The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments

Bienstock, Daniel; Verma, Abhinav

doi:10.1137/08073562x

Cited by 150 publications

(136 citation statements)

References 21 publications

Supporting

Mentioning

135

Contrasting

Order By: Relevance

“…Of specific relevance to our work is the literature on security-constrained optimal power flow in situations where large numbers of system components fail. This literature is mostly based on worstcase network interdiction analysis and includes solution methods based on bi-level and mixed-integer programming (see [24,25,1,8,33,32]) and graph algorithms (see [22,3,8,15,16]). …”

mentioning

confidence: 99%

Contingency-constrained unit commitment with post-contingency corrective recourse

et al. 2014

View full text Add to dashboard Cite

We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-ε reliability criterion. This reliability criterion is a generalization of the wellknown N-k criterion, and dictates that at least (1 − ε j ) fraction of the total system demand must be met following the failures of k or fewer system components. We refer to this problem as the Contingency-Constrained Unit Commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network, which demonstrate the effectiveness of our proposed methods relative to current state-of-the-art.

show abstract

mentioning

confidence: 99%

Contingency-constrained unit commitment with post-contingency corrective recourse

et al. 2014

View full text Add to dashboard Cite

show abstract

“…This linearization is used in a variety of different integer linear programs concerning power grid problems, cf. [3,4,6].…”

Section: The DC Power Flowmentioning

confidence: 99%

Designing AC Power Grids Using Integer Linear Programming

Koster

Lemkens

2011

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Recent developments have drawn focus towards the efficient calculation of flows in AC power grids, which are difficult to solve systems of nonlinear equations. The common linearization approach leads to the well known and often used DC formulation, which has some major drawbacks. To overcome these drawbacks we revisit an alternative linearization of the AC power flow. Work on this model has already be done in the 1990s but was intractable at that time. In view of recent developments in the field of integer programming, we show that this model is computationally tractable.

show abstract

“…Several models have been proposed for explaining the complex behavior of cascading failures in power networks [25]- [28]. Generally speaking, there are two kinds of technical approaches.…”

Section: Vulnerability and Network Hierarchy Evolutionmentioning

confidence: 99%

Network Hierarchy Evolution and System Vulnerability in Power Grids

Luo

Han

Rosas-Casals

2018

IEEE Systems Journal

View full text Add to dashboard Cite

UPCommonsPortal del coneixement obert de la UPC http://upcommons.upc.edu/e-prints (c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1Abstract-The seldom addressed network hierarchy property and its relationship with vulnerability analysis for power transmission grids from complex systems point of view is given in this paper. We analyze and compare the evolution of network hierarchy for the dynamic vulnerability evaluation of four different power transmission grids of real cases. Several meaningful results suggest that the vulnerability of power grids can be assessed by means of a network hierarchy evolution analysis. Firstly, the network hierarchy evolution may be used as a novel measurement to quantify the robustness of power grids. Secondly, an anti-pyramidal structure appears in the most robust network when quantifying cascading failures by the proposed hierarchy metric. Furthermore, the analysis results are also validated and proved by empirical reliability data. We show that our proposed hierarchy evolution analysis methodology could be used to assess the vulnerability of power grids or even other networks from a complex systems point of view.

show abstract

The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments

Cited by 150 publications

References 21 publications

Contingency-constrained unit commitment with post-contingency corrective recourse

Contingency-constrained unit commitment with post-contingency corrective recourse

Designing AC Power Grids Using Integer Linear Programming

Network Hierarchy Evolution and System Vulnerability in Power Grids

Contact Info

Product

Resources

About