A transient voltage stability prediction method based on cost-sensitive multivariate decision tree

Abstract

This invention proposes a transient voltage stability prediction method based on Cost-Sensitive Multivariate Decision Tree (HCS-MDT). It utilizes a Cost-Sensitive Support Vector Machine (CS-SVM) with improved empirical risk as the classifier for internal nodes of the MDT, generating analytical combination feature-based stability judgment rules as a visual basis for stability assessment, effectively reducing false instability predictions. The Hierarchical Adaptive (HSA) criterion is integrated into the CS-MDT for online transient voltage stability prediction, improving early prediction capabilities while effectively ensuring prediction accuracy. The HCS-MDT method of this invention has certain application potential in transient voltage stability prediction of power systems.

Description

Technical Field

[0001] This invention belongs to the field of power grid voltage prediction technology, and in particular relates to a transient voltage stability prediction method based on cost-sensitive multivariate decision trees. Background Technology

[0002] my country has established the world's largest and most complex power grid with a high proportion of renewable energy integrated into it. To avoid catastrophic safety incidents like the blackouts in India, Argentina, and the United States, transient voltage stability analysis is a crucial aspect of ensuring the safe operation of the power system. In recent years, the rapid development of Wide Area Measurement Systems (WAMS) has greatly facilitated efficient and reliable online situational awareness of modern power grids. Particularly with the widespread deployment of phasor measurement units (PMUs) in the grid, transient voltage stability prediction can simultaneously acquire large amounts of PMU data to capture real-time system status. This makes it possible to reliably execute data-driven transient voltage stability prediction based on PMU data.

[0003] Scholars both domestically and internationally have conducted research on how to extract data from massive datasets. In response-based transient voltage stability analysis, common methods include the energy function method and the rapidly developing artificial intelligence method. Among these, compared to "black box" algorithms such as neural networks, prediction methods represented by decision trees are highly suitable for uncovering potential patterns in transient voltage stability prediction due to their ability to generate visual analytical criteria, simple algorithms, and strong generalization capabilities. These methods have already been preliminarily applied to practical power systems.

[0004] Currently, most transient stability prediction methods based on decision trees employ univariate decision trees, constructing internal nodes by comparing single features with threshold values, with decision boundaries always parallel to the variable axes. However, univariate decision trees cannot directly capture decision boundaries on non-parallel axes; they must be approximated by parallel boundaries on continuous axes, leading to considerable complexity in the univariate decision tree model. In real-world systems, electrical quantities always exhibit some correlation; using only univariate decision trees to construct stability rules cannot effectively capture these interrelationships, limiting the algorithm's accuracy and generalization ability. Furthermore, in real-world power systems, if transient instability conditions are misjudged as stable conditions and not addressed promptly, they often escalate into widespread voltage collapse accidents, causing severe consequences. This necessitates that prediction methods accurately identify instability conditions. Therefore, improving interpretable decision tree algorithms to better suit transient voltage stability prediction is a pressing issue that needs to be addressed. Summary of the Invention

[0005] To address the above problems, this invention proposes a transient voltage stability prediction method based on a cost-sensitive multivariate decision tree, comprising the following steps:

[0006] Step 1, Sample Acquisition and Feature Generation: Transient samples are generated based on the actual system simulation model. The generated transient samples are collected in the transient sample library, and the corresponding features are extracted and dimensionality reduced. The features of each dimension are standardized to form a transient feature set.

[0007] Step 2, Model Construction and Training: A cost-sensitive support vector machine (CS-SVM) is used to construct internal nodes of a multivariate decision tree (MDT). The SVM machine learning algorithm is used to automatically find the optimal decision hyperplane and maximize the margin of unstable class samples. A hierarchical adaptive HSA criterion is introduced to achieve early prediction capability and reduce the prediction time of unstable samples, thus constructing the HCS-MDT model. The transient feature set from Step 1 is input into the HCS-MDT model for training. The optimal decision hyperplane equations of the internal nodes of each level of the HCS-MDT classifier are used to extract hierarchical multi-combination feature stability rules.

[0008] Step 3, Online prediction of transient voltage stability: Based on the established HCS-MDT, online prediction is performed using the stability judgment rules extracted in Step 2.

