The operating status of power systems is influenced by growing varieties of factors, resulting from the developing sizes and complexity of power systems. In this situation, the model-based methods need to be revisited. A data-driven method, as the novel alternative on the other hand, is proposed in this paper. It reveals the correlations between the factors and the system status through statistical properties of data. An augmented matrix as the data source is the key trick for this method and is formulated by two parts: 1) status data as the basic part; and 2) factor data as the augmented part. The random matrix theory is applied as the mathematical framework. The linear eigenvalue statistics, such as the mean spectral radius, are defined to study data correlations through large random matrices. Compared with model-based methods, the proposed method is inspired by a pure statistical approach without a prior knowledge of operation and interaction mechanism models for power systems and factors. In general, this method is direct in analysis, robust against bad data, universal to various factors, and applicable for real-time analysis. A case study based on the standard IEEE 118-bus system validates the proposed method.
Also, some data-driven methods for correlation analysis are proposed recently, such as the principal components analysis, the artificial neural networks, the support vector machine @cite_12 . Eltigani utilizes artificial neural networks (ANNs) in assessing the transient stability @cite_21 . In his approach, the power system is described by an equivalent single machine infinite bus system, which cannot reflect accurately the actual state of the system. Moreover, with the scale-up of the system and increase of training samples, the training speed of ANNs progressively slows down.
@cite_21 @cite_12
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This paper aims at verifying the accuracy of Artificial Neural Networks (ANN) in assessing the transient stability of a single machine infinite bus system. The fault critical clearing time obtained through ANN is compared to the results of the conventional equal area criterion method. The multilayer feedforward artificial neural network concept is applied to the system. The training of the ANN is achieved through the supervised learning; and the back propagation technique is used as a learning method in order to minimize the training error. The training data set is generated using two steps process. First, the equal area criterion is used to determine the critical angle. After that the swing equation is solved using the point-to-point method up to the critical angle to determine the critical clearing time. Then the stability of the system is verified. As a result we find that the critical clearing time is predicted with slightly less accuracy using ANN compared to the conventional methods for the same input data sets unless the ANN is well trained. Artificial neural networks (ANNs) have become the driving force behind recent artificial intelligence (AI) research. An important problem with implementing a neural network is the design of its architecture. Typically, such an architecture is obtained manually by exploring its hyperparameter space and kept fixed during training. This approach is both time-consuming and inefficient. Furthermore, modern neural networks often contain millions of parameters, whereas many applications require small inference models. Also, while ANNs have found great success in big-data applications, there is also significant interest in using ANNs for medium- and small-data applications that can be run on energy-constrained edge devices. To address these challenges, we propose a neural network synthesis methodology (SCANN) that can generate very compact neural networks without loss in accuracy for small and medium-size datasets. We also use dimensionality reduction methods to reduce the feature size of the datasets, so as to alleviate the curse of dimensionality. Our final synthesis methodology consists of three steps: dataset dimensionality reduction, neural network compression in each layer, and neural network compression with SCANN. We evaluate SCANN on the medium-size MNIST dataset by comparing our synthesized neural networks to the well-known LeNet-5 baseline. Without any loss in accuracy, SCANN generates a @math smaller network than the LeNet-5 Caffe model. We also evaluate the efficiency of using dimensionality reduction alongside SCANN on nine small to medium-size datasets. Using this methodology enables us to reduce the number of connections in the network by up to @math (geometric mean: @math ), with little to no drop in accuracy. We also show that our synthesis methodology yields neural networks that are much better at navigating the accuracy vs. energy efficiency space. We propose a methodology for designing dependable Artificial Neural Networks (ANN) by extending the concepts of understandability, correctness, and validity that are crucial ingredients in existing certification standards. We apply the concept in a concrete case study in designing a high-way ANN-based motion predictor to guarantee safety properties such as impossibility for the ego vehicle to suggest moving to the right lane if there exists another vehicle on its right. At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit, thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of an ANN, the network function (which maps input vectors to output vectors) follows the so-called kernel gradient associated with a new object, which we call the Neural Tangent Kernel (NTK). This kernel is central to describe the generalization features of ANNs. While the NTK is random at initialization and varies during training, in the infinite-width limit it converges to an explicit limiting kernel and stays constant during training. This makes it possible to study the training of ANNs in function space instead of parameter space. Convergence of the training can then be related to the positive-definiteness of the limiting NTK. We then focus on the setting of least-squares regression and show that in the infinite-width limit, the network function follows a linear differential equation during training. The convergence is fastest along the largest kernel principal components of the input data with respect to the NTK, hence suggesting a theoretical motivation for early stopping. Finally we study the NTK numerically, observe its behavior for wide networks, and compare it to the infinite-width limit.