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Academic Commons Search Resultsen-usChance Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty
http://academiccommons.columbia.edu/catalog/ac:156182
Bienstock, Daniel; Chertkov, Michael; Harnett, Seanhttp://hdl.handle.net/10022/AC:P:18933Tue, 05 Feb 2013 00:00:00 +0000When uncontrollable resources fluctuate, Optimum Power Flow (OPF), routinely used by the electric power industry to re-dispatch hourly controllable generation (coal, gas and hydro plants) over control areas of transmission networks, can result in grid instability, and, potentially, cascading outages. This risk arises because OPF dispatch is computed without awareness of major uncertainty, in particular fluctuations in renewable output. As a result, grid operation under OPF with renewable variability can lead to frequent conditions where power line flow ratings are significantly exceeded. Such a condition, which is borne by simulations of real grids, would likely resulting in automatic line tripping to protect lines from thermal stress, a risky and undesirable outcome which compromises stability. Smart grid goals include a commitment to large penetration of highly fluctuating renewables, thus calling to reconsider current practices, in particular the use of standard OPF. Our Chance Constrained (CC) OPF corrects the problem and mitigates dangerous renewable fluctuations with minimal changes in the current operational procedure. Assuming availability of a reliable wind forecast parameterizing the distribution function of the uncertain generation, our CC-OPF satisfies all the constraints with high probability while simultaneously minimizing the cost of economic re-dispatch. CC-OPF allows efficient implementation, e.g. solving a typical instance over the 2746-bus Polish network in 20 seconds on a standard laptop.Industrial engineering, Operations researchdb17, srh2144Applied Physics and Applied Mathematics, Industrial Engineering and Operations ResearchArticlesModels for managing the impact of an influenza epidemic
http://academiccommons.columbia.edu/catalog/ac:153905
Bienstock, Daniel; Zenteno Langle, Ana Ceciliahttp://hdl.handle.net/10022/AC:P:15119Mon, 29 Oct 2012 00:00:00 +0000We present methodologies for managing the impact of workforce absenteeism on the operational continuity of public services during an influenza epidemic. From a plannerâ€™s perspective, it is of paramount importance to design contingency plans to administer resources on the face of such an event; however, there is significant complexity underlying this task, stemming from uncertainty on the likely severity and evolution of the epidemic. Our approach involves the procurement of additional resources in response to a robust model of the evolution of the epidemic. We develop insights on the structure of optimal robust strategies and on practical rules-of-thumb that can be applied should an epidemic take place. We present numerical examples that illustrate the effectiveness of our results.Public healthdb17, acz2103Applied Physics and Applied Mathematics, Industrial Engineering and Operations ResearchArticlesChance Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty
http://academiccommons.columbia.edu/catalog/ac:153902
Bienstock, Daniel; Chertkov, Michael; Harnett, Seanhttp://hdl.handle.net/10022/AC:P:15118Mon, 29 Oct 2012 00:00:00 +0000When uncontrollable resources fluctuate, Optimum Power Flow (OPF), routinely used by the electric power industry to redispatch hourly controllable generation (coal, gas and hydro plants) over control areas of transmission networks, can result in grid instability, and, potentially, cascading outages. This risk arises because OPF dispatch is computed without awareness of major uncertainty, in particular fluctuations in renewable output. As a result, grid operation under OPF with renewable variability can lead to frequent conditions where power line flow ratings are significantly exceeded. Such a condition, which is borne by simulations of real grids, would likely resulting in automatic line tripping to protect lines from thermal stress, a risky and undesirable outcome which compromises stability. Smart grid goals include a commitment to large penetration of highly fluctuating renewables, thus calling to reconsider current practices, in particular the use of standard OPF. Our Chance Constrained (CC) OPF corrects the problem and mitigates dangerous renewable fluctuations with minimal changes in the current operational procedure. Assuming availability of a reliable wind forecast parameterizing the distribution function of the uncertain generation, our CCOPF satisfies all the constraints with high probability while simultaneously minimizing the cost of economic redispatch. CCOPF allows efficient implementation, e.g. solving a typical instance over the 2746bus Polish network in 20s on a standard laptop.Industrial engineering, Operations researchdb17Applied Physics and Applied Mathematics, Industrial Engineering and Operations ResearchArticlesOptimal adaptive control of cascading power grid failures
http://academiccommons.columbia.edu/catalog/ac:129328
Bienstock, Danielhttp://hdl.handle.net/10022/AC:P:9744Mon, 20 Dec 2010 00:00:00 +0000Power grids have long been a source of interesting optimization problems. Perhaps best known among the optimization community are the unit commitment problems and related generator dispatching tasks. However, recent blackout events have renewed interest on problems related to grid vulnerabilities. A difficult problem that has been widely studied, the N-K problem, concerns the detection of small cardinality sets of lines or buses whose simultaneous outage could develop into a significant failure event. This is a hard combinatorial problem which, unlike the typical formulations for the unit commitment problem, includes a detailed model of flows in the grid. A different set of algorithmic questions concern how to react to protect a grid when a significant event has taken place. This is the outlook that we take in this paper. In this context, the central modeling ingredient is that power grids display cascading behavior. In this paper, building on prior models for cascades, we consider an affine, adaptive, distributive control algorithm that is computed at the start of the cascade and deployed during the cascade. The control sheds demand as a function of observations of the state of the grid, with the objective of terminating the cascade with a minimum amount of demand lost. The optimization problem handled at the start of the cascade computes the coefficients in the affine control (one set of coefficients per demand bus). We present numerical experiments with parallel implementations of our algorithms, using as data a snapshot of the U.S. Eastern Interconnect, with approximately 15000 buses and 23000 lines.Electrical engineeringdb17Applied Physics and Applied Mathematics, Industrial Engineering and Operations ResearchArticlesThe N-k Problem in Power Grids: New Models, Formulations and Numerical Experiments (Extended Version)
http://academiccommons.columbia.edu/catalog/ac:125318
Bienstock, Daniel; Verma, Abhinavhttp://hdl.handle.net/10022/AC:P:8574Wed, 17 Mar 2010 00:00:00 +0000Given a power grid modeled by a network together with equations describing the power flows, power generation and consumption, and the laws of physics, the so-called N-k problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. The case where k is small is of practical interest. We present theoretical and computational results involving a mixed-integer model and a continuous nonlinear model related to this question.db17Applied Physics and Applied Mathematics, Industrial Engineering and Operations ResearchArticles