[0009] Specifically, in CS-SVM, different penalty parameters are applied to the two classes of samples to construct the objective function:

[0010] ;

[0011] In the formula, C is the structural cost; C is the penalty parameter. These are slack variables; Can Mapped to a higher-dimensional space; The improved experience cost represents the sum of the experience costs for the false positive and false negative classes; and These are the cost sensitivity coefficients for positive and negative class samples, respectively. Their sum is 1, forming the cost sensitivity matrix. Binary classification training vectors ( )and label vector ;

[0012] Solve the following dual problem:

[0013] ;

[0014] in, It is a vector of all 1s. for Semi-positive definite matrix; , For kernel functions;

[0015] After solving the quadratic programming problem in the above equation, using the primordial-dual relation, the optimal... satisfy

[0016] ;

[0017] Optimal bias It can be obtained from KKT conditions;

[0018] The decision function is:

[0019] ;

[0020] The cost-sensitive optimal decision hyperplane is:

[0021] ;

[0022] Furthermore, based on the traditional CART model, the internal nodes are classified by replacing the original univariate boundary with the optimal decision hyperplane. After the optimal decision hyperplane divides the corresponding samples, two branches are created for this node: the left branch is used to store samples with a positive distance from the decision hyperplane, and the right branch is used to store samples with a negative distance from the decision hyperplane.

[0023] Furthermore, the splitting principle of the left and right branches adopts Gini gain. The calculation method is as follows:

[0024] ;

[0025] In the formula, For nodes to be divided, The left child node of the partition, The right child node of the partition, For category At the node All samples The proportion of the total for Number of samples included for Number of samples included; setting the split threshold ,like If the node is a leaf node, then no further division is needed; the node contains samples of the type with more subclasses, and this leaf node is the subclass of that leaf node. If so, then further division is necessary.

[0026] Furthermore, the cost sensitivity coefficient The method for determining this is to set a certain search step size. The grid search method is used from the initial Gradual change and , generate The optimal CS-MDT is used, and the search stops when the negative class misclassification rate is minimized.

[0027] Furthermore, the HSA prediction method is combined with CS-MDT. At each prediction node, the time from the fault occurrence T0 to that time {T1, T2, ..., T...} is used. f Spatiotemporal features are used to construct the CS-MDT. The prediction result for a sample is accepted or rejected according to the adaptive MOP strategy. Accepted results are directly output as the prediction result. If the result is rejected, i.e., it falls into the fuzzy domain, the sample is pushed to the next prediction node, and more measurement features are used to construct the CS-MDT for that moment. HSA continues until all prediction results are successfully delivered or the maximum allowable prediction window T is reached. f .

[0028] Furthermore, the adaptive MOP strategy is as follows:

[0029] 1) Set the expected threshold TH for the misclassification rate of positive and negative samples. + TH - The shortest expected prediction window and the longest acceptable prediction window t min t max and prediction time interval According to t min t max and Calculate the maximum number of allowed classifiers. :

[0030] ;

[0031] 2) Determine the set of observation values ​​for the sample to be tested. Given the optimal positive sample misclassification rate M and the number of classifiers I, the MOP problem is:

[0032] ;

[0033] in, , Let be the total number of positive samples for the i-th level classifier. Let be the total number of misclassified positive samples at level i. For the classification boundary of negative samples in the i-th level fuzzy domain, , These are linear weighting coefficients;

[0034] 3) For samples in the fuzzy domain of the final classifier, all are conservatively considered to be unstable, and this is used as the final prediction result.

[0035] The transient voltage stability prediction method based on cost-sensitive multivariate decision trees describes a classification boundary for positive samples in the fuzzy domain of each classifier. All adopt strict boundaries and do not participate in the optimization; when it is impossible to satisfy both M and I requirements, satisfying M is the primary condition.

[0036] Furthermore, in the construction of the HCS-MDT model, reasonable linear weighting coefficients are determined according to actual needs. , Select the final option from the Pareto optimal boundary. I is then assigned to each level of classifier.

