Title: Numerical Solutions for Detecting Contingency in Modern Power Systems
This paper is devoted to the detection of contingencies in modern power systems. Because the systems we consider are under the framework of cyber-physical systems, it is necessary to take into consideration of the information processing aspect and communication networks. A consequence is that noise and random disturbances are unavoidable. The detection problem then becomes one known as quickest detection. In contrast to running the detection problem in a discretetime setting leading to a sequence of detection problems, this work focuses on the problem in a continuous-time setup. We treat stochastic differential equation models. One of the distinct features is that the systems are hybrid involving both continuous states and discrete events that coexist and interact. The discrete event process is modeled by a continuous-time Markov chain representing random environments that are not resented by a continuous sample path. The quickest detection then can be written as an optimal stopping problem. This paper is devoted to finding numerical solutions to the underlying problem. We use a Markov chain approximation method to construct the numerical algorithms. Numerical examples are used to demonstrate the performance. more »« less
Chadwick, A; Ho, S; Y, Li; Wang, M
(, International Journal of Difference Equations)
Anderson, Douglas R; Eloe, P; Goodrich, C; Peterson, A
(Ed.)
In this paper, a discrete Markov chain model is developed to describe the inventory at a bike share station. The uniqueness of solutions is first studied. Then the model calibration is considered by investigating a constrained optimization problem. Numerical simulations involving real data are conducted to demonstrate the model effectiveness as well.
Bhat, Harish S.; Huang, Li-Hsuan; Rodriguez, Sebastian
(, Proceedings of the 53rd Asilomar Conference on Signals, Systems, and Computers)
In this paper, we develop methods to find the most sparse perturbation to a given Markov chain (either discrete- or continuous-time) such that the perturbed Markov chain achieves a desired equilibrium.
Tran, Ky_Q; Yin, George
(, IMA Journal of Mathematical Control and Information)
Abstract This paper is devoted to the study of stochastic functional differential systems with Markov switching. It focuses on the stability of numerical solutions. To gain insight on how impulses, functional past dependence, random switching and stochastic disturbances can have impact on dynamic systems, this paper addresses exponential stability of the Euler–Maruyama approximations of stochastic functional differential equations with impulsive perturbations and Markovian switching. It begins with a presentation of the definitions of exponential stability in mean square and in the almost sure sense for stochastic functional differential equations with impulsive perturbations and Markovian switching. Then, it is devoted to showing that if the underlying system is stable in the aforementioned sense then the Euler–Maruyama approximation method faithfully reproduces exponential stability in the mean square and almost sure sense for sufficiently small step sizes and large iteration number. Two examples are provided to demonstrate the effectiveness of our results.
This paper presents a novel learning-based adaptive optimal controller design for linear time-delay systems described by delay differential equations (DDEs). A key strategy is to exploit the value iteration (VI) approach to solve the linear quadratic optimal control problem for time-delay systems. However, previous learning-based control methods are all exclusively devoted to discrete-time time-delay systems. In this article, we aim to fill in the gap by developing a learning-based VI approach to solve the infinite-dimensional algebraic Riccati equation (ARE) for continuous-time time-delay systems. One nice feature of the proposed VI approach is that an initial admissible controller is not required to start the algorithm. The efficacy of the proposed methodology is demonstrated by the example of autonomous driving.
Budhiraja, Amarjit; Fraiman, Nicolas; Waterbury, Adam
(, Advances in Applied Probability)
Abstract We consider a collection of Markov chains that model the evolution of multitype biological populations. The state space of the chains is the positive orthant, and the boundary of the orthant is the absorbing state for the Markov chain and represents the extinction states of different population types. We are interested in the long-term behavior of the Markov chain away from extinction, under a small noise scaling. Under this scaling, the trajectory of the Markov process over any compact interval converges in distribution to the solution of an ordinary differential equation (ODE) evolving in the positive orthant. We study the asymptotic behavior of the quasi-stationary distributions (QSD) in this scaling regime. Our main result shows that, under conditions, the limit points of the QSD are supported on the union of interior attractors of the flow determined by the ODE. We also give lower bounds on expected extinction times which scale exponentially with the system size. Results of this type when the deterministic dynamical system obtained under the scaling limit is given by a discrete-time evolution equation and the dynamics are essentially in a compact space (namely, the one-step map is a bounded function) have been studied by Faure and Schreiber (2014). Our results extend these to a setting of an unbounded state space and continuous-time dynamics. The proofs rely on uniform large deviation results for small noise stochastic dynamical systems and methods from the theory of continuous-time dynamical systems. In general, QSD for Markov chains with absorbing states and unbounded state spaces may not exist. We study one basic family of binomial-Poisson models in the positive orthant where one can use Lyapunov function methods to establish existence of QSD and also to argue the tightness of the QSD of the scaled sequence of Markov chains. The results from the first part are then used to characterize the support of limit points of this sequence of QSD.
Ma, Xiaohang, Qian, Hongjiang, Wang, Le Yi, Nazari, Masoud H., and Yin, George. Numerical Solutions for Detecting Contingency in Modern Power Systems. Retrieved from https://par.nsf.gov/biblio/10429194. Proc. 2023 4th IEEE Inform. Comm. Tech. Conference . Web. doi:10.1109/ICTC57116.2023.10154790.
Ma, Xiaohang, Qian, Hongjiang, Wang, Le Yi, Nazari, Masoud H., & Yin, George. Numerical Solutions for Detecting Contingency in Modern Power Systems. Proc. 2023 4th IEEE Inform. Comm. Tech. Conference, (). Retrieved from https://par.nsf.gov/biblio/10429194. https://doi.org/10.1109/ICTC57116.2023.10154790
@article{osti_10429194,
place = {Country unknown/Code not available},
title = {Numerical Solutions for Detecting Contingency in Modern Power Systems},
url = {https://par.nsf.gov/biblio/10429194},
DOI = {10.1109/ICTC57116.2023.10154790},
abstractNote = {This paper is devoted to the detection of contingencies in modern power systems. Because the systems we consider are under the framework of cyber-physical systems, it is necessary to take into consideration of the information processing aspect and communication networks. A consequence is that noise and random disturbances are unavoidable. The detection problem then becomes one known as quickest detection. In contrast to running the detection problem in a discretetime setting leading to a sequence of detection problems, this work focuses on the problem in a continuous-time setup. We treat stochastic differential equation models. One of the distinct features is that the systems are hybrid involving both continuous states and discrete events that coexist and interact. The discrete event process is modeled by a continuous-time Markov chain representing random environments that are not resented by a continuous sample path. The quickest detection then can be written as an optimal stopping problem. This paper is devoted to finding numerical solutions to the underlying problem. We use a Markov chain approximation method to construct the numerical algorithms. Numerical examples are used to demonstrate the performance.},
journal = {Proc. 2023 4th IEEE Inform. Comm. Tech. Conference},
author = {Ma, Xiaohang and Qian, Hongjiang and Wang, Le Yi and Nazari, Masoud H. and Yin, George},
}
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