Dynamic security analysis is an important problem of power systems on ensuring safe operation and stable power supply even when certain faults occur. No matter if such faults are caused by vulnerabilities of system components, physical attacks, or cyber-attacks that are more related to cyber-security, they eventually affect the physical stability of a power system. Examples of the loss of physical stability include the Northeast Blackout of 2003 in North America and the 2015 system-wide blackout in Ukraine. The nonlinear hybrid nature, that is, nonlinear continuous dynamics integrated with discrete switching, and the high degree of freedom property of power system dynamics make it challenging to conduct the dynamic security analysis. In this article, we use the hybrid automaton model to describe the dynamics of a power system and mainly deal with the index-1 differential-algebraic equation models regarding the continuous dynamics in different discrete states. The analysis problem is formulated as a reachability problem of the associated hybrid model. A sampling-based algorithm is then proposed by integrating modeling and randomized simulation of the hybrid dynamics to search for a feasible execution connecting an initial state of the post-fault system and a target set in the desired operation mode. The proposed method enables the use of existing power system simulators for the synthesis of discrete switching and control strategies through randomized simulation. The effectiveness and performance of the proposed approach are demonstrated with an application to the dynamic security analysis of the New England 39-bus benchmark power system exhibiting hybrid dynamics. In addition to evaluating the dynamic security, the proposed method searches for a feasible strategy to ensure the dynamic security of the system in the face of disruptions.
Generally, state-of-the-art DSA tools rely heavily on deterministic computation methods @cite_4 , such as the aforementioned EEAC, BCU, SBS, etc. Security limits are searched based on exhaustively examining many predefined contingencies using a rigorous approach. Advantages of such methods are the accurate results available at the expense of computation time, since precise models of the system dynamics are used as the basis. With the development of data science, the probabilistic methods, including machine learning and artificial intelligence @cite_43 @cite_51 , are recently proposed again to DSA, utilizing accumulated knowledge and data. Some probabilistic models for the causal relation could be trained using certain learning methods based on data obtained via simulation, and the built models are further employed to conduct the on-line DSA. The advantage of such methods are the rapid results, while the reliability of the obtained models is still in study, and simulation still plays a fundamental role on supplying the data. In addition, a rigorous and concrete strategy to maintain the system security is not provided in the state-of-the-art tools and methods.
@cite_51 @cite_43 @cite_4
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In recent years, complex operating conditions have greatly reduced the predictability of electric grid operations and hence, there is an urgent need to improve grid security more than ever before. The best approach would be to improve grid intelligence rather than simply hardening the grid. An implementation of dynamic security assessment (DSA) would require carrying out time-domain simulations that are computationally too involved to be performed in real-time. This paper presents an approach using machine learning (ML) techniques that would enable the grid to assess its current dynamic state instantaneously. A database consisting of steady-state operating points of the power system and outputs of time-domain simulations is generated in order to train and test the algorithm. A few operating points termed as “landmarks” are identified through a ranking methodology proposed in this paper. Finally, it is shown that prediction accuracy improves through use of such landmarks. We present automated techniques for the verification and control of partially observable, probabilistic systems for both discrete and dense models of time. For the discrete-time case, we formally model these systems using partially observable Markov decision processes; for dense time, we propose an extension of probabilistic timed automata in which local states are partially visible to an observer or controller. We give probabilistic temporal logics that can express a range of quantitative properties of these models, relating to the probability of an event's occurrence or the expected value of a reward measure. We then propose techniques to either verify that such a property holds or synthesise a controller for the model which makes it true. Our approach is based on a grid-based abstraction of the uncountable belief space induced by partial observability and, for dense-time models, an integer discretisation of real-time behaviour. The former is necessarily approximate since the underlying problem is undecidable, however we show how both lower and upper bounds on numerical results can be generated. We illustrate the effectiveness of the approach by implementing it in the PRISM model checker and applying it to several case studies from the domains of task and network scheduling, computer security and planning. Most tasks require a person or an automated system to reason -- to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality. Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs. Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying a new formulation in deep networks. Three aspects in convolutional neural networks (CNN) style architectures are being looked at: (1) transparency of the intermediate layers to the overall classification; (2) discriminativeness and robustness of learned features, especially in the early layers; (3) effectiveness in training due to the presence of the exploding and vanishing gradients. We introduce "companion objective" to the individual hidden layers, in addition to the overall objective at the output layer (a different strategy to layer-wise pre-training). We extend techniques from stochastic gradient methods to analyze our algorithm. The advantage of our method is evident and our experimental result on benchmark datasets shows significant performance gain over existing methods (e.g. all state-of-the-art results on MNIST, CIFAR-10, CIFAR-100, and SVHN).