[0037] Furthermore, in step 3, after a transient fault occurs, the system PMU continuously measures the required U / I / P / Q quantities and generates corresponding feature sets, which are then substituted into each rule for if-then rule matching and the prediction results are quickly given; if an unstable situation occurs, an alarm is issued.

[0038] The beneficial effects of this invention are as follows: The transient voltage stability prediction method proposed in this invention, by incorporating a cost-sensitive method, can effectively perceive the development trend of system instability samples, significantly reduce the probability of false alarms, and effectively prevent the further development of instability problems. The MDT constructed based on CS-SVM avoids the cumbersome optimal feature combination search process, deeply explores the correlation between multiple features, expands the rule dimension, and generates easily understandable analytical combination feature stability judgment rules, providing a visual stability judgment basis for online applications. The proposed HSA mechanism can improve the early prediction without sacrificing evaluation accuracy, especially significantly advancing the prediction time for severe instability conditions, buying time for emergency control measures. The HCS-MDT method has certain application potential in power system transient voltage stability prediction. Attached Figure Description

[0039] Figure 1 This is a flowchart of the transient voltage stability prediction method based on HCS-MDT of the present invention;

[0040] Figure 2 This is a flowchart of the HSA prediction method proposed in this invention;

[0041] Figure 3 This is an example of the improved IEEE 39-node system topology in this invention.

[0042] Figure 4 (a) is a critical sample in an example of the present invention. Figure 4 (b) is an early prediction sample in an example of the present invention;

[0043] Figure 5 This is a schematic diagram of the first-level judgment process of the HCS-MDT model in an example of the present invention. Detailed Implementation

[0044] The embodiments will now be described in detail with reference to the accompanying drawings.

[0045] The method of this invention is a hierarchical self-adaptation (HSA) transient voltage stability prediction method that integrates cost-sensitive multivariate decision trees (CS-MDT). It uses cost-sensitive support vector machines (CS-SVM) to construct the internal nodes of the multivariate decision tree (MDT), and uses the SVM machine learning algorithm to automatically find the optimal decision hyperplane and maximize the margin of unstable samples. The generated combined feature criteria can effectively utilize more relevant information between features. In online applications, the HSA criterion is introduced to achieve early prediction capability, especially to reduce the prediction time of unstable samples.

[0046] Figure 1 The diagram shows the flow of the transient voltage stability prediction method based on HCS-MDT of the present invention, which is divided into three stages.

[0047] (1) Sample acquisition and feature generation

[0048] Transient samples are generated based on the actual system simulation model. The electrical quantities collected for each sample include bus voltage, line current, active power, and reactive power (the simulation time window is 5 seconds after the fault). The remaining required electrical quantities are calculated indirectly. The generated samples are collected in a transient sample library, and the corresponding features are extracted and dimensionality reduced. All features in each dimension are standardized to form a transient feature set.

[0049] (2) Model building and training

[0050] Construct an HCS-MDT model and use a transient feature set as input for batch learning. Some hyperparameters need to be manually specified, while other parameters can be left at their default values. After training, evaluate the model performance using various metrics, and manually adjust the model parameters if necessary. Utilize the optimal hyperplane equations of the internal nodes of each level of the HCS-MDT classifier to extract hierarchical multi-combination feature stability rules, providing a visual basis for subsequent online applications.

[0051] The following is the construction process of the HCS-MDT model:

[0052] Cost-sensitive Support Vector Machine (CS-SVM)

[0053] Given binary classification training vectors ( )and label vector SVM solves the following original optimization problem.

[0054] (1)

[0055] In the formula For structural costs; C is the empirical cost, and C is the penalty parameter. These are slack variables; Can Mapped to a higher-dimensional space.

[0056] The original SVM uses a single penalty parameter, meaning that the cost of misclassification is the same for each class of samples. For binary classification problems, we can consider applying different penalty parameters to the two classes to construct the objective function. Then, CS-SVM can be represented as follows:

[0057] (2)

[0058] In the formula The improved experience cost represents the sum of the experience costs for the false positive and false negative classes. and These are the cost sensitivity coefficients for positive and negative class samples, respectively. Their sum is 1, forming the cost sensitivity matrix. .

