtained.

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