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We develop upper bounds for line failure probabilities in power grids, under the DC approximation and assuming Gaussian noise for the power injections. Our upper bounds are explicit, and lead to characterization of safe operational capacity…

Systems and Control · Computer Science 2016-11-09 Tommaso Nesti , Alessandro Zocca , Bert Zwart

One of the most common control decisions faced by power system operators is the question of how to dispatch generation to meet demand for power. This is a complex optimization problem that includes many nonlinear, non convex constraints as…

Optimization and Control · Mathematics 2013-06-14 Russell Bent , Daniel Bienstock , Michael Chertkov

The stable operation of the electric power grid relies on a precisely synchronized state of all generators and machines. All machines rotate at exactly the same frequency with fixed phase differences, leading to steady power flows…

Adaptation and Self-Organizing Systems · Physics 2020-01-09 Chiara Balestra , Franz Kaiser , Debsankha Manik , Dirk Witthaut

We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times…

Physics and Society · Physics 2007-05-23 Marian Anghel , Kenneth A. Werley , Adilson E. Motter

In this paper, in an attempt to improve power grid resilience, a machine learning model is proposed to predictively estimate the component states in response to extreme events. The proposed model is based on a multi-dimensional Support…

Systems and Control · Computer Science 2018-02-19 Rozhin Eskandarpour , Amin Khodaei , Ali Arab

Energy systems resilience is becoming increasingly important as the frequency of major grid outages increases. In this work, we present a methodology to optimize a behind-the-meter distributed energy resource system to sustain a site's…

Systems and Control · Electrical Eng. & Systems 2021-06-29 Sakshi Mishra , Kate Anderson

Given increasing risk from climate-induced natural hazards, there is growing interest in the development of methods that can quantitatively measure resilience in power systems. This work quantifies resilience in electric power transmission…

Physics and Society · Physics 2019-06-18 Molly Rose Kelly-Gorham , Paul. D. H. Hines , Ian Dobson

A reliable supply with electric power is vital for our society. Transmission line failures are among the biggest threats for power grid stability as they may lead to a splitting of the grid into mutual asynchronous fragments. New conceptual…

Systems and Control · Electrical Eng. & Systems 2022-10-18 Maurizio Titz , Franz Kaiser , Johannes Kruse , Dirk Witthaut

We study a smart grid with wind power and battery storage. Traditionally, day-ahead planning aims to balance demand and wind power, yet actual wind conditions often deviate from forecasts. Short-term flexibility in storage and generation…

Systems and Control · Electrical Eng. & Systems 2022-12-08 Thom S. Badings , Arnd Hartmanns , Nils Jansen , Marnix Suilen

Wind integration in power grids is very difficult, essentially because of the uncertain nature of wind speed. Forecasting errors on output from wind turbines may have costly consequences. For instance, power might be bought at highest price…

Optimization and Control · Mathematics 2016-04-28 Luckny Zéphyr , C. Lindsay Anderson

Extreme weather events stemming from climate change can cause significant damage and disruption to power systems. Failure to mitigate and adapt to climate change and its cascading effects can lead to short and long term issues. The profound…

Applied Physics · Physics 2022-09-22 Rouzbeh Shirvani , Tarannom Parhizkar

We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…

Optimization and Control · Mathematics 2021-06-25 Joshua L. Pulsipher , Victor M. Zavala

We investigate the total resistive losses incurred in returning a power network of identical generators to a synchronous state following a transient stability event or in maintaining this state in the presence of persistent stochastic…

Chaotic Dynamics · Physics 2012-10-01 Bassam Bamieh , Dennice F. Gayme

The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on…

Physics and Society · Physics 2021-09-24 Takashi Nishikawa , Adilson E. Motter

This paper concerns the potential of corrective actions, such as generation and load dispatch on minimizing the effects of transmission line failures in electric power systems. Three loss functions (grid-centric, consumer-centric, and…

Systems and Control · Electrical Eng. & Systems 2022-12-13 Siyu Liu , Marija Ilic

Power systems, including synchronous generator systems, are typical systems that strive for stable operation. In this article, we numerically study the fault transient process of a synchronous generator system based on the first benchmark…

Numerical Analysis · Mathematics 2025-02-25 Sixu Wu , Feng Ji , Lu Gao , Ruili Zhang , Cunwei Tang , Yifa Tang

Robust synchronization is indispensable for stable operation of a power grid. Recently, it has been reported that a large number of decentralized generators, rather than a small number of large power plants, provide enhanced synchronization…

Physics and Society · Physics 2017-05-24 Mi Jin Lee , Beom Jun Kim

We use a power grid model with $M$ generators and $N$ consumption units to optimize the grid and its control. Each consumer demand is drawn from a predefined finite-size-support distribution, thus simulating the instantaneous load…

Statistical Mechanics · Physics 2009-10-21 Lenka Zdeborová , Aurélien Decelle , Michael Chertkov

We consider power line outages in the transmission system of the power grid, and specifically those caused by a natural disaster or a large scale physical attack. In the transmission system, an outage of a line may lead to overload on other…

Systems and Control · Computer Science 2012-06-07 Andrey Bernstein , Daniel Bienstock , David Hay , Meric Uzunoglu , Gil Zussman

We analyze a power distribution line with high penetration of distributed generation and strong variations of power consumption and generation levels. In the presence of uncertainty the statistical description of the system is required to…

Optimization and Control · Mathematics 2010-06-02 Konstantin S. Turitsyn