[0059] Due to vectors It may have high dimensionality and typically solves the following dual problems:

[0060] (3)

[0061] in, It is a vector of all 1s. for Semi-positive fixed matrix , This is the kernel function.

[0062] After solving the quadratic programming problem in equation (3), the optimal solution is obtained by using the primal-dual relation. satisfy

[0063] (4)

[0064] Optimal bias It can be obtained from KKT conditions.

[0065] The decision function is:

[0066] (5)

[0067] The cost-sensitive optimal decision hyperplane is:

[0068] (6)

[0069] The optimal decision hyperplane equation is an optimized boundary that satisfies two types of penalty parameter conditions and is expressed as a linear combination of multidimensional features. The predicted class of a sample under the current optimal decision hyperplane can be obtained using the decision function.

[0070] Multivariate Decision Tree (CS-MDT) Generation

[0071] CS-MDT can be built upon the traditional CART model. Its internal nodes utilize the optimal decision hyperplane instead of the original univariate splitting plane for classification. After the hyperplane partitions the corresponding samples, it creates two branches for this node: the left branch stores samples with a positive distance from the hyperplane, and the right branch stores samples with a negative distance. The splitting principle uses Gini gain. The calculation method is as follows:

[0072] (7)

[0073] In the formula, For nodes to be divided, The left child node of the partition, The right child node of the partition, For category At the node All samples The proportion of the total for Number of samples included for Number of samples included.

[0074] Set split threshold ,like If the node is a leaf node, then no further division is needed; the node contains samples of the type with more subclasses, and this leaf node is the subclass of that leaf node. Then it needs to continue splitting. Except In addition, cost sensitivity coefficient It is also an important hyperparameter for constructing CS-MDT, and its determination method is: set a certain search step size. The grid search method is used from the initial Gradual change and , generate The optimal CS-MDT is then used, and the search stops when the false positive rate for the negative class is minimized. At this point, the CS-MDT is complete.

[0075] Hierarchical Adaptive HSA Criterion

[0076] This invention also proposes an HSA prediction method and combines it with CS-MDT, which is the HCS-MDT of this invention. The HSA concept is as follows: Figure 2 As shown. Where T0 is the time of fault occurrence, {T1, T2, ..., T...} f} represents the time node for executing the predicted action, T f To maximize the allowable prediction window, at each prediction node, a CS-MDT is constructed using the spatiotemporal features from the time of the fault occurrence to that time. The prediction result for a sample can be accepted or rejected according to the adaptive strategy (MOP) described later. Accepted results are directly output as the prediction result. However, if the result is rejected, i.e., falls into the fuzzy domain, the sample is pushed to the next prediction node, and a CS-MDT for that time is constructed using more measurement features. HSA continues until all prediction results are successfully delivered or T is reached. f .

[0077] Taking a CS-MDT containing a single layer of internal nodes as an example, Figure 1 Various fuzzy domain boundaries are illustrated. The relaxed boundary is closest to the original optimal hyperplane, with fewer samples within the fuzzy domain, thus requiring only a small number of classifiers for prediction; however, it suffers from severe misclassification in the acceptor domain. The strict boundary is furthest from the original optimal hyperplane, offering the highest prediction accuracy within the acceptor domain; however, a large number of fuzzy samples may put significant pressure on subsequent classifiers, especially when prediction time is insufficient, potentially leading to incomplete classification and a loss of prediction performance. Therefore, determining the optimal fuzzy domain boundaries for each classifier level is crucial for effectively improving early prediction performance while maintaining accuracy.

[0078] In related research, the multi-objective optimization problem (MOP) has shown unique advantages in explaining such trade-offs. Therefore, this invention proposes an adaptive MOP strategy for the existing trade-off problem, as described below:

[0079] 1) Set the expected threshold TH for the misclassification rate of positive and negative samples. + TH - The shortest expected prediction window and the longest acceptable prediction window t min t max and prediction time interval According to t min t max and Calculate the maximum number of allowed classifiers. for:

[0080] (8)

[0081] 2) Determine the set of observation values ​​for the sample to be tested. The optimal positive sample misclassification rate M is related to the number of classifiers I. The MOP problem is:

[0082] (9)

[0083] in , Let be the total number of positive samples for the i-th level classifier. Let be the total number of misclassified positive samples at level i. For the classification boundary of negative samples in the i-th level fuzzy domain, , These are linear weighting coefficients. This is because the accuracy requirements for the negative class are more stringent (i.e., the expected TH). - =0), therefore the fuzzy domain of each classifier has a positive sample classification boundary. All methods employ strict boundary conditions and do not participate in the optimization process. When it is impossible to satisfy both M and I requirements, satisfying M becomes the primary condition.

