The effect of energy on the natural environment has become increasingly severe as human consumption of fossil energy has increased. The capacity of the synchronous generators to keep working without losing synchronization when the system is exposed to severe faults such as short circuits is referred to as the power system's transient stability. As the power system's safe and stable operation and mechanism of action become more complicated, higher demands for accurate and rapid power system transient stability analysis are made. Current methods for analyzing transient stability are less accurate because they do not account for misclassification of unstable samples. As a result, this paper proposes a novel approach for analyzing transient stability. The key concept is to use deep forest (DF) and a neighborhood rough reduction approach together. Using the neighborhood rough sets, the original feature space is obtained by creating many optimal feature subsets at various granularity levels. Then, by deploying the DF cascade structure, the mapping connection between the transient stability state and the features is reinforced. The weighted voting technique is used in the learning process to increase the classification accuracy of unstable samples. When contrasted to current methods, simulation results indicate that the proposed approach outperforms them.

The development of grid interconnection and intelligence makes today's power grids increasingly complex and open; while the scale of power grids continues to expand, uncertain risk factors are also increasing [

The application of various power transmission methods and new energy technologies have made the grid structure and operating conditions more complex, leading to more risks for the safe and stable operation of the power system. Transient stability analysis is an important content of power system safety analysis. At present, the commonly used traditional analytical methods such as time domain simulation, direct method, etc., because the former is computationally intensive and time-consuming, the latter is used in complex systems. It is difficult to construct an energy function that satisfies the conditions and other defects, and cannot meet the real-time requirements of the security and stability assessment of large power grids. Therefore, how to accurately and quickly identify transient stability in the early stage of system failure is a problem that needs to be solved urgently in the online security analysis link, and it is also an important foundation for the realization of the idea of “measurement, identification, and control”.

The transient stability evaluation method based on data mining has attracted more and more scholars’ attention in recent years because it can meet the requirements of real-time online evaluation and has high evaluation accuracy [

The current research on transient stability assessment methods based on data mining mainly includes two aspects: feature selection and classifier construction. In the study of feature selection, there have been methods such as principal component analysis [

In light of the aforementioned issues, this research provides a power system transient stability assessment approach that combines neighborhood and deep forest rough reduction. The forest created by decision tree integration is further integrated, and the original transient features’ representation learning is accomplished using the cascade approach to abstractly produce a high-dimensional feature space that is better suited to classification learning. To further boost the deep forest's characterization learning capacity, we used neighborhood rough reduction to locate numerous sets of various optimal feature subsets at varying degrees of granularity to re-characterize the original feature space. The classification algorithm now pays greater attention to transient instability samples thanks to the addition of a weighted voting mechanism. The experimental findings suggest that the proposed strategy may successfully minimize the misclassification rate of transient instability samples while also improving evaluation accuracy. In comparison to classic deep learning approaches, the suggested technique produces superior assessment results even when the sample size is small, is less impacted by irrelevant features and sample set imbalance, and has some robustness and application.

The core of the transient stability assessment method based on data mining is to design a classification model to learn and fit the complex non-linear mapping relationship between the transient characteristic quantity of the power grid and the transient stable state (category). The transient feature set with highly correlated state is the foundation and key of this kind of method. There are currently two ways to construct the initial transient feature set of the power grid. The first type directly constructs the initial transient feature set based on the power flow of the system before and after the fault, such as the voltage amplitude, phase, active and reactive power distribution of each bus in the system. This method directly learns the classifier based on the original data at the bottom of the power grid, and does not rely on expert experience for feature selection [

When using the “combined feature quantity” method to construct the initial transient feature set, three aspects: the systematic principle, the mainstream principle and the real-time principle are usually considered [

It can be seen that the transient characteristic quantities constructed in this paper are not affected by the scale of the system, and are all combined indicators of the state variables of the components in the system. In terms of time, it covers the three different phases of the system state at the time of steady state (features 1 and 2), the time of fault occurrence (features 3∼11) and the time of fault clearing (features 12∼32), which can fully reflect the fault brought to the system impact. The selection of characteristic quantities is mainly based on the combination of system physical quantities reflecting the rotor state and system operation level. Among them, the characteristics 6, 7, 17∼19, 29 are related to the rotor angle, reflecting the synchronous operation state of the generator; the characteristics 5, 8∼15, 20∼27, 30, 31 are related to the rotor speed and acceleration, reflecting the disturbance The influence of rotor movement; characteristics 1∼4, 16, 28, 32 are related to the operating level of the system, reflecting the influence of the fault on the power balance of the system. Therefore, the established transient feature set can well reveal the impact of fault impact on the system stability trend.

