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14
Chance Constrained Optimal Power Flow: RiskAware Network Control under Uncertainty
, 2012
"... Abstract. When 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, cascadi ..."
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Abstract. When 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.
Identification of K Most Vulnerable Nodes in Multilayered Network Using a New Model of Interdependency
"... Abstract—The critical infrastructures of the nation including the power grid and the communication network are highly interdependent. Recognizing the need for a deeper understanding of the interdependency in a multilayered network, significant efforts have been made by the research community in the ..."
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Abstract—The critical infrastructures of the nation including the power grid and the communication network are highly interdependent. Recognizing the need for a deeper understanding of the interdependency in a multilayered network, significant efforts have been made by the research community in the last few years to achieve this goal. Accordingly a number of models have been proposed and analyzed. Unfortunately, most of the models are over simplified and, as such, they fail to capture the complex interdependency that exists between entities of the power grid and the communication networks involving a combination of conjunctive and disjunctive relations. To overcome the limitations of existing models, we propose a new model that is able to capture such complex interdependency relations. Utilizing this model, we provide techniques to identify the K most vulnerable nodes of an interdependent network. We show that the problem can be solved in polynomial time in some special cases, whereas for some others, the problem is NPcomplete. We establish that this problem is equivalent to computation of a fixed point of a multilayered network system and we provide a technique for its computation utilizing Integer Linear Programming. Finally, we evaluate the efficacy of our technique using real data collected from the power grid and the communication network that span the Maricopa County of Arizona. I.
A STATISTICAL METHOD FOR SYNTHETIC POWER GRID GENERATION BASED ON THE U.S. WESTERN INTERCONNECTION
"... In order to develop algorithms that identify power grid vulnerabilities, there is a need to evaluate their performance with real grid topologies. However, due to security reasons, such topologies (and particularly, the locations of the nodes and edges) may not be available. Therefore, we focus on ..."
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In order to develop algorithms that identify power grid vulnerabilities, there is a need to evaluate their performance with real grid topologies. However, due to security reasons, such topologies (and particularly, the locations of the nodes and edges) may not be available. Therefore, we focus on a method for generating test networks with similar characteristics to the real grid. Smallworld and scalefree networks [1, 7] are two of the models that were suggested for representing power grids. However, [4] showed that none of these models can properly represent the U.S. Western Interconnection (WI) power grid transmission network (see Fig. 1). An alternative model was proposed in [6] but does not consider the nodes ’ spatial distribution. While there are models for generating spatial networks [2], most of them were not designed to generate networks with properties similar to the power grid. Hence, we present a procedure to generate synthetic networks with similar structural properties and spatial distribution to the WI. It is based on a Gaussian Mixture Model (GMM) that generates the positions of the nodes and a Quadratic Discriminant Analysis (QDA) that is used to connect them. We show that obtained networks have properties similar to the ones of the real grid. Positions of the Nodes The positions of the nodes, denoted by xi ∈ R2 (i = 1,..., 13992 in the WI), in the power transmission network are correlated with populations and geographical properties (see for example Fig. 1). Thus, the nodes can be clustered into groups based on their geographical proximity. There are several clustering techniques that can be used. However, we are interested in generating similarly distributed set of points on the plane. Hence, we use
Joint Cyber and Physical Attacks on Power Grids: Graph Theoretical Approaches for Information Recovery
"... Recent events demonstrated the vulnerability of power grids to cyber attacks and to physical attacks. Therefore, we focus on joint cyber and physical attacks and develop methods to retrieve the grid state information following such an attack. We consider a model in which an adversary attacks a zone ..."
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Recent events demonstrated the vulnerability of power grids to cyber attacks and to physical attacks. Therefore, we focus on joint cyber and physical attacks and develop methods to retrieve the grid state information following such an attack. We consider a model in which an adversary attacks a zone by physically disconnecting some of its power lines and blocking the information flow from the zone to the grid’s control center. We use tools from linear algebra and graph theory and leverage the properties of the power flow DC approximation to develop methods for information recovery. Using information observed outside the attacked zone, these methods recover information about the disconnected lines and the phase angles at the buses. We identify sufficient conditions on the zone structure and constraints on the attack characteristics such that these methods can recover the information. We also show that it is NPhard to find an approximate solution to the problem of partitioning the power grid into the minimum number of attackresilient zones. However, since power grids can often be represented by planar graphs, we develop a constant approximation partitioning algorithm for these graphs. Finally, we numerically study the relationships between the grid’s resilience and its structural properties, and demonstrate the partitioning algorithm on real power grids. The results can provide insights into the design of a secure control network for the smart grid.
Analysis of Failures in Power Grids
, 2015
"... This paper focuses on line failures in the transmission system of power grids. Recent largescale power outages demonstrated the limitations of percolation and epidemicbased tools in modeling failures and cascades in power grids. Hence, we study failures and cascades by using computational tools a ..."