[0084] 3) For samples in the fuzzy domain of the final classifier, all can be conservatively considered as unstable, and this can be used as the final prediction result.

[0085] The optimal objective vector set is called the Pareto optimal frontier (POF). Appropriate linear weighting coefficients should be determined based on actual needs. , Select the final one from the Pareto set. I is then assigned to classifiers at each level to complete the overall HCS-MDT construction.

[0086] (3) Transient voltage stability prediction

[0087] Online prediction is performed using extracted stability rules. After a transient fault occurs, the system's PMU continuously measures the required U / I / P / Q quantities and generates corresponding feature sets. These features are then substituted into the respective rules for if-then rule matching, and prediction results are quickly provided. If instability occurs, an alarm will be issued, informing the user to take immediate action to prevent a large-scale system collapse. Furthermore, based on the incremental learning capabilities of both SVM and decision trees, when new samples are generated, only the trained model needs to be updated without retraining. This can be achieved by supplementing the HCS-MDT model with real-world power grid fault samples collected from actual power grids for updating and learning; and by setting a certain update cycle to promptly generate new transient samples through offline simulation and learning.

[0088] Case Analysis

[0089] The effectiveness of the proposed method is verified in a new power system with wind power integration. To closely reflect actual engineering and overcome the shortcomings of previous studies that only analyzed power systems composed of traditional thermal power units, the original thermal power units at node 37 of the IEEE 39-node system were replaced with an equivalent number of doubly-fed wind turbines to construct a new energy integration research scenario. All wind turbines operate in maximum power point tracking mode. Furthermore, considering that the high-voltage transmission lines in the actual system operate in multiple circuits, all 220kV transmission lines are configured as double-circuit lines to facilitate fault scenario setup. The example wiring is as follows: Figure 3 As shown.

[0090] Sample and Feature Generation

[0091] Faults were simulated on lines 25 and 26, located at distances ranging from 10% to 90% from the beginning of the circuit, increasing by 10% in increments. One of the two lines experienced multiple short-circuit fault types, including symmetrical and asymmetrical faults. Eight fault clearing times were set for cycles 3 to 10, with the clearing method involving the tripping of circuit breakers on both sides of the affected line. The load model employed a hybrid model of 20% constant impedance and 80% induction motors, with load levels randomly fluctuating between 90% and 110%. The sampling frequency was 10kHz. A total of 4950 samples were obtained from the simulation. 80% was randomly selected for the training set, and 20% for the test set. Figure 3 The purple area represents the spatial feature range, from which a 700-dimensional original feature is constructed. In the test, t is set... min =0.1s, t max =0.5s and =0.02s. Therefore, HCS-MDT allows for a maximum of 21 classifier levels. The original features used in each classifier level range from 140 to 700 dimensions. Pearson correlation coefficient is used to select features for each level, where... =0.5. The feature sets at each level are obtained separately for subsequent model training, denoted as... .

[0092] Model performance evaluation

[0093] Cross-sectional prediction performance was compared between training traditional decision tree CART, cost-free sensitive MDT, CS-MDT, and HCS-MDT models. Cost-free sensitive MDT used traditional C-SVC to construct its internal nodes, while CS-MDT and HCS-MDT used linear kernel CS-SVM. The relevant hyperparameters were set as follows: =[0.5,0.5], =0.01, TH - =0%, TH + =3%, = =0.5, and the remaining parameters are set to their default values. First, the HCS-MDT model is trained. CART, MDT, and CS-MDT are constructed using the HCS-MDT adaptive prediction window. Considering the potential randomness in model training, both model training and validation are repeated 10 times. The average validation results for all models on the test set are shown in Table 1.