From the point of view of data mining, power system transient stability assessment is essentially a process of learning and classifying the corresponding data set. In order to facilitate the analysis, this article describes the classification task as a decision system

Index | Expression | Performance measurement |
---|---|---|

AC | The model's classification accuracy of the total sample | |

SD | The correct rate of the model's classification of unstable samples | |

GM | Comprehensive classification and evaluation performance of the model for two types of samples | |

FM | The model comprehensively evaluates the performance of unstable samples in terms of accuracy and recall |

Since the construction of transient features relies on expert experience, after the initial transient feature set is constructed, it can usually be further compressed or reduced to extract key features and reduce the redundancy of the feature set [

For a classification task of transient stability assessment

In the formula,

Further, the entire sample set is divided into a stable sample set 1d and an unstable sample set

It can be seen from

For the classification task of transient stability assessment

For each feature

If

By setting different neighborhood thresholds

A decision tree is a classification model with a tree structure, which starts from the root node and performs feature selection and sample partitioning at each child node to obtain different node rules. Each child node corresponds to a feature, and each node rule represents a way to divide the sample under the selected feature. According to the obtained node rules, different samples are assigned to each child node in turn. The above process is recursive, and the sample is continuously divided until it reaches the leaf node. Each leaf node represents a category label of the sample. For decision trees, the feature selection at each node and the way of sample division are very important. The commonly used measurement methods for feature selection of decision tree nodes usually include information gain ratio and Gini index. For a classification task of transient stability assessment

If the sample set

The information gain ratio of feature

For the sample set

The Gini index of feature

Through the integration of multiple decision trees, a decision tree forest can be further formed. The decision tree forest is an ensemble learning model, which votes in a way that the minority obeys the majority and gives the final decision result. Because it comprehensively considers the prediction results of multiple models, it has high evaluation accuracy and strong robustness. According to the input space composition of the sub-classifier and the feature selection method, the decision tree forest can be further divided into random forests [

Deep forest [

The deep forest is composed of multiple learning layers in series, where each learning layer is integrated by several decision tree forests. The output probability vector of each layer to the sample label together with the original input features reconstitutes the input features of the next learning layer, and the cascade structure is shown in

The decision tree forest is composed of several decision trees, and each decision tree will output the corresponding transient stability assessment results. For each decision tree forest in the learning layer, by calculating the proportion distribution of trees with stable evaluation results and trees with unstable evaluation results in the forest, a two-dimensional class distribution vector is finally generated, indicating that the samples are located in different transient states probability in the state. If each level contains

In the power system transient stability assessment problem, the transient instability samples are often small, and there is an obvious imbalance in the number of transient stability samples, so the classifier tends to learn in the direction that is conducive to the classification of transient stability samples. However, the cost of misjudging transient instability samples is higher, so in practice, more attention should be paid to improving the assessment accuracy of transient instability samples. For this reason, when the class distribution vector is generated at each level, the weighted voting mechanism shown in

For a classification task of transient stability assessment

In the training process of the deep forest, each additional level will be aligned with each level of the forest on the verification set for verification and evaluation. For each input of a prediction sample, the probability vectors generated by all forests are averaged at each level of learning, and the category with the largest probability output will be used as the prediction label of the sample. If the classification performance does not increase, stop training.

Compared with the shallow learning model, the advantage of the deep learning method lies in its powerful ability to deal with feature relationships. By re-characterizing the original feature space, the relationship between the feature quantity and the label attribute can be strengthened. Non-linear mapping relationship, thereby further strengthening the representation learning ability of deep forest [

In

The transient stability assessment model framework proposed by the transient stability assessment process combining rough reduction of neighborhood and deep forest is shown in

In order to verify the effectiveness of the evaluation model proposed in this paper, time-domain simulation was performed on the IEEE 10-machine 39-node system [

The above simulations are all realized in MATLAB/Simulink. The simulation have total 8000 data samples, which 5104 is specified for training set and 2896 is for test set. The K-Means method is deployed to discretize the continuous input value. After completing the sample sampling, the Min-Max standardization method is used to normalize all the sample data to eliminate the influence of the difference in attribute dimension on the learning process.