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This paper focuses on line failures in the transmission system of power grids. Recent largescale power outages demonstrated the limitations of percolation and epidemicbased tools in modeling failures and cascades in power grids. Hence, we study failures and cascades by using computational tools and a linearized power flow model. We first obtain results regarding the MoorePenrose pseudoinverse of the power grid admittance matrix. Based on these results, we analytically study the impact of a single line failure on the flows on other lines and introduce metrics to evaluate the robustness of grids to failures. We also illustrate via simulation the impact of the distance and resistance distance on the flow increase following a failure, and discuss the difference from the epidemic models. We use the pseudoinverse of admittance matrix to develop an efficient algorithm to identify the cascading failure evolution, which can be a building block for cascade mitigation. Finally, we show that finding the lines whose removal results in the minimum yield (the fraction of demand satisfied after the cascade) is NPHard and present a simple heuristic for finding such a set. Overall, the results demonstrate that using the resistance distance and the pseudoinverse of admittance matrix provides important insights and can support the development of algorithms for designing robust power grids and controlling the evolution of a cascade upon failures.
Computational Analysis of Cascading Failures in Power Networks
"... We focus on cascading line failures in the transmission system of the power grid. Recent largescale power outages demonstrated the limitations of epidemic and percolationbased tools in modeling the cascade evolution. Hence, based on a linearized power flow model, we obtain results regarding the ..."
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We focus on cascading line failures in the transmission system of the power grid. Recent largescale power outages demonstrated the limitations of epidemic and percolationbased tools in modeling the cascade evolution. Hence, based on a linearized power flow model, we obtain results regarding the various properties of a cascade. Specifically, we consider performance metrics such as the distance between failures, the length of the cascade, and the fraction of demand (load) satisfied after the cascade. We show, for example, that due to the unique properties of the model: (i) a set of initial line failures may have a smaller effect than a failure of one of the lines in the set, (ii) the distance between subsequent failures can be arbitrarily large and the cascade may be arbitrarily long, and (iii) minor changes to the network parameters may have a significant impact. Moreover, we show that finding the set of lines whose removal has the most significant impact (under different metrics) is NPhard. Finally, for specific graphs, we develop a fast algorithm to determine if a set of line failures initiates a cascade. The results can provide insight into the design of smart grid measurement and control algorithms that can mitigate a cascade.
Splitting method for speedy simulation of cascading blackouts
"... Abstract—Simulation of cascading blackouts poses many challenges, including fast simulation of long series of rare interactions in large grid models. The splitting method advances the simulation by stages, resampling from each stage to advance to the next stage. We apply the splitting method to th ..."
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Abstract—Simulation of cascading blackouts poses many challenges, including fast simulation of long series of rare interactions in large grid models. The splitting method advances the simulation by stages, resampling from each stage to advance to the next stage. We apply the splitting method to the simulation of cascading blackouts to efficiently determine the probability distribution of blackout size. Testing on a blackout simulation shows that splitting can quickly compute large blackouts inaccessible to other methods. Index Terms—Simulation, failure analysis, probability, power transmission system reliability I.
Summary
"... We study control algorithms that stop power grid cascading failures by minimally shedding load (i.e., reducing demand). The control is computed at the beginning of the cascade and applied as the cascade unfolds on the basis of realtime measurements; as the primary focus of this paper we consider a ..."
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We study control algorithms that stop power grid cascading failures by minimally shedding load (i.e., reducing demand). The control is computed at the beginning of the cascade and applied as the cascade unfolds on the basis of realtime measurements; as the primary focus of this paper we consider an environment where measurements are noisy, missing, or erroneous.
Accepted with minor revisions by TNNLS Special Issue on Learning in Nonstationary and Evolving Environments Learning GeoTemporal NonStationary Failure and Recovery of Power Distribution
"... Abstract—Smart energy grid is an emerging area for new applications of machine learning in a nonstationary environment. Such a nonstationary environment emerges when largescale failures occur at power distribution networks due to external disturbances such as hurricanes and severe storms. Power ..."
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Abstract—Smart energy grid is an emerging area for new applications of machine learning in a nonstationary environment. Such a nonstationary environment emerges when largescale failures occur at power distribution networks due to external disturbances such as hurricanes and severe storms. Power distribution networks lie at the edge of the grid, and are especially vulnerable to external disruptions. Quantifiable approaches are lacking and needed to learn nonstationary behaviors of largescale failure and recovery of power distribution. This work studies such nonstationary behaviors in three aspects. First, a novel formulation is derived for an entire life cycle of largescale failure and recovery of power distribution. Second, spatialtemporal models of failure and recovery of power distribution are developed as geolocation based multivariate nonstationary GI(t)/G(t)/ ∞ queues. Third, the nonstationary spatialtemporal models identify a small number of parameters to be learned. Learning is applied to two reallife examples of largescale disruptions. One is from Hurricane Ike, where data from an operational network is exact on failures and recoveries. The other is from Hurricane Sandy, where aggregated data is used for inferring failure and recovery processes at one of the impacted areas. Model parameters are learned using real data. Two findings emerge as results of learning: (a) Failure rates behave similarly at the two different provider networks for two different hurricanes but differently at the geographical regions. (b) Both rapid and slowrecovery are present for Hurricane Ike but only slow recovery is shown for a regional distribution network from Hurricane Sandy. Index Terms—Nonstationarity, queuing model, mixture model, real data I.