[0094]

[0095] Table 1 shows that the traditional CART model has low performance across all metrics, indicating mediocre predictive performance. The cost-sensitive MDT based on improved CART significantly reduces both false alarm rates, demonstrating improved performance compared to CART. Under cost-sensitivity, the CS-MDT model shows a significantly lower false alarm rate compared to MDT, although the missed alarm rate increases slightly but still meets the 3% expectation requirement. The HCS-MDT model achieves the prediction task with the lowest two false alarm rates, resulting in the highest overall accuracy among all models. This demonstrates that the proposed HCS-MDT model effectively suppresses false alarms while maintaining the required low missed alarm rate, validating its accurate predictive performance.

[0096] Regarding prediction time, in HCS-MDT, more than half of the test samples were successfully predicted within 0.14s (levels 1 to 3), and 92.63% of the test samples were successfully predicted within 0.3s (levels 1 to 11). For the instability samples, which are of high concern, 36.3% of the samples were successfully predicted within 0.2s, and 87.06% were successfully predicted within 0.3s, with an average prediction window of 0.243s, which significantly shortens the prediction time for instability conditions. In contrast, the other three models require a wait of 0.4s for all types of samples to make a prediction, which is detrimental to the action of power system remedial control measures. Figure 4 (b) Demonstrates representative unstable samples successfully predicted by the first to third-level classifiers. Figure 4 (a) The comparison clearly shows that many of the instability samples predicted by the early classifier exhibit voltage collapse and voltage-power angle coupling instability, which are extremely harmful to the system. Compared with the model without hierarchical adaptive links, HCS-MDT can significantly shorten the prediction time of severe instability samples and trigger earlier remedial control actions to eliminate these severe instability conditions. Its HSA concept can effectively meet the needs of online operation of actual systems, verifying the early prediction performance of the proposed method.

[0097] Analysis of Stability Judgment Rules

[0098] From the 10 models constructed above, randomly select one set and extract the stability rules from top to bottom. List the stability rules of the HCS-MDT first-level classifier. The first-level judgment process of the model is as follows: Figure 5 As shown.

[0099] Rule 1: Stable. Support level: 38.59%, Confidence level: 100%.

[0100] Rule 2: Stable. Support level: 3.03%, Confidence level: 100%.

[0101] Rule 3: Instability. Support level: 3.23%, Confidence level: 99.22%.

[0102] Rule 4: Unable to determine, proceed to the next level.

[0103] in, for Combined features after linear transformation The characteristic coefficient matrix, This is the optimal bias coefficient.

[0104] This embodiment is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A transient voltage stability prediction method based on cost-sensitive multivariate decision trees, characterized in that, Includes the following steps: Step 1, Sample Acquisition and Feature Generation: Transient samples are generated based on the actual system simulation model. The generated transient samples are collected in the transient sample library, and the corresponding features are extracted and dimensionality reduced. The features of each dimension are standardized to form a transient feature set. Step 2, Model Construction and Training: A cost-sensitive support vector machine (CS-SVM) is used to construct internal nodes of a multivariate decision tree (MDT). The SVM machine learning algorithm is used to automatically find the optimal decision hyperplane and maximize the margin of unstable class samples. A hierarchical adaptive HSA criterion is introduced to achieve early prediction capability and reduce the prediction time of unstable samples, thus constructing the HCS-MDT model. The transient feature set from Step 1 is input into the HCS-MDT model for training. The optimal decision hyperplane equations of the internal nodes of each level of the HCS-MDT classifier are used to extract hierarchical multi-combination feature stability rules. Step 3, Online prediction of transient voltage stability: Based on the established HCS-MDT, online prediction is performed using the stability judgment rules extracted in Step 2; In the CS-SVM, different penalty parameters are applied to the two classes of samples to construct the objective function: ； In the formula, C is the structural cost; C is the penalty parameter. These are slack variables; Can Mapped to a higher-dimensional space; The improved experience cost represents the sum of the experience costs for the false positive and false negative classes; and These are the cost sensitivity coefficients for positive and negative class samples, respectively. Their sum is 1, forming the cost sensitivity matrix. Binary classification training vectors ( )and label vector ; Solve the following dual problem: ； in, It is a vector of all 1s. for Semi-positive definite matrix; , For kernel functions; After solving the quadratic programming problem in the above equation, using the primordial-dual relation, the optimal... satisfy ； Optimal bias It can be obtained from KKT conditions; The decision function is: ； The cost-sensitive optimal decision hyperplane is: 。 2. The transient voltage stability prediction method based on cost-sensitive multivariate decision tree according to claim 1, characterized in that: Based on the traditional CART model, the internal nodes are classified by replacing the original univariate boundary with the optimal decision hyperplane. After the optimal decision hyperplane divides the corresponding samples, two branches are created for this node: the left branch is used to store samples with a positive distance from the decision hyperplane, and the right branch is used to store samples with a negative distance from the decision hyperplane.