Given that the power system transient stability assessment problem has the characteristics of sample imbalance and misclassification cost imbalance, in order to describe the performance of the model more comprehensively, the classification accuracy (AC) and safety (SD) shown in

The model parameters mentioned in this paper mainly fall into two categories, including the setting of the neighborhood threshold in the rough reduction stage of the neighborhood and the number of trees contained in the decision tree forest in the model. In the rough reduction stage of the neighborhood, first, according to the recommended neighborhood threshold range [0.1, 0.3] in [

Granularity level | Reduce feature subset |
---|---|

1 | 13, 9, 17, 7, 6, 26, 8, 12, 4, 2, 1, 11, 25, 3, 5, 30 |

2 | 13, 16, 9, 8, 26, 15, 7, 6, 4, 10, 20, 17, 2, 14, 3, 1, 30, 5, 31, 11, 21 |

3 | 13, 16, 9, 8, 7, 3, 26, 15, 6, 20, 10, 2, 11, 4, 12, 1, 17, 14, 5, 22, 31, 19, 21 |

4 | 13, 9, 14, 26, 12, 8, 6, 15, 4, 2, 11, 3, 25, 1, 5, 19, 20, 21, 27, 7, 10, 30, 17 |

5 | 13, 16, 20, 1, 8, 26, 9, 6, 10, 4, 7, 2, 15, 17, 14, 23, 3, 21, 30, 31, 5, 11, 22, 12, 28 |

6 | 13, 9, 14, 26, 7, 12, 6, 4, 8, 15, 2, 11, 25, 1, 3, 5, 19, 20, 21, 27, 10, 16, 17, 30, 18, 29 |

The order of the features in

Further study the influence of the number of trees contained in the decision tree forest on the performance of the model. With 5 as the step size, the number of trees in the decision tree forest is set to change from 5 to 25. Ten-fold cross-validation was used to evaluate the performance of the model under different parameters. The results are shown in

Number of trees | AC | SD | GM | FM |
---|---|---|---|---|

5 | 0.9807 | 0.9850 | 0.9816 | 0.9481 |

10 | 0.9834 | 0.9862 | 0.9840 | 0.9552 |

15 | 0.9825 | 0.9852 | 0.9823 | 0.9504 |

20 | 0.9833 | 0.9887 | 0.9844 | 0.9550 |

25 | 0.9820 | 0.9877 | 0.9832 | 0.9519 |

It can be seen from

In order to verify the performance of the model, the commonly used power system transient stability assessment classifiers are selected for comparative analysis. The selected classifier models include C4.5 decision tree, classification regression tree (CART), naive Bayes (NB), support vector machine (SVM), and artificial neural network (ANN). Among them, the ANN uses a three-layer hidden layer structure, and the training algorithm uses a momentum gradient descent algorithm; SVM uses the default parameter settings of the MATLAB toolbox (linear kernel, sequence minimum optimization algorithm). For convenience, the algorithm in this paper is abbreviated as NRRDF in the following. The results are shown in

Classification model | AC | SD | GM | FM |
---|---|---|---|---|

C4.5 | 0.9467 | 0.9383 | 0.9449 | 0.8599 |

SVM | 0.9476 | 0.9509 | 0.9483 | 0.8632 |

CART | 0.9526 | 0.9107 | 0.9429 | 0.8714 |

ANN | 0.9507 | 0.9236 | 0.9445 | 0.8669 |

NB | 0.8930 | 0.8842 | 0.8909 | 0.7342 |

Proposed NRRDF | 0.9834 | 0.9862 | 0.9840 | 0.9552 |

It can be seen from

In order to further reflect the adaptability of the model to the characteristic data under the untrained grid topology, all 800 sets of data collected under a certain grid topology are randomly selected as test data, and the remaining 7200 sets of data collected under other topologies are used as training data to test the performance of the above models, and the results are shown in

Classification model | AC | SD | GM | FM |
---|---|---|---|---|

C4.5 | 0.9100 | 0.8494 | 0.8931 | 0.7386 |

SVM | 0.8900 | 0.7645 | 0.8522 | 0.6727 |

CART | 0.9237 | 0.8649 | 0.9074 | 0.7749 |

ANN | 0.9087 | 0.8669 | 0.9293 | 0.7788 |

NB | 0.6675 | 0.9421 | 0.7106 | 0.4644 |

Proposed NRRDF | 0.9487 | 0.9691 | 0.9539 | 0.8565 |

It can be seen from

This section further studies the performance of the model under different sample sizes. Since one of the characteristics of deep learning is the ability to efficiently learn big data, this section selects the most representative deep belief network (DBN) in deep learning for performance comparison. From the original 8000 sets of sample data, using 1000 as the step size, randomly select 1000 to 8000 sets of sample data; under different sample sizes, ten-fold cross-validation is used to evaluate the performance of the proposed model and DBN. The DBN has selected a 3-layer network structure of {10-15-20}, which has been passed many times according to the empirical method. The experiment selects the network structure parameters under the optimal results. The experimental results are shown in

Add irrelevant feature dimension | AC | SD | GM | FM | |
---|---|---|---|---|---|

20 | DF | 0.9778 | 0.9790 | 0.9778 | 0.9402 |

Proposed | 0.9818 | 0.9840 | 0.9822 | 0.9506 | |

40 | DF | 0.9776 | 0.9793 | 0.9780 | 0.9400 |

Proposed | 0.9822 | 0.9844 | 0.9827 | 0.9522 | |

60 | DF | 0.9776 | 0.9744 | 0.9769 | 0.9395 |

Proposed | 0.9817 | 0.9849 | 0.9824 | 0.9510 | |

80 | DF | 0.9758 | 0.9731 | 0.9752 | 0.9343 |

Proposed | 0.9817 | 0.9851 | 0.9824 | 0.9507 | |

100 | DF | 0.9750 | 0.9752 | 0.9750 | 0.9330 |

Proposed | 0.9820 | 0.9838 | 0.9823 | 0.9516 |

It can be seen from

Since the establishment of the transient feature set relies on expert experience, it may be affected by certain human subjective factors. This section studies the influence of irrelevant features on the model. Irrelevant features are generated by random variables that follow a standard normal distribution. Take 20 as the step size to the original data set, add 20–100 dimensional irrelevant features, and use ten-fold cross-validation to calculate the performance index changes of the model when adding different dimensional irrelevant features. In order to show the performance of the proposed model more intuitively, the corresponding evaluation results of the original deep forest model (denoted as DF) that do not adopt the neighborhood rough reduction method to strengthen and re-characterize the input features are given. The results are shown in

In the actual power grid operation process, because the transient instability of the power grid is very rare, the transient instability samples in the actual power grid data tend to be relatively small. In order to evaluate the performance of the proposed model under different sample imbalance ratios, this paper first randomly selects transient stable samples equal to the transient instability samples from the total sample, so that the proportion of transient instability samples reaches 50%. Then on this basis, some samples were randomly deleted from the transient instability samples, so that the proportion of transient instability samples in the total samples was reduced to 40%, 30%, 20% and 10%. The performance evaluation of the model is carried out under different imbalance degrees, and the G-means and F-measures indicators obtained from the evaluation of each model are shown in

It can be seen from

Aiming at the problems of current power system transient stability assessment methods that have limited learning accuracy of shallow models and insufficient attention to transient instability samples, a transient stability assessment method combining rough neighborhood reduction and deep forest is proposed. A comparative experiment analysis of the proposed model is carried out on an IEEE 10-machine 39-node system. Experimental results show that: 1) Compared with the commonly used shallow learning models, the proposed model can effectively improve the classification performance. The introduction of the weighted voting mechanism can effectively improve the model's attention to transient instability samples during the learning process, reduce the misjudgment of transient instability samples, and improve the imbalance of different samples. Both have good performance; 2) Compared with traditional deep learning methods represented by deep belief networks, the proposed method has fewer hyper-parameters. The multi-level sequential structure can not only realize the multi-layer representation learning of the input features, but also can adaptively determine the depth of the model through the layer-by-layer evaluation of the training process during the learning process, so that the proposed model has different scales of data and good performance; 3) Enhancing and re-characterizing the original input features through the neighborhood rough reduction method can not only provide more sufficient information than the original feature space, but also enable the model to maintain high classification performance even when a large number of irrelevant features are added. Therefore, the model robustness is stronger.

In view of some current problems, this paper studies the power system transient stability assessment problem under the deep forest framework. In practice, the loss of transient characteristic data may be caused due to problems such as the loss of measurement devices and communication delay. Therefore, the feasibility analysis of the proposed model under circumstances such as missing data will be perfected in the future.