3. The transient voltage stability prediction method based on cost-sensitive multivariate decision tree according to claim 2, characterized in that: The splitting principle of the left and right branches adopts Gini gain. The calculation method is as follows: ； In the formula, For nodes to be divided, The left child node of the partition, The right child node of the partition, For category At the node All samples The proportion of the total for Number of samples included for Number of samples included; setting the split threshold ,like If so, no further division is needed; this node is a leaf node, and the category with more samples is the category of this leaf node. Then it needs to continue splitting.

4. The transient voltage stability prediction method based on cost-sensitive multivariate decision tree according to claim 2, characterized in that: Cost sensitivity coefficient The method for determining this is to set a certain search step size. The grid search method is used from the initial Gradual change and , generate The optimal CS-MDT is used, and the search stops when the negative class misclassification rate is minimized.

5. The transient voltage stability prediction method based on cost-sensitive multivariate decision tree according to claim 2, characterized in that: By combining the HSA prediction method with CS-MDT, at each prediction node, the time from the fault occurrence time T0 to that time {T1, T2, ..., T...} is used. f Spatiotemporal features are used to construct the CS-MDT. The prediction result for a sample is accepted or rejected according to the adaptive MOP strategy. Accepted results are directly output as the prediction result. If the result is rejected, i.e., it falls into the fuzzy domain, the sample is pushed to the next prediction node, and more measurement features are used to construct the CS-MDT for that moment. HSA continues until all prediction results are successfully delivered or the maximum allowable prediction window T is reached. f .

6. The transient voltage stability prediction method based on cost-sensitive multivariate decision tree according to claim 5, characterized in that, The adaptive MOP strategy is as follows: 1) Set the expected threshold TH for the misclassification rate of positive and negative samples. + TH - The shortest expected prediction window and the longest acceptable prediction window t min t max and prediction time interval According to t min t max and Calculate the maximum number of allowed classifiers. : ； 2) Determine the set of observation values ​​for the sample to be tested. Given the optimal positive sample misclassification rate M and the number of classifiers I, the MOP problem is: ； in, , Let be the total number of positive samples for the i-th level classifier. Let be the total number of misclassified positive samples at level i. For the classification boundary of negative samples in the i-th level fuzzy domain, , These are linear weighting coefficients; 3) For samples in the fuzzy domain of the final classifier, all are conservatively considered to be unstable, and this is used as the final prediction result.

7. The transient voltage stability prediction method based on cost-sensitive multivariate decision tree according to claim 6, characterized in that, The fuzzy domain of each classifier and the classification boundary of positive samples All adopt strict boundaries and do not participate in the optimization; when it is impossible to satisfy both M and I requirements, satisfying M is the primary condition.

8. The transient voltage stability prediction method based on cost-sensitive multivariate decision tree according to claim 6, characterized in that, In the construction of the HCS-MDT model, reasonable linear weighting coefficients are determined according to actual needs. , Select the final option from the Pareto optimal boundary. I is then assigned to each level of classifier.

9. The transient voltage stability prediction method based on cost-sensitive multivariate decision tree according to claim 1, characterized in that, In step 3, after a transient fault occurs, the system PMU continuously measures the required U / I / P / Q quantities and generates corresponding feature sets. These features are then substituted into each rule for if-then rule matching, and the prediction results are quickly provided. If an unstable situation occurs, an alarm is issued.

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